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THE ECONOMIC CONSEQUENCES OF THE INTEREST-

FREE ISLAMIC BANKING SYSTEMS
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THE ECONOMIC CONSEQUENCES OF THE INTEREST-FREE
ISLAMIC BANKING SYSTEMS

BY

NADER HABIBI

A DISSERTATION

Submitted to the
Michigan State University
in partial fulfilment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

1987

ABSTRACT

The Economic Consequences of the
Interest-Free Banking Systems

by

Nader Habibi

To ensure full compliance with the teachings of Islam,
which forbid interest charges on loans, several Islamic
nations have modified their financial systems by eliminating
all interest paying assets and establishing new banking

institutions called interestefree banking systems. This

study addresses questions concerning the economic
consequences of interest free banking systems. The
objectives are threefold: 1) To analyze the impact of
interest-free banking on risk~taking and the savings

behavior of households at the micro level, 2) to analyze the
impact of interest-free banking on the rate of aggregate
investment and the level of output at the macro level, and
3) to study the conduct of monetary and fiscal policies in
an Islamic economy and compare their effectiveness in
Islamic and regular economies.

The analysis begins at the micro level. To understand
the reaction of households to the elimination of interest
charges a two-period, two-person, two-commodity general

equilibrium model is developed. Utility maximizing

households must allocate their resources between consumption
and an investment portfolio which consists of a risky and a
riskless asset. The risky asset is a loan issued by the
less risk-averse household to the other one. Starting from
an economy with no interest charges (zero nominal interest
rates.) and allowing the interest rate to increase slightly,
we observe that moving away from the zero interest rate will
increase net savings and improve the allocation of risk.
The net welfare effects, however, are not determined.

The macro-economic analysis is based on a static macro
model with one commodity market and three asset markets for
savings deposits, money and equities. Using the method of
comparative statics, we observe that elimination of interest
charges on savings deposits will reduce the demand for
equities and lead to a reduction in the rate of private
investment. We expect this effect to be reinforced when
interest payment on private loans are reduced to zero. The
suppression of interest on government bonds, however, could
have an opposite effect. At zero interest, many people
might abandon the government bonds and switch to equity
stocks. The increased demand for \equity will increase
equity prices and encourage more investment.

A similar macro-economic model is used to study the
monetary and fiscal policy options available to the
government in an Islamic economic system. Since bonds are
eliminated, the open-market operations in the bond market

(which are used in the Western economies) are replaced with

11

open-market operations in equity markets. The other policy
options considered are variations in government deficit and
money supply. Using comparative static methods, we observe
that the policy multipliers for these three options have the
expected signs. An open-market purchase and an increase in
money supply are both expansionary; while an increase in
government deficit has an indeterminate effect.

To compare the effects of these policies in Islamic and
regular economies, we develop a macro model for the regular
economy by 'adding a market for government bonds to the
original model of Islamic economy. Then we derive the
policy multipliers of the three policy tools that were
mentioned above. Comparing the corresponding multipliers
for Islamic and regular economies, we observe that these
policies are more effective and less indeterminate under
Islamic regime. The higher level of uncertainty under
regular regime is attributed to a possible negative feedback
from the bond market to the equity and money markets. Such

a feedback will no longer exist in an Islamic economy.

iii

ACKNOWLEDGEMENTS

I would like to express my great appreciation to Dr. Norman
P. Obst, chairman of the committee, for his guidance, concern,
encouragement and patience. Also, I would like to thank Dr.
Anthony Koo, Dr. Timothy Lane and Dr. Stephen Martin who, as
members of the committee, made valuable contributions ever
since the project began. The forward and critical comments of
Dr. Martin are specially appreciated. Special thanks also to
Dr. C. L. Ballard who frequently offered useful suggestions.

Special acknowledgement is also extended to many good

friends who offered much needed support and friendship during
this lengthy and sometimes difficult project. I specially like
to thank Ingrid Butlevics, Lynne Roberts, Farshid Marzban and
Shabnam Marzban. Finally I’m greatful to my family for their

financial and emotional support.

iv

Chapter

TABLE OF CONTENTS

INTRODUCTION TO THE FINANCIAL INSTITUTIONS
OF ISLAM

1.1 The Socio-Economic Institutions of Islam
1.2 The Financial System of Islam
2.A The Attitude of Islam Towards Interest

2.8 The Institutions of an Interest-Free
Banking System

1.3 The Conduct of Monetary and Fiscal Policy
in the Absence of Interest-Paying Assets

THE CONSEQUENCES OF ISLAMIC BANKING IN A
MICRO-ECONOMIC FRAMEWORK

2.1 The Impact of Islamic Regulation
Under Certainty

1.A A Two-Person Equilibrium With
Intertemporal Allocation Only

1.8 A Two-Person Model With Savings
and Investment

2.2 The Impact of Islamic Regulation
Under Uncertainty

2.A A Two-Person Uncertainty Model with
Portfolio Choice Only

2.8 A Two-Person Uncertainty Model With
Portfolio and Intertemporal Choice
THE CONSEQUENCES OF ISLAMIC BANKING IN A
MACRO-ECONOMIC FRAMEWORK

3.1 The Consequences of Interest Charge
Elimination

32

37

44

56

88

90

Chapter

3.2 Fiscal and Monetary Policy in an
Islamic Economy

3.3 Fiscal and Monetary Policy in a Regular
Economy

3.4 A Comparison of Policy Effects for the
Regular and Equity-Based Regimes
4 ISLAMIC BANKING IN PRACTICE
4.A Independent Islamic Banks

4.B Islamic Banking Systems

5 CONCLUSION

APPENDICES

APPENDIX A (CHAPTER TWO)
APPENDIX B (CHAPTER TWO)
APPENDIX A (CHAPTER THREE)
APPENDIX B (CHAPTER THREE)
APPENDIX C (CHAPTER THREE)
BIBLIOGRAPHY

vi

1’11
Tm
lib

Chapter 1
INTRODUCTION TO THE FINANCIAL INSTITUTIONS OF ISLAM

In 1981, the government of Pakistan modified the entire
banking system of that nation to make it compatible with the
laws of Islam which forbid any loan transactions on the
basis of interest charge. In 1983, the new revolutionary
government of Iran undertook similar measures to establish

an "interest-free banking system. At the same time in every
other Islamic nation (which still tolerates a regular
banking system that allows loan transactions on the basis of
interest charge), independent interest-free banks are in
operation. These banks have had to compete against regular
commercial banks; and surprisingly, they have been able to
attract a significant number of depositors. A large number
of these depositors are devout Muslims who, for religious
reasons, prefer to conduct financial transactions with the
Islamic banks because these banks do not pay or receive any
interest. There are also other depositors who are attracted
by the high profit rate that Islamic banks have been able to
offer.1

The introduction of Islamic banking at the national
level could have some serious consequences for the economic
performance of these nations . Empirical research has shown

that the level of private savings in developing nations is

sensitive to the degree of financial development. As will

be demonstrated later, Islamic opposition to interest
charges will lead to the elimination of every kind of debt
instrument. To the extent that a large number of people put
their savings in various forms of interest-paying assets,
their intertemporal and portfolio allocations will be
affected. In the aggregate, the level of domestic savings
and investment might change.

In the last three decades, the issue of Islamic banking
has received a great deal of attention in the cleric and
academic circles. This attention has resulted in many books
and articles. The specific issues that have received most
attention are the Justifications for the abolition of
interest charges and the operational aspects of Islamic
banking. However, the review of the literature on Islamic
banking reveals that there is hardly any analytical research
on the consequences of Islamic banking. I believe that in
this area there are many unanswered questions which must be
addressed. In this project I will try to study some of these
questions. In specific, I will focus on the impact of
Islamic banking on household savings and risk taking, as
well as the implications of Islamic banking for fiscal and
monetary policy.

The opposition to interest charges is only one aspect
of Islamic views on the economic system . There are also
specific rules on taxation, property ownership, market

operation and many other issues. Before concentrating on

the main topic of this research, it would be helpful to
present a general background on the Socio- Economic views of

Islam and then gradually focus on Islamic banking.

One of the most surprising developments in the second
half of the 20th century which was hardly expected by anyone
is the re-emergence of religion as an important social force
in almost every corner of the world. The social thinkers of
the 19th century in Europe and the United States were
predicting that with the advancement of science and
technology the significance of religion in the mind of
mankind would diminish. Yet, to everyones surprise,
religion is still a source of hope and motivation to
millions of people all over the world. In the United States
and Europe, various religious groups are involved in
organizing campaigns on such important issues as disarmament
and abortion. In Latin America and Poland, the Catholic

church has become an outspoken advocate of political reform

“\l
‘ «\QNUCW A
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and social justice. ‘ A“ rmw'maii new ’xc’ «ya
‘11")er \ 55"“ x w" “
In other parts of the world also, religion is ‘oggsfl’

Ck.

attracting more and more people, especially the youth. This
renewed attention to religion has been most noticeable in
the Islamic nations of Africa and Asia. To the traditional
people of these nations who have felt insecure and threatend

by the intrusion of Western ideas in their lives, Islam has

become a source of identity and security. It has also
become an instrument of social and political unity. The
Iranian revolution, which led to the downfall of the Shah,
is one example of how Islam has grown into a strong
political and social force. Another example is the
nationalist struggle in Afghanistan. The single most
important element that has united the resistance movement
(against Soviet occupation) is Islam. The struggle against
the communist regime is viewed as a holy war or "Jihad".

Islam in many ways is similar to Orthodox Christianity.
For example, the ethical teachings on the role of family and
the individual responsibility towards God and society are
very similar. A visible difference, however, is that the
laws and teachings of Islam are much more detailed and
specific. They affect every aspect of an individual’s
social and private life. Unlike the early Christian fathers
who did not pay much attention to worldly affairsz, Islamic
clergy were strongly concerned with the affairs of both
worlds. The modern Islamic thinkers put a great emphasis on
the attention of Islam to material prosperity and economic
progress.

Comparing the modern political and social thought of
Islam and Christianity, the most important difference is on
the issue of secularism. While the separation of church and
state is almost fully accepted by the Christians, only a

small minority of Islamic scholars advocate secularism. The

mainstream political thought among- Muslims is that
government must function according to the rules of Islam.
Any law which is in conflict with the views of Islam must be
rejected. Further, it is argued that Islam gives exact
instructions on the political and economic structure of the
so called "Islamic society". There are two sources for
these instructions. The most important source is the holy
book of Islam Quran , and the second source is the comments
and teachings of the Prophet Mohammad during his lifetime.
The collection of these teachings is called "Sunnat" (also
called "Hadith”).

The emphasis on the link between state and religion has
led to two important trends in Islamic societies. The first
trend is political. The clergy and their followers are
putting pressure on the governments to modify the civil
codes and make them consistent with Islamic rule. In recent
years, the evidence of this pressure has been observed in
many countries such as Pakistan, Egypt and Sudan. And, of
course, in those nations that are ruled by the clergy or a
leadership that is highly committed to Islam (such as Iran,
Pakistan and Lybia), the entire legal system has already
been modified. The second trend is a literary movement
among Muslim scholars. The objective is to describe the
structure of an ideal modern Islamic society based on the

early teachings of Islam and study its dynamics.

To confront the growing popularity of the liberal and
communist ideologies in Islamic nations, these scholars
began to develop an independent Islamic socio-economic
school of thought. This concern started in the 1930’s in
Pakistan (then part of India). After the Second World War,
many of the Islamic lands gained independence and, even
though the leadership in many of these nations was secular,
the clergy and the Islamic scholars paid very strong
attention to the issue of the Islamic socio-economic system.
In the 1960’s and 1970’s, research intensified and
specialization emerged. Scholars began to address specific
questions such as the sociology of Islam, the Islamic
educational system, and the economic system of Islam.

Among these different fields of specialization, the
economic system of Islam has received the most attention.
There are currently two research centers, one in Pakistan
and one in Saudi Arabia, for the study of the Islamic
economic system. In recent years many books and articles on
this topic have been published; and starting in 1983, the
"Center for Research in Islamic Economics" in Saudi Arabia

began publishing the Journal of Research in Islamic

Economics. There have also been several conferences on
different aspects of the economics of Islam over the last 10
years.

The earlier works were mostly nontechnical and

descriptive. They were written by authors who had a strong

background in religion but very limited knowledge of
economic science. However, gradually several researchers
with formal economic training showed interest and in recent
years many technical papers have been published.3 These
authors reside in different parts of the world. In 1976, M.
Siddiqui published an extensive review of the literature on
the Islamic economic thought. His work is by far the most
detailed review published on the topic so far.

Before studying the Islamic banking system in detail,
we will briefly review the economic philosophy and the
economic system of Islam. The topic is further divided into
several subtopics, each covering the views of Islam on a
specific economic problem. These subtopics are:

1) The goals of Islamic Economic system.

2) The economic enterprise and ownership in Islam.

3) Economic competition and cooperation.

4) Views of Islam on economic growth and development.

5) The role of state in economic enterprise.

6) Taxation

7) Money, banking and the financial system.

***#*****xxxxxxxxxxxxxxxxxx*xxxxsasxxt
1) We The goals of the
Islamic economic system are interlinked with the objectives
and the responsibilities of man himself as defined by Islam.
According to Islam, man has spiritual and material needs

that must be satisfied. Therefore the goals of the economic

system are divided into economic and noneconomic. The
material prosperity is condoned and even encouraged as a
precondition for spiritual growth. According to Paidar,
"For most people, attention to spiritual needs and
development of moral personality before satisfaction of
material needs is very difficult if not impossible."4

Some of the ‘economic goals are: satisfaction of
material needs of people, the equitable distribution of
wealth and income and the optimum utilization of natural
resources. The noneconomic goals as listed by Maududi
include: fulfillment of "spiritual needs", moral growth,
social justice, "safeguarding the freedom of man", equality
of opportunity and cooperation. Taleghani presents another
view of the noneconomic goals of the system: "The basis of
legal ordinance and economic relations are the verses of
Quran and Hadith of Islam, all of which call upon one to
uphold justice, truth and equality.“5

2) Whin- smce "Islam
is concerned with the material welfare of the public, it
encourages any kind of economic activity in the fields of
agriculture, commerce and industry. The creation of
economic enterprise (whether private or public) is welcomed.
The goal of an economic enterprise must not be profit
maximization alone. It must also show concern for the
problems that confront the society. Some authors have

expressed negative views on excessive reliance on profit

motives. For example, Taleghani says "...The root of all
the problems and disorders, all these pressures upon workers
and their ensuing dissatisfaction is that the drive for
profit and accumulation of capital has been made the goal of
the society."6 The attitude of Islam towards ownership is
that the absolute ownership of every thing in this world
belongs to God. Man can only exercise limited ownership
rights over his private property. He is responsible before
God for the way that he utilizes his property. He must not
waste or misuse even his own property.

In Islam, three types of property ownership are
recognized. These are private, state, and communal
ownership. The last two items combined are equivalent to
public ownership. Even though almost all scholars agree
that Islam tolerates some degree of private ownership, they
disagree with each other on the extent of private ownership.
Some authors with strong socialist orientation like Pervez
and N. A. Sheik advocate a very limited private ownership
and see a very small role for the private sector in Islamic
economy. A more moderate view is given by Baghir Al Sadr
who argues that Islam gives equal importance to individual,
state and communal ownership.7 Overall, Islam views
ownership as conditional and limited. For example, the
ownership of agricultural land is conditional on farming
activity. If an individual farms land that has not been

farmed and which was not owned by anyone before, he will be

10

recognized as the owner of that piece of land. On the other
hand, if the owner leaves his land idle for a long period of
time without any justification, he will lose his title to
that piece of land.

3) Wanner: Islam
strongly condemns any form of monopoly power in the private
sector. To this extent, competition is prefered to
monopoly. However, excessive competition, which reduces the
bond of brotherhood among men, is also rejected as equally
harmful. With some regulations, the operations of a free
market is acceptable. The common view is that there must be
a middle ground between competition and cooperation such
that the economy can operate with efficiency and at the same
time a feeling of solidarity and brotherhood can exist among
the people. Not much research has yet been done on how
actually to achieve this balance.

4) gas—Wm. Islam
encourages the individual as well as the entire society to
work towards economic growth and development. This growth
however, must be associated with economic justice which is
basically reflected in a fair distribution of income. To
achieve this balance, Islam calls for full exploitation of
natural resources to ensure economic growth, and it also
calls for an active role by the state in the economic

affairs of the society.8

ll

5) W
The views of Muslim scholars on the role of state is very
similar to the Keynesian/liberal view in Western economic
thought.9 The commonly accepted view is that an Islamic
society is organized as a welfare state. Therefore, the
government must be actively involved in the economic affairs
of the society. Siddiqi proposes the following duties for
the government in an Islamic society:

(a) Ensuring compliance with the Islamic code of
conduct by individuals through education and, whenever
necessary, through coercion.

(b) Maintaining healthy conditions in the market to
insure its proper functioning.

(c) Modifying the market allocation of resources and
distribution of income by guiding and regulating it as well
as by direct intervention and participation in the process,

(d) Taking positive steps in the field of production
and capital formation to accelerate growth and ensure social
justice.

Other authors add the provision of a social security
program to the above list. Baghir Al-Sadr (pp. 615-636)
argues that every individual in the society, regardless of
his ability to work, is entitled to government assistance if
needed because in Islam the natural resources belong to the
entire society and the state is the guardian of these

resources. Similarly, Awsaf Ali argues that the call for

12

active participation of the state in the economic affairs of
Othe society is the direct result of ”the social philosophy
of Islam."

6) Qn_I§xatign. Islamic law has specifically defined a
wealth tax called Zakat. Paying Zakat is considered a
religious duty for every Muslim.Zakat is a 2.5% annual
wealth tax on accumulated net worth of the individual. There
are some disagreements among Muslim scholars on the coverage
of Zakat and its flexibility. Some. authors, including
Maududi, believe that Zakat does not apply to machinery and
capital goods. Others believe that it should apply to all
forms of wealth. On the flexibility of the tax rate for
Zakat, the disagreement is mostly between the clergy and the
Muslim scholars. The clergy unanimously agree that the 2.5%
Zakat rate is fixed by Islamic law and it cannot be altered
by the state. The non-clerical scholars are more concerned
with the economic consequences and recommend that the state
must have the power to adjust the Zakat rate whenever
appropriate.

Islam’s holy book, Quran, gives clear direction on how
the Zakat funds are to be used. Surah 9, Verse 61 of the
Quran mentions the following uses for Zakat funds: ” The
poor, needx,employees of the Zakat office, those whose
hearts have been recently reconciled, those in bondage and

in debt, in the cause of Allah (God), and wayfarer.“ It is

13

also commonly accepted that the state has the right to
impose other taxes besides Zakat to raise revenue.

7) NW (The
institutions of Islamic banking will be covered in detail in

the next section.)

2] I] E' . 1 S I . I 1 .

Since Islam condemns any form of usury and interest
charge, the conventional banking institutions practiced in
the rest of the world cannot be applied in Islamic nations.
At the same time, everyone agrees that, to promote economic
growth, a nation needs a sound and efficient financial
system. Every developing country has to finance all or a
portion of her gross investment from domestic savings. The
efficiency of the banking system will help raise the level
of domestic savings and channel it to the most productive
projects.

Aware of this issue, the Muslim scholars have tried to
design an efficient financial system without a bond market
and interest charge. The research in the area of Islamic
banking has covered three major areas:

1) The attitude of Islam towards the interest charge.

2) The operation of a banking system without an
interest charge.

3) The conduct of monetary policy in the absence of

interest-paying assets.

14

We will study each of these areas separately and review the
related literature. The emphasis will be on the second area
which introduces the institutions of interest-free banking
as perceived by the majority of Muslim scholars. The
assumptions needed for the analytical chapters that follow
are derived from these institutions.

Win—Wlmjv The
opposition to interest charges in Islam is deeply rooted in
the Muslim holy book, Quran. On several occasions in this
book, "Riba", which is the Arabic word for usury, is
condemned and anyone involved in lending or borrowing based
on Riba is considered an enemy of God. Since Quran is the
undisputed source of guidelines for all Muslims, there is
unanimous agreement on the fact that Islam has forbiden the
practice of usury. There is(§jhowever, some disagreement on
exactly what it is that Islam has forbidden. A minority of
writers have claimed that what was prohibited by Islam was
the interest charge on consumer loans. Since business loans
were not common in the early years of Islam, we cannot say
that they are also forbidden. The advocates of this view
include Syed Yaqub Shah(60), Fazalur Rahman(55), Jafar Shah
Phalwarwi(52), and Tamanna Imadi(28). Shah presents two
historical records to support his view:

1. In the early years of Islam commercial borrowing

was not practiced. Profit sharing and partnership

15

were the only ways to increase the stock of
capital.

2. In that period only consumption loans were
prevalent and the rate of interest charged was very
high.

Therefore, he argues that an interest charge on business
loans is not forbidden in Islam.

On the opposite side of this issue, Mufti Shafi(59) and
Maulavi Fazalur Rahman(55) have argued that even if some kind
of interest-based transaction was not practiced in the same
time that this rule was made, it is still subject to that
same rule. To support_ their view, they reason that when
Islam prohibited alcoholic beverages, many of the drinks
which are common today did not exist. Yet every one agrees
that they are still prohibited. Maududi questions the
historical evidence presented by Shah. He presents some
other historical evidence to show that commercial loans were
indeed common in the early Islamic society. Maududi’s
position on this issue seems to be correct. The majority of
authors as well as the religious clergy agree that
prohibition of interest in Islam applies to all forms of
interest. The Quran and other sources of Islamic teachings
do not give exact explanations as to why the interest charge
is forbidden. Consequently, a number of Muslim scholars
have tried to provide some justification for this rule. The

explanations fall under two categories. Some authors present

16

historical and pragmatic reasons for the prohibition of
interest. For example Rudinson argues that: "It is
possible, some have thought, that it may have been designed
at a time when the little Muslim community, poor and
surrounded by enemies in Medina, was trying hard to collect
funds from the sympathizers and stigmatize those among the
latter who refused to lend money to the Muslims at
reasonable conditions. But it is also from the plain

meaning of the passages concerned, a question of getting the

to making more profane but more profitable use of their

resources by lending at interest."

Another historical reason is presented by Hamidollah(23).

In his view, the interest charges were prohibited to
nationalize the credit, than the state provided interest-
free loans to the public. Another group of scholars takes a
different approach and tries to present rational arguments
on why the Islamic prohibition of interest charges is
justified. They generally give two types of arguments.
First, they try to argue that there is hardly any economic
justification for interest and, secondly, they try to show
that the prohibition of interest charges will benefit
society.

In Western economic thought, attempts to rationalize
the institution of interest have led to the development of

several distinct theories such as: A) The Abstinence theory,

Muslims to prefer paying Zakat (wealth tax for the needy),£¥:*

17

B) The Time preference theory, C)The liquidity-preference
theory, and D)The productivity theory of capital. Several
Muslim scholars such as Uzair(71), Mettwally(47), and others
have criticized these theories as being either wrong or at
best weak. Both authors mentioned above have commented on
all or some of these theories.

On the abstinance theory, Uzair argues that today most
of the saving is done by the 'rich individuals and
corporations. These agents do not really sacrifice any of
their well-being by saving. From this argument, it seems as
if Uzair believes in the satiation of human wants. He seems
to be saying that, since the standard of living is not
damaged by saving, the saver does not deserve any interest.
Mettwally also mentions that banks do not sacrifice when
creating money(47,p20). He and Uzair both note that, even in
the absence of interest, people will still save a portion of
their income and corporations can use retained earnings.

Mettwally notes that the productivity theory of
interest is circular. To calculate the rate of interest, we
must know the value of the capital assets, and to arrive at
the value of capital there must already be a rate of
interest at hand. (This point has been observed by Western
economists as well.) Besides, the productivity theory does
not explain why interest must be paid when the borrower

suffers a loss.

18

Unfortunately, these authors ignore the concept of
opportunity cost. The lender in any loan transaction could
have invested the funds directly instead of lending them.
Thus, if he does agree to lend, he deserves some
compensation. Some authors such as Mettwally have
mistakenly argued that, since Islam prohibits speculation,
there is no opportunity cost to lending. First of all,
there is no unanimous agreement on the attitute of Islam
towards speculation. Secondly, Islam tolerates the earning
of profits and rents. Therefore, a lender can always find
an alternative use for his financial capital. Overall, the
criticisms of Western theories of interest by Muslim
economists are not very convincing. They often lack strong
logic and evidence.

The second line of argument against interest charges is
based on pointing out their undesirable consequences for the
economy. Several authors including Khan(32), Ahmed(3),
Mannan(41), and Sheikh(63) argue that interest charges cause
unemployment. (Note that this is not the same as saying
high interest rates lead to unemployment.) According to
them, this is because interest becomes a component of the
capital cost and causes the prices to be higher. The higher
prices in turn will lead to less consumption and less
production, thus leading to less employment.

This chain of reasoning might appear correct in

surface, but one must ask what will be the level of

19

employment without interest? If the same amount of lending
credit is being generated without interest charges then the
argument seems valid. However, if the elimination of
interest reduces the supply of credit, the level of
investment and production will decline and, as a result,
unemployment will be even higher.

Some authors have refered to the well known inverse
relation between the rate of interest and the rate of
investment which is known as the marginal efficiency of
investment function. Since in this relation higher levels of
investment are associated with lower rates of interest,
these authors claim that by eliminating interest charges
altogether, the level of investment will increase. This,
however, is not true because the validity of the above
argument depends on the availability of credit for the given
rate of interest. If, when the interest rate is suppressed
to zero, no one will agree to lend, the firms will face a
shortage of credit and the rate of investment might even
decline.

One issue that has been raised by almost every author
is that the existence of interest charges leads to
inequality because it transfers resources from the poor and
the middle class to the wealthy lenders. If this claim is
correct, it only applies to the consumer loans. In the case
of business loans, the borrowers are corporations and the

owners of businesses while the lenders (who save in the

20

banks and‘ buy bonds) include many of the middle class and
the blue-collar workers.

In other areas, Khan(35) has tried to show that the
interest charge is one of the causes of the international
monetary crisis. Several authors including Siddiqui(65)
Ahmed(3), Abu Su’ud(1), Maududi(44), and Sheikh(62) have
argued that the institution of interest is one of the main
causes of trade cycles in the economy. Unfortunately, none
of them has tried to elaborate and prove this point.
Western economists such as Fisher and many others have also
raised the same possiblity that monetary fluctuations such
as expansion and contraction of credit cause trade cycles.

Aside from the arguments that were reviewed above,
there is yet another explanation for the prohibition of
interest which appears to be built on more solid grounds.
The return to capital could fall under three categories:
interest, profit and rent. Islam allows the earning of

profit and rent but prohibits an interest charge. The Muslim

economists and jurists argue that, .according R9131§TLMQPIY {

those who participate in a productive venture or provide a
valuable service deserve to be rewarded. (Islam also insists
wthatkany (reward to capital owners must be linked to the
outcome of the project for which the capital is utilized.
The interest charge is prohibited because, assuming that the
borrowed credit was used for a profitable investment, the

lender is promised a fixed rate of return on his capital

21

while the borrower must face all the risk and uncertainty of
the project. Since the lender does not share in the risk of
the project, from the Islamic point of view, his return(the
interest) is undeserved.

Profit, on the other hand, is acceptable because it’s
directly related to the outcome of the project. In general
than, Islam requires that the return to capital must not be
pre-specified as is the case when lending at interest.
Instead, it must be linked to the productivity of capital in
the project that it is used for. In the next section, we
will see that this last argument is the main rationale for
the model of Islamic banking that is the most commonly
accepted.

Waking
System. The concept of the Islamic banking system is very
new. It has emerged as a natural consequence of the Islamic
opposition to interest charges on loans. Since the lending
and borrowing operations of the modern banks are primarily
based on an interest charge, Muslim scholars were faced with
the challenge of developing an alternative model of a
banking system which could allocate credit by some other

means. The early research in this area began with the works

of Qureshi(54), Siddiqui(64) and Ahmed(3) in the 40’s and 50’s.

They essentially proposed that profit- and loss-sharing
arrangements should replace the interest charge as the basis

for operations of Islamic banks. The profit- and loss-

22

sharing (PLS) arrangement was a common commercial practice
in Arabia before and during the early years of Islam. In
Islamic culture it is known as Mudarabah. Mudarabah is an
agreement between an owner of capital and an agent. The
owner provides the capital which is invested by the agent in
a profitable project. If the project is profitable, they
share the profits on a predetermined ratio. In case of
loss, however, the full burden falls on the capitalist. The
agent loses only the value of time and effort that he has
put into the project. The authors that were cited above
argued that similar arrangements could be applied to the
relations between the bank and the public.

In the 1960’s, research on the details of interest-free
banking intensified . A very detailed and organized account
of the topic was given in Banking Without Interest hy
Siddiqui. His work was followed by several articles in the
same direction by Al-Jarhi(6), Uzair(71), Al-Araby(5), Najjar(49)
and many others in the 1970’s. In addition to improving the
earlier model of Siddiqui, these authors proposed some
mechanisms for central banking and monetary intervention
under an interest-free banking system.

In recent years, scepticism towards this version of
interest-free banking has diminished. Today, the existing
banking systems of Pakistan and Iran operate on the basis of
the PLS.mechanism and it is gaining more acceptance in other

areas as well. In the remaining pages of this section, I

23

will describe the basic institutions of interest-free
banking which are commonly accepted. This will be followed
by a brief review of the possible deficiencies and
weaknesses of this particular model.

Aside from their interactions with the central bank,
the commercial banks basically transact with two types of
agents: the depositors and the borrowers. In the regular
banking systems the primary assets and liabilities of these
banks are interest-paying debt instruments such as savings
deposits and business loans. Under an interest-free banking
system, these debt instruments will be unacceptable. They
will be replaced with PLS and equity instruments. We will
describe the Islamic banking system by defining the
relations and arrangements that would exist between the bank
and its depositors as well as the bank and its credit
customers.

5 I] E I‘D 'l R J l' .

To attract the savings of households, Islamic banks
will offer two types of accounts. These are the profit- and
loss-sharing accounts and the demand deposits.

W. The
PLS accounts are substitutes for savings and time deposits.
They are "Modarabah-type" arrangements. The depositor
provides financial capital and the bank acts as his agent.
The bank invests these PLS funds along with its own capital

and additional funds that are raised through other types of

24

accounts in profitable projects. The performance of the
.bank’s operations are assessed periodically. At the end of
each investment period, the generated profits (or losses)
will be shared among the bank and the PLS account holders.
The division of the profits takes place in two steps. Since
the profits were generated by the entire financial capital
of the bank, the first step is to divide the profits in
proportion to the PLS funds and the rest of the capital.
The second step is to divide the portion of the profits that
are accrued to the PLS funds between the depositors and the
bank. This division will be based on a predetermined ratio
called the profit-sharing ratio which was agreed upon at the
time the PLS account was opened. In case of 'a loss, the
bank and the PLS depositors will share in proportion to
their capital contribution. To clarify the procedure
further, we will give a numerical example. We assume that

the period of investment is one year.

The total financial capital of the bank = 1000,000 3
Funds raised through PLS accounts. = 400,000 $
Bank’s own financial capital and other funds = 600,000 3
The profit sharing ratio = (30% bank,
70% PLS
depositor)
The total profits of the bank in one year = 100,000 3

25

The share of PLS accounts from total profits 100,000 * 0.4

40,000

This 40,000 $ profits will be divided between the bank and

the PLS depositors:

The share of the PLS depositors = 40,000 * 0.7
= 28,000

The rate of return to PLS deposits = 28,000/409000
= .07 (7%)

Bank’s share in PLS account profits 40,000 * 0.3

= 12,000 $

(12,000 + 60,000)/

The rate of return on bank’s investment

600,000

.12 (or 12%)

On the other hand, if the bank reports a loss at the
end of the period, this loss is shared in proportion to its
capital contribution. Consider a 100.0008 loss in the same

example.

100.000 * .4

Loss to the PLS depositors =loss on PLS accounts

40,000 3

26

Since this procedure does not guarantee a fixed
predetermined return to the PLS depositors, it is acceptable
to Islam. This advantage, however, comes with a price which
is the added risk. As the annual profits of the bank
'fluctuate, so does the rate of return on PLS deposits.
Indeed, their variances are highly correlated. Some risk-
averse households might stay away from these accounts in
order to avoid assuming any risk. If a minimum return on
these accounts is guaranteed by the bank, public trust will
be higher and more funds could be raised. But,
unfortunately, such an insurance will make the return on the
PLS the same as interest and thus it would not be
acceptable.

At the operational level, the calculation of profits on
PLS accounts poses a major problem . If the dividend payment
interval is too long, the PLS accounts will become highly
illiquid. Therefore, the profits on these accounts must be
assessed in 3- or 6-month intervals. On the other hand,
banks generally have long-term investments and it would be
dificult for them to evaluate profits in short periods.
Unfortunately, no satisfactory solution to this problem has
been found yet.

Aa2;__Ih§__ngand__Deanits. The Islamic banks, like
regular commercial banks, will offer demand deposits to the
public. These demand deposits are fully insured and do not

earn any return. Whether or not a service fee must be

27

charged on demand deposits is not an issue on which Islamic
law implies any position. The services that Islamic banks
provide for demand depositors are no different from those
provided by regular banks.

In Western banking systems, the commercial banks are
required to keep reserves on demand and savings deposits.
The primary reason for these reserves is that, by altering
them, the government would be able to change the supply of
credit whenever necessary. In an interest-free 'financial
system, it would still be desirable if a central bank could
change the money supply through the banking system. Such an
option is even more important in an Islamic regime because
some of the other instruments of monetary control will no
longer exist. (These are the instruments that deal with
bonds and interest rates.)

The imposition of the reserve requirement on demand
deposits of Islamic banks is fully acceptable. However,
there is controversy over application of such a requirement
to. the PLS accounts. These accounts are not debt
instruments. They are indeed very similar to equity. If
banks have to keep a portion of these funds idle, their rate
of return will be further reduced, causing a reduction in
public demand for these accounts. Furthermore, it should be
noticed that, in managing the PLS accounts, Islamic banks
operate very similar to the Mutual Funds in the West and the

latter do not have to keep any reserves.11 More on the

28

similarity of Islamic banks to the Mutual Funds will be said
later.
We.

Since the interest charge cannot be used in any banking
transactions, the lending and investing operations of
commercial banks must also be modified. The banks advance
credit to the rest of the economy for three purposes:
investment, consumption and government expenditures. In a
regular banking system, all three types of borrowing are
conducted on the basis of interest charge. In an Islamic
banking system, alternative mechanisms must be used. The
investment loans are used for profitable projects. The
lender of an investment loan could receive dividends instead
of interest on the basis of PLS arrangements. Islamic
scholars have suggested that banks should lend credit on a
PLS basis or provide credit by direct equity investment.

The consumer and government loans, however, do not
generate any profits so they cannot be lent on the same
basis. Unfortunately, Islamic institutions do not provide
any alternatives other than profit and loss sharing.
Whenever the project financed by a loan is such that profits
cannot be assessed, no single scheme for lending is
available. The field remains wide open to speculation. Some
authors have proposed that banks must be required by law to
provide consumer loans at no interest by setting aside a

portion of demand deposits especially for these loans.

29

Another proposal is to let Islamic banks concentrate on
investment loans and have the government provide consumer
loans with no interest charge.

These and other proposals for consumer loans lack any
theoretical basis. Furthermore, they are not in any way
connected to the PLS mechanism which is the basis of Islamic
banking. The result is that proposed mechanisms for
consumer and government loans ignore market forces and the
opportunity cost of credit. With these schemes, it is not
clear how credit will be allocated between consumer and
business loans. Since my main objective is to study the
consequences of Islamic banking as it is proposed by Islamic
scholars, I have decided not to include the government and
consumer loans in any of the analytical chapters of my
model. This exclusion will make the model incomplete; but
including arbitrary institutions for consumption loans will
also equally reduce the value of the model. The model
without consumption loans is preferred because it could be
extended in the future to include such loans once a proper
mechanism has gained common acceptance. At the same time,
however, since the topic is still being debated, I will
present a brief review of the literature along with a new
proposal in an attached appendix to this chapter.

In the case of profitable loans, the primary mechanisms
are PLS arrangement and direct equity investment. The

operation of PLS loans is exactly the same as the PLS

30

deposits that were described earlier. The only difference
is that here the bank provides the capital and the borrower
acts as the agent.

Aside from these two mechanisms, another scheme has
also been proposed . This third scheme is called price mark-
up and can be used when a firm needs credit to purchase
certain commodities or machinery. First, the bank purchases
the goods that a firm needs, then it sells the same goods to
the firm at a higher price. The firm will agree to pay the
cost on an installment basis. It does not take too much
thought to realize that this scheme is indeed the same as
landing at interest. The only difference is that, instead
of credit being given, the commodity is sold by the bank at
a higher price. In a way, it’s like the bank landing the
money to the firm and taking care of the purchase on the
firm’s behalf. The interest is disguised in the difference
between the purchase and the resale price. To be consistent
with the Islamic requirement, this scheme and those similar
to it must be rejected. Overall, Islamic banks provide
credit for investment purposes by PLS loans and direct
equity lending.

The fact that Islamic banks are able to hold equity
will set them apart from Western commercial banks which are
not allowed to hold any equity. On the other hand, it makes
Islamic banks very similar to the mutual funds. In the

Western Financial systems, a mutual fund is an investment

31

company that purchases a wide variety of primary securities
and issues a secondary security on itself called a mutual
fund share. The shares are claims on the mutual funds
entire assets. The value of these shares depends on the
value of the primary securities held by the mutual fund.
Because of diversification, the risk on these shares will be
less than any of the primary securities that are included in
the mutual funds portfolio. If we consider the PLS deposits
as equivalent to the mutual fund shares, the similarity
between these two types of institutions becomes obvious.

Of the many services that commercial banks provide to
the public, perhaps the most important ones are risk
arbitrage and denomination arbitrage. While Islamic banks
can offer many of these services, they are not able to
arbitrage risk because to do so would require transactions
based on interest charges. Furthermore, by eliminating the
private loan' markets, Islamic code destroys all the
possibilities of risk arbitrage. One expects that this
phenomena will be harmful to the welfare of borrowers and
lenders alike. This and other questions about the welfare
results of Islamic economic system are addressed in the next
chapter. To analyze these questions, a two-agent, micro-
economic model is developed. The model reveals that
elimination of risk arbitrage will lead to suboptimal

allocation of risk and a reduction in savings.

32

3, ,; up .‘ a”; .. ~ ._,._ ‘ . 'o’ ' .- ;. -, -
- a ' t .

One of the most interesting problems in the area of
Islamic banking is the question of monetary policy under
such a regime. In a regular economy, the government bond
market and depository institutions are the major channels of
monetary control. The Islamic prohibition of interest will
eliminate the debt instruments and cause serious changes in
depository institutions. Consequently, the conduct of
monetary policy in an Islamic economy will differ from the
regular economy in several respects.

Siddiqui(65), Al-Jarhi(6) and Chapra(18), among others,
comment on this issue. They note that while a central bank
can no longer intervene in the government bond market (since
it no longer exists), it can alter the money supply by
intervening in the equity and PLS loan markets. It will
still have control over the reserve requirement on demand
deposits as well. To expand the money supply, a central
bank can open PLS deposits in Islamic banks and deposit any
desired quantity of newly created high-powered money in
these accounts. Then the process of money creation within
the banking system will expand the money supply.

The creation of money in Islamic banking will be
similar to money creation in Western commercial banks. If
the supply of high-powered money goes up, a portion of it

will end up in an Islamic bank as a PLS deposit or demand

33

deposit. That bank will reinvest these additional funds by
providing credit to a firm or a household. A portion of
this credit will eventually end up in the same or another
Islamic bank and the process continues. Since it is very
similar to the process of money creation by commercial banks
and this latter process is described in any intermediate
book on macro-economics, I will not describe it here any
further.

A central bank could use the equity market for day-to-
day monetary intervention. By the purchase and sale of
equity, the central bank can expand and contract the money
supply respectively. This process, however, requires direct
government ownership in some industries and that might cause
concern about the excessive powers of government. Also, it
is possible that different industrial groups might pressure
the central bank to buy the stocks of one particular
industry at the expense of others. These are clearly
serious concerns. One possible remedy for this is to create
well-diversified mutual funds and limit the central bank to
trading on the shares of these funds only. In this way, no
particular industry will lose or gain as a result of
monetary intervention. In Chapter 3, we develop a macro
model of Islamic economy and analyze the conduct of monetary
and fiscal policy. We will also compare the performance of

these policies under regular and Islamic regimes.

34

Wanna.

Since the idea of Islamic banking is totally unfamiliar
to the majority of Western readers, this first chapter was
devoted to presenting an introduction to the topic. There
is no question that Islamic opposition to an interest charge
is taken seriously by the scholars and politicians in the
Muslim world. This attention is observed in moderate
nations like Saudi Arabia and Egypt as well as radical ones
such as Syria and Iran. Some countries such as Iran have
gone as far as modifying their entire banking system.

Gradually, a consensus has emerged among Muslim
scholars on two issues. First of all, there is a general
agreement that Islamic opposition to an interest charge
applies to all forms of interest charges and not just to the
consumer loans. Secondly, most scholars agree that profit
and loss sharing is the appropriate replacement for interest
charges. We described the operations of a banking system
based on PLS arrangement. The PLS arrangement and equity
ownership will allow the banks to function as intermediaries
but they will be very limited in their capacity to arbitrage
risk. While the regular commercial banks can offer fully
insured savings and time deposits, the Islamic banks can
only offer a diversified low-risk portfolio in their PLS
accounts. Unfortunately these accounts cannot be insured.
The consequences of this type of banking is the main topic

of study in the next chapter. As expected, the model

35

indicates that elimination of risk arbitrage leads to
welfare loss.

The elimination of government bonds along with the
reforms in the banking system will eliminate many of the
channels of monetary control that are available to Western
central banks. Thus, it has been proposed that the central
bank in an Islamic economy should be allowed to invest in
the equity market and PLS accounts. The consequences of this
and other options for monetary policy will be studied in the
third chapter. The analysis in that chapter reveals that,
while monetary and fiscal policies have similar effects in a
regular and an Islamic economy, some differences persist.
These differences could be explained by the fact that a
regular economy has a bond market and an Islamic economy
does not.

Finally, it must be noted that the survival of Islamic
banking systems is more of a political decision than an
economic one. Nevertheless, since this policy could have
serious affects on savings and investments, this and other
studies on the topic are well justified. Unfortunately, so
far the literature has been filled with unproven conjectures
and speculations which are often erroneous. There are many
questions at the theoretical level that have not been
resolved yet. In this project I hope to address some of
these issues analytically and reject some of the false views

that have been expressed by others on this subject.

10.

ll.

36

NOTES
(CHAPTER ONE)

Independent Islamic banks are currently in operation in
several countries such as Egypt, Sudan, Jurdan, and
Saudi Arabia. Their progress will be reviewed in the
last chapter.

Winer and Jackob give some examples from early

Christian writings to support this point, see pages 20
and 21.

In 1981, at conference held in Pakistan on Islamic
Economics, several Muslim scholars, who teach in
various European and American universities, presented
research papers.

See Paidar, page 10.

See Taseghani, page 50.
Ibid., page 54.

See Bagir Al—Sadr, page 257.
See Tahawi, pages 229-232.

This similarity could be partly explained by the fact
that most of these authors received their formal
economic training in Western universities during the
1960’s and 1970’s.

In practice so far, the Islamic banks have ignored this
religious objection. In Iran, for example, the nominal
value of PLS deposits is fixed and they are fully
insured along with the demand deposits.

Rafi Khan (page 10) gives a comparison of the Islamic
banks and Western Mutual Funds. For more detail on
Mutual Funds, see George Kaufman, ”The U.S. Financial
Systems, Money Markets and Institutions".

Chapter 2

THE CONSEQUENCES OF ISLAMIC BANKING IN A
MICRO-ECONOMIC FRAMEWORK

The analysis of the consequences of Islamic banking
must start at the micro level. Islamic regulations will
modify the financial markets. The firms and households who
interact with these markets will face a different set of
financial opportunities. Some types of assets are
eliminated while some other types are added. At the same
time, 'these changes might alter the rates of return on
different assets. In reaction to these changes, the
economic agents will adjust their resource allocation. This
means the households will change their intertemporal and
portfolio allocations while the firms will modify their
choices of production level, investment level and financial
mix.

The cumulative effect of these micro changes will
affect the aggregate demand for the real and financial
assets. Through this channel, the Islamic restriction might
have some effects on the real economy. For example, if the

Islamic regulations lead to a reduction in demand for

37

38

capital and as a result the rate of return on capital rises,
the real investment will decline.

In this chapter, we will study the impact of Islamic
regulations on the behavior of households and firms . Then
we will use the findings to develop a macro-economic model
in the next chapter. The economic institutions of Islam in
general and the institutions of Islamic banking in
particular were described in Chapter 1. To conduct our
analysis, we must first define the economic institutions
that must be incorporated in our model. While the market
mechanism is not directly advocated in Islam,~ it is not
rejected either. The same is true for the institution of
private ownership with certain limitations. Therefore, the
first_ assumption of our model is that, in an Islamic
economy, a market mechanism exists and the private ownership
of real and financial assets is tolerated. We also assume
that, aside from the interest rate restrictions, the other
requirements of perfect capital markets are satisfied. (This
is necessary to single out the effects of Islamic banking
from the other imperfections.)

The other two characteristics of Islamic banking are: a
zero nominalinterest rate on bonds and the application offs
profit- and loss-sharing arrangement in banking operations.
According to Islam, the suppliers of capital to a profitable
project are entitled to a portion of the profits only if

they share in the risk of the project. The interest charge

39

is forbidden because the lender is entitled to a fixed
return from the uncertain profits of the borrower. The PLS
contract is recommended as a substitute for interest-paying
loans and deposits in the banking operations. In a more
general view, the banks are supposed to transact with the
depositors and the borrowers on the basis of equity
arrangements. (The PLS is a specific type of equity
contract.)

Our method of analysis is to develop a model of
household resource allocation and then see how this
allocation changes after the Islamic restrictions are
imposed. The emphasis is on the interactions of the
households with the capital markets. _Each householdmust
make two major decisions with regard to the accumulation and
the composition of his wealth. First:\ he must decide how
much to save and then he must choose a suitable portfolio
from the existing assets. The analytical tools needed for
this analysis have already been deve10ped in the field of
finance. They are provided by the modern portfolio theory
which is specifically concerned with the financial decisions
of the households. iThe portfolio theory has two major
sources of strength. First of all, it explicitly takes
account of the sensitivity of investors to risktaking.
Secondly, the resource allocations of the households are
derived from utility maximizing behavior. Our model relies

heavilly on tools borrowed from the portfolio theory. To

40

familiarize the reader with the portions of the theory which
are used in the model, a brief review is provided in
appendix B to this chapter.

One of the surprising characteristics of the model that
follows is that, despite the fact that the P.L.S.
arrangement is_claimed to be the basis of Islamic banking
transactions, we have not explicitly included it in the
.model: There are several reasons for this decision. One
reason is that P.L.S. assets are very similar to equity
assets. Indeed, every P.L.S. loan is linked to an equity or
a risky project. To the household investor, a P.L.S. loan
will not be much different from other risky assets. _Our
model includes one risky and one riskless asset? The risky
asset is a_representative equity asset. It could be an
equity stock, a P.L.S. deposit or a portfolio which consists
of many risky assets. Since we are interested in how the
overall risktaking changes, having one representative risky
asset seems to be sufficient.

The second and perhaps more important reason for
ignoring the P.L.S. .assets is that unless the transaction
and information costs in the equity markets are significant,

the market for P.L.S. loans will fail. As was explained

earlier, the P.L.S. lender and the P.L.S. ‘borrower _will

 

‘5...“ _.___ __._._.—--——-~

share the profits when the profits are £98391V91I1b2t any
{/hf. possible loss is entirely born_ by the lender.__Since ,the

borrower does not have to share in the losses, he will not

41

face increased risk by P.L.S. borrowing. At the same time,
the more he borrows, the higher his expected profits will be
so he would have an indefinite demand for P.L.S. loans. The
P.L.S. lender, on the other hand, could directly invest his
funds in the same project that the P.L.S. borrower would
have invested in originally. The lender’s risk of loss
would be the same under both cases (equity holding and
P.L.S. lending for the same project). His expected gain,
however, will be smaller under P.L.S. because the borrower
will take away a portion of the profits whenever they are
positive. Therefore, the savers will be reluctant to lend
on the P.L.S. basis whenever there are opportunuties for
equity investment at low transaction and information costs.
The P.L.S.. lending is preferred when the portfolio
selection and trade in the equity markets is costly.

Since small investors are more likely to face high
information and transaction costs in the equity markets,
they would be the primary demanders of P.L.S. deposits which
are offered by the Islamic banks. These banks, on the other
hand, enjoy significant economies of scale in the financial
markets which helps them reduce the information and
transaction costs of direct investment. Consequently, they
would prefer providing credit to the firms by direct
investment instead of P.L.S. lending. The evidence from the
portfolio selection of Islamic banks in Pakistan confirms

this tendency. These banks actively offer P.L.S. accounts

42

to the depositors but so far they have been reluctant to
provide credit to their customers on the P.L.S. basis.
Instead, they prefer other mechanisms such as direct equity
holding and short-term leasing contracts. V

Overall, it seems that the introduction of the P.L.S.
institution does not alter the financial system
significantly. Therefore, in our analytical model, we will
ignore the P.L.S. arrangement and instead concentrate on the
elimination of the interest charge. The relative advantages
and disadvantages of the P.L.S. contracts versus direct
equity holding are discussed in more detail in Appendix B to
this chapter.

Before starting the analysis, one more institutionnal'
detail must be explained. At zero interest rate, the
private loan market will clearly fail because the savers
have no incentive to lend their savings. Instead, they can
keep them in cash or demand deposits. At zero interest rate,
the banks will continue to offer demand deposits and they
will be allowed to utilize a large portion of these funds
after setting aside the appropriate reserve requirements.
This implies that the demand depositors are indirectly
lending a portion of their money to the banks. Under this
institutional arrangement, the supply of loans at zero
interest rate will be positive. The model presented in this
chapter is based on this assumption because most of the

operating Islamic banks offer demand deposits and invest the

43

funds that are gathered in this way. However, the
alternative outcome of complete loan market failure could
also happen if, for some reason, the the public preferred to
keep their savings in safe boxes instead of putting them in
demand deposits. The consequenses of the model under this
assumption will be studied in Appendix A to this chapter.

In a decentralized economy, each household makes
several important decisions such as: 1) the quantity of
labor services to be supplied. 2) the allocation of income
in each period between savings and consumption, and 3) the
allocation of wealth among different assets. To make the
analysis managable, .we ignore the employment decisions and
instead concentrate on Evintertemporal and _ portfolio
_decisions. These later decisions are influenced by the
characteristics of the financial and real assets that are
.available, to the investors. The most important
characteristics which receive formal treatment in the theory

of finance are the expected return and risk of each ”asset,

 

The other important elements that also affect the decisions
of households are their degrees of risk aversion and time
preference. These characteristics are reflected in each
rpersons’ utility function.

We study the impact of interest-free banking under two

environments. In_the first section, investors have perfect

 

'- *-— -—--_ ——___,_.____._. _—

information about prices and income in the future. In this

_ ._._._._.

certainty model, the portfolio choice is irrelevant because

44

all the assets are riskless and, therefore, rates of return
are equal. To the investor, they are all perfect substitutes
and their rate of return is the pure rate of interest. In
the second section, we consider the more realistic case of
incomplete information about the future. In this case,
there will be many assets with different risk/return
characteristics. To make the model manageable, however, we
include only two assets. One asset represents bonds and is
assumed to be risk free and the other asset represents

physical capital or equity and is assumed to be risky.

SECTION 1
W.

In this section, we use a number of two-period models
to demonstrate how the intertemporal allocations of
households change when there is no uncertainty about prices
in the second period. ‘Each person has a fixed endowment at
the_beginnin8 of the first “period. He must allocate his
endowmentmebetween- consumption -and_ savings in period one.
The total return on savings is then consumed in the second

‘.___

(last) period. He chooses that allocation which will

 

maximize his utility of consumption over two periods:

Max U(Ci,Cz) , U1 , U2>0 , Ull<0 , Uzz<0.

’Ci , 02 = Consumption in the first and second periods.

45

The models developed in this section consist of _twgJ
utility:maximizing individuals with different degrees of
intertemporal preference. Having two agents allows us to
simulate a condition of general equilibrium. In the more
limited first model, each agent will only choose the optimal
level of savings and consumption. In the second model, we

have added the option of direct investment in a productive

process. ‘Now each household must allocate his endowment
. 1mg

among consumption, savings and direct investment. In both

models, we try to find out how these allocations change as

the rate of interest is reduced to zero.

1-A- W1
W1!-

In this model, we ggnsider_two persons who can trade
present and future goods with each other. First, in a
regular capital market, the interest rate will be
endogenously determined to clear the loan market. Each
person maximizes his lifetime utility of consumption subject

to his endowment constraint:

Person A Max U(CIA,CZA)

S.T. C1A + CzA/(1+r) = 010A + CzOA/(1+r)

46

Person B Max U(CiB,C29)
S.T. C1B + CzB/(1+r) = C103 + CzOB/(1+r)

Ci°A,C2°A Person A’s endowment in each period.

0103,0203 = Person B’s endowment in each period.

r Rate of interest.

The first order conditions are:

UzA/UlA

1/(1+r) UzB/UiB = 1/(1+r)
The loan market equilibrium is shown by:
(CiA - 0104): -(C13 - C103). ‘

These three equations along with the budget constraint will
solve for r,ClA,CzA,CiB andCzB . The solution is pareto
optimal because the tangency conditions are satisfied.

Under the Islamic restriction, individuals cannot earn

——____,

any interest when lending money to each other. We assume

 

that at zero interest rate the supply of loans will be
restricted to whatever the lenders are willing to save at
that rate. To find the solution, we will first find the
optimal allocation for each person at zero rate of interest.

If both were found to be net savers, no loans are traded and

47

their optimal allocations will be ~the market allocation
under zero interest. If one is a saver and the other one is
a net borrower, the market solution will be the same for the
saver. For the borrower, the maximization is repeated
subject to the quantity constraint on the amount that he can
borrow. He can at most borrow what the other person is
saving

In the first stage we will have:

Max UA(CIA , CzA) Max(U3(Cla , C23)

S.T. CiA+CzA = Ci°A+Cz°A S.T. 013+023 = C1°3+CzoB
If, for example, it was found that person A is a net lender:
010A-01A = ZA>0,

then we must repeat the maximization for person B subject to

a quantity constraint.

Max UB(Ci*B , can)
S.T. 01*3 + 02*3 = 0103 + C20B

01°3+ZA-Ci*B 2 0

(01*3,Cz*3) will be different from (013,023) if the

inequality constraint is binding. The final allocations are

,/

//

 

48

CiA,CZA,C1*B,Cz*B. The equilibrium under perfect markets is
demonstrated in Fig. 6. The equilibrium interest line is

R1Rz. The: optimal allocation point is E. H represents the

 

initial positions of persons A and B. The solution under no

interest charge is shown in Fig. 7 by point F. _sisz is the

zero interest line. Comparing the welfare of person A at E

/and F, we see that as a net lender he is clearly worse off

::// under the Islamic regime. Person B could be worse off or

better off depending on the amount that he can borrow. In
Fig. 7, he is shown to be worse off: 023(013 . ’Again, _we

cannot make a general statement on how the net savings

changes.

9\

 

 

    

¢
a s 6.A a.

 

 

 

 

 

 

Figure 7 Figure 6

cfi_-_____-___ ————-c1

‘49

l-B. - ' v t.

In this part, we add production opportunities to the
two-person model presented in l-A. Each person now has two
options: to lend or to invest according to a concave
nondecreasing production function. The production functions

are 3

TA(K14,KzA)=0 T3(K13,K23)=0

K1<0 is the input and Kz>0 is the output.

Fig. 8-A demonstrates how an agent allocates his resources
between savings and investment. The production possiblities
are shown by the concave curve 01°. 010 is his initial
endowment. To maximize his utility, he will invest
K1=-01°.X1 and save X’Y’. Then he will be able to consume

02 in the second period.
C1

 

 

 

Figure 8-A

50

In our two-person model the equilibrium conditions are
derived from each person’s maximization subject to the
production and budget constraints. In a regular capital
market with free movement of the interest rate, we will

have:

Max UA(CIA,CZA)

S.T. C14+Czh/(l+r) 010A+th/(1+r)+K1A , TA(K14,K2A)=O

Max UB(013,023)

S.T. C13+CZB/(1+r) C10A+K24/(1+r)+K1A , T3(K13,K23)

Using the Kuhn-Tucker method, the Lagrangians are
LA: UA(C14,CzA)-q14.TA(K14,KzA)
+q24.(K14+KzA/(1+r)-CiA-CzA/(1+r)+Ci°A)

Ls: 03(013,023)-q13.TB(K13,K23)
+qu.(K13+K23/(1+r)-CiB-CzB/(1+r)+0103)
The first order conditions are:
UiA-q14=0 , UzA-qib/(1+r)=0

q24.T14+q14=0 , q24T24+q14/(1+r)=0

U13-q13=0 , UzB-qIB/(1+r)=0

q23.T13+q13=0 , quTzB+q13/(1+r)=0

51

Simplication gives:

UzA/U1421/(1+r) , U23/01321/(1+r)
TzB/T13=-1/(1+r) , Tzh/T14=-1/(1+r)

For equilibrium in the loan market, we have:
CIA+KIA-CIOA=‘(C13+K13-C103)

The above 5 equations plus the two budget constraints will
solve for these seven parameters: r,ClA,Czfl,K14,C13,CzB,K13.
This is the market equilibrium under perfect capital
markets. We demonstrate the solution in Fig. 8.B. A is the
lender and B is the borrower. The equilibrium in the loan

market means YsstYAXA.

 

Fig. 8.B

 

 

 

 

Figure 8-B

52

Under the Islamic restriction, the interest rate is
fixed at zero and the borrower faces a restriction on how
much he can borrow. To find the new equilibrium, first we
find the optimal solution for each person under zero rate of
interest and no limitations on lending or borrowing. If it
is seen that they are both lenders, the feasible solution
will be same as what was found for each one of them. If
they are both net borrowers, then to find the feasible
solution we repeat the optimization for each person under
the condition that no borrowing is allowed.

Finally, if one person was a lender and the other one
was a borrower, the allocation of the lender will be already
feasible. To find the feasible solution for the borrower,
his maximization problem will be repeated subject to the
restriction that he can’t borrow more than what the other
person is willing to lend.

Formally in the first stage we will have:

Max UA(CU\,Czh)
S.T. TA(K14,K25)=0

01 A+C3A=C1OA+K1 A+K2A

Max 03(013,CzB)
S.T. TB(K13,K23)=0

C18+CzB=C103+K13+KzB

53

If they are both net borrowers, the feasible solution is

obtained by the following optimizations:

Max UA(Cih,CZA)
S.T. TA(K14,K25)=0
ClA+C2A2C1OA+K1A+K2A

C145C1°A+K1A

Max U3(CIB,C23)
S.T. TB(K18,K23)=0
cla+cgazcloa+xla+xza

C13$C109+K18

Figures 9-A and 9-B demonstrate this situation.

 

 

 

 

 

Figure 9-A

54

Under the positive market rate of interest, A is a lender
and B is a borrower. Setting the interest rate at zero will
rotate the interest rate line R1R2 to 8182 for both of them.
Now if unrestricted borrowing was allowed, they would both
be better off, achieving utility levels 02A and 023. But
since they can’t borrow, the feasible optimal allocations
are ZA and 28 . Both persons are worse off.

If in the first stage one of them was a net lender and
the other one was a net borrower, the lender’s allocation is
feasible but we must repeat the borrower’s optimization

problem. Assuming B is the borrower:

Max U*B(Ci*B.Cz*9)
S.T. T*B(K1*B,Kz*3)=0
clts+c2ts=clos+xlts+xzxa

ZA-CI*B+C1°3+K1*320

where ZA=CI°A‘CIA+KIA. ZA is the amount that person A lends
at zero interest. Then, the optimal allocations under
Islamic restriction are C14,CzA,Ci*B,Cz*B,K14,K25,K1*A,K1*B.
Figs. 10-A and 10-B show the feasible solutions and the

welfare results in this case:

55

 

 

 

- C1 C1

f
R;

Fig. 10-A Fig. 10-B

 

Under Islamic restriction, person A chooses Ya and person B
wants to choose YB but, since he can’t borrow enough to
reach YB, he borrows all that A,is willing to lend. Person
B achieves the highest level of utility at we: Max
UBIrzozUai. In Fig. 10-B, UsB>U1B implies that the borrower
will be better off. But this is not a general conclusion.
We could easily give other examples where UsB<U13. We could
say with certainty that A will be worse off because he is a

lender and the rate of interest has been reduced to zero.

56

Section 2

THE IMPACT OF ISLAMIC REGULATION UNDER UNCERTAINTY

The model of section one is insightful on the welfare
results of the Islamic Economic regime, but it is not
capable of determining the direction of change in total
savings. It also reveals nothing about portfolio decisions
and above all it is unrealistic because it does not take
into account the existing risk in the asset markets.
Clearly, any risk-averse investor will be sensitive to the
risk of every asset in his portfolio, and he would choose a
portfolio with minimum risk for any given expected return.
In this section, we study the reaction of risk-averse
investors to the elimination of interest in a model that
formally incorporates uncertainty. The objective is to see
how the portfolio and intertemporal allocations change as
the interest-paying assets are eliminated. Another goal is
to see how their welfare changes.

The model introduced here is a two-period, two-person,
two-asset model. Individuals will invest their savings in a
portfolio of risky and safe assets. Under regular capital
markets, the rate of interest adjusts until the loan market
clears. Under Islamic regime, the interest rate is set at
zero and the loan market will be at disequilibrium. Clearly

the private investors will not agree to lend funds to each

57

other at a zero rate of interest. Instead, they will keep
their money in cash and demand deposits which together
represent the safe asset of our model. Therefore, one might
be tempted to say that at zero interest no credit is lended,
but this observation is not correct because when a person
opens a demand deposit account, he is indeed lending money
to the bank. The bank keeps only a small portion of this
money as reserve and invests the rest (in loans or direct-
equity holdings). We divide the investors into two groups.
Let one group be the stockholders of banks and another group
be everyone else. (These will be the two persons in our
model.) Then under the Islamic regime, the second group will
be lending money to the first group through the demand
deposits.

We start the analysis by first solving the optimization
problems of both individuals for a general value of the rate
of interest ro. Then we differentiate the first order
conditions with respect to re to see how the savings and
risk-taking behavior of each individual changes as we change
the interest rate slightly. Our model is basically a
disequilibrium model where the rate of interest is a policy
tool. It could be set at any level between 0 and its
equilibrium value. The direction of local change in saving
and risk taking that is obtained by differentials remains
valid for any original value of interest rate in this range.

Our goal is to approximate the direction of change in risk

58

taking and savings when the interest rate is suppressed from
its original positive value to zero. The differentiation
approach, however, is only valid for small changes in the
interest rate. When the interest rate is reduced from its
positive value to zero, the change might be too large ‘to
justify this method. To go around this difficulty, we will
change our point of origin. We assume that the rate of
interest is originally zero, then we use the differentials
to approximate the change in the savings and risk taking as
the rate of interest is allowed to take a small positive
value. In other words, we observe how the behavior of
people changes as we go from an Islamic economy to a regular
economy with financial suppression, then based on this
finding, we will approximate the changes in household
behavior when switching from a regular to an interest-free
economy. The argument of Islam is that the interest rate
must be zero as opposed to any positive rate.. Comparing the
welfare and allocative results of the Islamic economy
against a regular economy with any level of interest rate
suppression will still give some insights about the relative
performance of an Islamic economy. The analysis reveals
that, for even a slight increase in the rate of interest
(from its original position at zero), the total saving
increases and risk allocation improves.

There is already vast literature on financial

suppression which indicates that the interest-rate ceiling

59

is nonpareto optimal compared to the competitive loan
markets. Using this result, we can argue that, since Islamic
economy is inferior to a similar economy with financial
suppression and the latter is itself inferior to a similar
economy with no interest ceiling, the Islamic economy will
be inferior to a competitive economy. We start the analysis
with a general equilibrium model of a one-period portfolio
choice and extend it to a two-period model with portfolio

and intertemporal choice.

241. W' '
W11.

Consider two individuals with fixed initial endowments
W1 and W2. Each person should allocate his endowment
between holdings in a risky asset and a safe bond. If the
individual is a net borrower, his bond holdings will be
negative. The objective is to choose an allocation which
will maximize the expected utility of final wealth. Before
developing the model, note that in this case the expected
'return to the risky asset is fixed because the total savings
of each person is given: r=r(W1,Wz). The bonds issued by
one person to another do not affect the aggregate investment
since all the existing funds are invested. The maximization

problem for each person is:

60

Max EUA(W1.(1+ro+XA(r*-ro)))
W.R.T. XA
Max EUB(W,,.(1+ro+Xn(r*-ro)))

W.R.T. XB
XA,XB = Portions of wealth invested in risky asset by
A and B.
r* = The random rate of return on the risky asset.

For equilibrium in the bond market we must have:

(1'XA).W1= -(1-Xs).Wz (1)
The first order conditions are:

dEUA/dXA20, dEUB/anzo (2)

We have three equations which could be solved for the
equilibrium values of XA,XB and r0. The equilibrium is
demonstrated in Fig. 11. The optimal allocations are shown
by points F and G. r0 is the interest rate for which EFzEG,
total landed equals total borrowed.The outcomes are pareto
optimal because the slopes of the indifference curves are

the same for both persons.

61

7.

 

 

 

Figure 11

When we suppress the interest rate, it is the borrower
who faces quantity constraint in the bond market. The
lender will simply save as much as he desires under zero

interest rate. The optimal allocations at zero interest

rate are shown by points H and J. B
.t “1
03 r
g .1
" o,
a o
u.
a: '
F E

 

 

 

 

 

Figure lZ-A Figure 12-3

62

If person B could borrow all that he wishes, he would
choose point N, but he is forced to choose a position on EH.
In Figs. 12-A and 12-B, we see that the lender is clearly
worse off while the impact on the borrower is not
determined. On one hand, the cost of borrowing is lower and,
on the other hand, he can’t borrow as much as he desires; he
could be worse off or better off. Nevertheless, we see that
the outcome under zero interest rate is not pareto optimal
because the rate of substitution between risk and return is
not the same for both persons.

To gain further insight and also to find out how the
risk allocation changes, we have to develop an algebraic
treatment. To do so, we must choose specific utility
functions for the two persons in our model. We assume that
the investors in our model are only concerned with the mean
and the variance of the returnJThen their expected utility
of wealth function will be equivalent to a quadratic utility
function. Even though quadratic utility functions have a
number of weaknesses that have been pointed out in the
literature, we have chosen to work with them because they

make the algebraic derivation possible.

Let: UA(C*A)

c*A-a.cu2 , U3 (on )=C*B-d’ .cnz

C*A,C*B The random final wealth.

63

The expexted utilities are:

EUA(C*A)=EA-d.EA2-d.sc*Az
EUB(C*B)=EB-d'.Ehz-d'.5c*32

s = The standard deviation

As we can see, the expected utility can be written as a

function of mean and variance. In our model we have:

C*A=W1.(1+ro+XA.(r*-ro)) C*B=W1.(1+ro+Xs.(r*-ro))
CA=W1.(1+ro+XA.(;-ro)) Ee=W1.(1+ro+xB.(?-ro))
sc*A2 : W12.XA2.5r2 sc*32 : W12.X32.Sr3

The first order condition for the lender is:

dEUA/dxiz[1-2.a.éhj.(E-ro).W1 - 4.d.5r3.W13.XA2
=[1-2dW1.(1+ro+XA(;-ro))](§-r0)-4dW12.XAZ.5r3=0

Next, we differentiate this F.O.C. with respect to ro, the

rate of interest.

dxi/dro=[exA.W12.sr3+2d.W1.(E-ro)2]
=—1—2aw:.(1-xA)(E-ro)

We can see that dXA/dro < 0. The change in the interest
rate when going from regular to Islamic regime is
dr=0~ro=-ro.

As explained earlier, for any interest rate less than
the equilibrium rate ro, the borrower will face quantity

constraint in the bond market. His optimization problem is:

64

Max EUB(W2(1+ro+Xs(;-ro))
S.T. (l-XA)W1+(l-XB)W220

The Lagrangian is: L=EUB-q1((l-XA)W1+(1-XB)W2)

dL/dst (1-2d’.W2.(1+ro+Xs(;-ro))).(f-ro)
-4d’W22.X32.s:3+q1Xs.W2=0

dL/dq1= (1LXA)W1+(1-XB)W220 and dL/dql. q1=0.

If the degree of risk aversion is small enough, the
constraint will become binding. In this case, we can derive
the dXs/dr by differentiating the bond market constraint

W.R.T. ro.

(dXA/dr).W1-(dXB/dr).W2=0
or

dXB/dr=-dXA/dr . W1/W2= (‘)(‘)(+) > 0.

Now that the signs of dXA/dr and dXB/dr have been
determined, we can find the direction of change in X3 and XA
when the interest rate is allowed to increase (starting from
zero interest rate). As the interest rate increases, the
highly risk-averse person is able to reduce his risk taking

and the less risk-averse person can do the opposite.

6S

dXA= dXA/dr . dr (-)(+)<O

dXBz dXs/dr . dr = (*)(+)>0

To find the impact on the utility of each person, we

will first determine the signs of dEUA/dr and dEUB/dr.

dEUA/droszUA/dCA.W1(l-XA)+dEUA/dXA.dXA/dro.(f—ro)
+(dEUA/d5c43).2XA.dXA/dr.W1.Srz
=dEUA/dCA.W1.(1-XA)+dXA/dr.[dEUA/dXA]
=dEUA/dCA.W1.(1-XA).

The second term is zero since we have dEUA/dXA

Therefore we get: dEUA/drszUA/dCA.W1.(l-XA)=(+)(+)>O. The
impact of moving away from zero interest on the welfare

~

ofthe more risk-averse person is: dEUA _
dEUA/dro.dro=(+)(+)>0. An increase in the rate of interest
- improves his welfare. For the borrower we again have:

dEUB /dr=dEUB /dCB . (1-Xs )2:an /dr. [anus /dX.B J;

but since the borrower faces quantity constraint, we have
dEUB/dXs #0. since for the borrower X3 is smaller than the
desired dEUB/dXs>0. We also know that Xs>1. Therefore,

dEUB/drszUB/dC?(1-Xs)+dXs/dr.[dEUB/dXs] <>o.
The direction of change in the utility of the less
risk-averse person is not clear. On one hand, the quantity

of loans increases and, on the other hand, he must now pay a

66

positive interest. Whatever the impact on the welfare of
the borrower may be, under the Islamic regime, the
conditions of pareto optimality are violated. We explained

this in Figs. 12-A and 12-B.

2-B. I] I ! E I J . E ! . !° . I ‘E . 1

In this model, we extend the model presented in 2-A to
include savings/consumption decisions as well as portfolio
choice. Each person has an initial endowment which must be
allocated between consumption in two periods.The first
period savings must be allocated between safe and risky
assets as described in 2-A. In this model, the rate of
return on the the risky asset is endogenously determined and
it is a decreasing function of net savings by both persons.
This rate of return is derived from a general stochastic

investment function:

Y*=Y(W1-014+W2-C1B,€)

The only argument of this function besides the error
term is the total investment of both individuals which is in
turn equal to the total savings of both of them. The
stochastic element reflects the uncertainty about the
outcome of the investment project. We assume that €~N(0,1).
For this general investment function, the stochastic, one-

period rate of return is:

67

r*=(Y*-I)/I = r*(W1-C1A+W2-013,E) where I=(W1-C14)+(W2-C1B).

We assume that the production function is concave such
that dEY*/dI<0, then the expected rate of return is also a
declining function of total savings.
(dY*/dI-1).I - (T-I)

d?/dI= < o.
12

 

Furthermore, dr/dI<0 2) dr/d(W1-C1A)<0 and dr/d(W2-C19<O.
Since the source of savings is not relevant to the process

of investment, we also have:
d?/d(W1-C1A)=d§/d(Wz-01B)

In the analysis we assume a linear-expected rate of return
function which is derived from a quadratic investment

function.

Y*=ZI-e12+€I =9 §=2I-e12.
;=(T-l)/I=1-e.(W1-C1A+W2-C13)
For this expected return function, we have:

dP/d(W1~C1A)=d;/d(Wz-C1B)=-e

e is a positive number which is small enough to give a
positive expected rate of return for the acceptable range of
total savings. In other words, we require that $20. This

implies:

e< 1/[W1-C14+W2-013].

68

The choice of this specific investment function is only
for algebraic ease. The same results will still hold if we
consider a general form for the expected return function and

write:
dE/d(W1-Cih)=d;/d(W2-CiB): -e.

However, the same restrictions that are imposed on e must
still be imposed in the general case.
Each person is assumed to have a quadratic utility

function over the two periods.

U11(014,CzM)=C14-d.Cil\2+C1"‘l\-d.Cz"‘A2
02*A=(W1-C14)(1+ro+XA(r*-ro))
UB(C13,C2*B)=C13-d.C132+Ci*B-d.Cz*BZ
Cz*3=(W1-C13)(1+ro+Xs(r*-ro))

Then, the expected utilities are:

EUA(Cib,Cz*A)=C15-dC142+CzA-d.CzAZ-d.scAZ
EU?(C13,Cz*3)=C1B-dC132+CsB-d.Cz32-d.ach

We will first study the behavior of the lender who does not
face any quantity consrtaints. Allow A to be the more risk-avers

person (the lender). His optimization problem is:

Max EUA(C1A,Cz*A)=fiA(cln,Eza,5cAz)
XA,C1A

S.T. 02*A=(W1-C1A)(1+ro+XA(;-ro))

The first order conditions are:

69

dEUA/dCithih-UZA.(1+ro+XA(f -ro))
-2.U3A.XA2(W1-Cih).5r2:0 (4)
dEUA/dXA=62A(?-ro)+2.fiaA.xA(W1-01A).s.2=o (5)

Even though the rate of return to the risky asset is
endogenous, each consumer treats r a given parameter when
maximizing his expected utility. The reason for so doing is
that we want the model to reflect the conditions of
competitive general equilibrium. We can further write
equation 4 as:

dEUA/dC1t=Uf-Uzh(1+ro)-XA.dEUA/dXA
=U1A-U24(1+r0) (6)
Expanding equations 5 and 6 for the quadratic utility
function we get:
dUA/dciheU1A-Uzb(1+ro)
=1-2d.Clh-(1+ro)+2d.(W1-C1A)(1+ro+XA(;-ro)).(1+ro)=0. (7)
dfih/dxi=2d.(W1-C:A)z.xA2.s:3-(§-ro)
+2d.(W1-C1A)(1+ro+XA(;-ro)).(1+ro)=0 (8)

Solving 7 and 8 for 014 and XA will tell us the optimal
choice of the lender. However, what we are interested in is
how his choice changes as the interest rate varies. To
achieve this, we totally differentiate the F.O.C.’s with
respect to ro. The total differentiation of equation 7

gives:

70

d(W1-Cll)/dro.[2d+2d.(1+ro)2+2d.(f—ro)(1+ro).XA+2d.(W1-
C14).XA.(l+ro)(-e)]+ dXA/dro.[2d.(W1-Clh).(f—ro)(1+ro)]=
1-2d.(W1-Cih).(1+ro).2-2d.(W1-C1A).XA.(1+ro).(-1-e.d(Wz-Q;B))
-2a.(wl-01A).xl.(E-ro). dro
and the total differentiation of equation 8 gives:
d(W1-Cll)/dro.[2d.sr3.XA2.(Wi-Cih).2+e+2d.(1+ro+XA(;-
ro)).(f-ro)+2d.(W1-C1A).XA.(r-ro).(-e)+2d.(W1-C1A).[1+
ro+XA(;-ro).(-e)]]+an/dro.[4d.sr3.XA.(Wi-Cib)2+2d.(W1-

CiA).(f-ro)2]=(-1-e.d(H1;QL£1)-2d.(Wi-Cih).[1+ro+XA(;-
dro

ro)].(-1-e.d(fl1:QLil)

dro
Using A,B,C,D,H and G for the coefficients in these
equations, we can rewrite them as:

d(W1-ClA)/dro.A+ dXA/dro.B=H for dUA/d014=0
d(W1-014)/dro.C+ dXA/dro.D=G for dUA/dXA=0

In the matrix form we have:

A B A B d(W1-C14)/dro H
s4 1 l H H]
C D C D dXA/dro G
d(W1-C1A)/dro
System 9 could be solved for . Since we are
dXA/dro

not using any numerical values, we can only solve for the
signs of these items. To do so, we must first find the
signs of A,B,C,D,H and G and det(S). We will investigate the
signs below: Since d,8r,XA and (Wi-Cih)>0; B and D are

clearly positive.

71

**Sign of A**

A=2d+2d.(1+ro)2+2d.xl.(E-ro).(1+ro)+
2d.(W1-Cih).XA.(1+ro)(-e)

We know that E>o, E:1-e.(W1-01A+Wz-cla) =>

2) e<l/(W1'C14+W2-C13)<1/(W1-C15).

In the last term of A, we replace e by 1/(W1-CiA). This
makes the term a larger negative number, then by rearranging

the terms, we will have:
A>2d+2a.(1+ro)2+2a.xi.(i-ro).(1+ro)-2d.xl.(1+ro).

The sum of the last two terms is positive so the whole

phrase is positive A20.

**Sign of C**
C=[2d.8r3.XAz.(Wl-CIA).2+e+2d.(1+r0+XA(;-r0)).(;-ro)+
2d.(Wi-Cib).XA.(f-ro).(-e)+2d.(W1-C14).[l+ro+XA(;-ro).(-e)]

Again we have: e<1/(W1-C1A) which allows us to claim:

C‘)[4d.5r3.XA2.(Wi-Cih)+e+2d.(1+ro+XA(r-ro)).(r-ro)+
2d.XA.(r-ro).(-1)+2d.(Wi-Cih).(1+ro)+2d.XA(r-ro).(-1))¢>
9.2.0.

72

**Sign of H**
H=1-4d.(W1-C1A).(1+ro)-2d.(W1-CiA).XA.(1+ro).(-1-e.d(Wg-C;B))
-2d.(W1-C14).XA.(;-ro). dro
If d and e are small enough, this statement is positive.

This will happen if W1 and W2 are large numerical values.

**Sign of G**
G=(-1-e.d(flz -Q1.B_._).)-2d. (W1 -011), [1+ro+XA(r-ro )l. (-1-e-111E1.:§1_“_1)

dro dro
filflazfiiil
Assuming that e<1/(Wz-C1B) and dro ==>
(-1-e.diEz_-_Q1ll) < (-1-e. [d(W2 -C13 )/dro l/(Wz -CIB ))
dro

As a result Q59.

Then we can write the system in the following form.
[+ +1 [d(W1-Clb)/dro] [+}
+ + dXA/dro -
The only remaining step is to find the size of the

determinant [S]=AD-BC. Applying the formulas for B and D we

get:

)5]:A.2X1.2a.(W1-01A)2.sr3+
2d.(W1-C1A).(Eero)[(;-ro).A-(1+ro).C] (10)

After expanding the bracket in the second and collecting

terms we get:

73

[(f—ro).A-(1+ro).C]=
(f-ro).2d-4d.s:3.XA2.(W1-C1A).(1+ro)-
e.(1+ro).[1-2d.(l+ro+XA(;-ro)).(W1-C1A)].

Then, by carrying out all of the mathematics in equation 10,

we have:

lSl=4d2.(f-ro)2(W1-Cih)-8d2.5r3.XAZ.(W1-Cifi)2.(1+ro).(;-ro)-
2d.e.(l+ro).(;-ro)).(W1-C1A)+
4d2.e.(1+ro)2.(;ero)).(W1-C1A)2 +
4d3.e.(1+ro).(;-ro)).(W1-C1A)2.XA +
8d2.sr3.XA2.(W1-Clh)2+ 8d2.5r3.XA.(W1-C1A)2.(1+ro)2+
8dz.srs.xlz.(W1-C:A)z.(1+ro).(E-ro)-
8d3.sr3.XA2.(W1-Clh)3.(1+ro).e

After rearranging terms, we get:

)8): 8d3.sr3.XA3.(W1-CIA)2.[-(1+r0).(;-r0).XA2+
(1+ro).(;-ro).XA3+(1+ro)2.XA-(1+ro)3.XA.e]+
2d.(W1-C14).(;-ro)[(;-ro).2d+4d.s:3.XA2.(W1-C1A)/(;ero)-

e.(1+ro)]+4d3.(W1-C1A).(F-ro).(1+ro).e.[1+ro+XA.(;-ro)].

The first and the third terms are clearly positive. The
second term will be positive if e is small enough. Recall

that e<1/(W1-C14). Therefore, if (W1-Cih) is large enough,

74

e will become small and this term will also become positive.

Thus |S|>0.
With a positive determinant, we can now determine the
++
signs of the elements in the inverse matrix 8'1. If S=l+ +

and det(S)>0, then:

5.4:]

And, finally, we will get: [d(W1-C1A)/dro] [+ -J[ + ] [ +
dXA/dro - - + - - -

0
g; ;90; . 1.: ::f '7. ._gs_ ,3. :11. : “ no ;

W

W

From the lender’s behavior we know that when the
interest rate increases, the quantity of bonds increases.
Next we find out how the borrower reacts to this increase in
quantity of bonds and the rate of interest. The bond market

equilibrium is given by:
(l-XA)(W1-C1A)=-(1-Xs)(W2-C1B) (12)

Totally differentiating the bond market equation (12) with
respect to ro, we get:
(1-Xa).d(W1-C1A)/dro- (Wz-C1B).dXA/dro=
(l-XB).d(W1-C13)/dr0- (W2-C1B).dXs/dro

75

We can rewrite this equation as:
(1-Xs).d(W1-C1B)/dro- (W2-C13).dXs/dro=K<0
d(W1-Cih)/dro>0 and dXA/dro<0 ==e K<0 (13)

Besides equation 13, we need one more equation to determine
the signs of d(Wl'C13)/dr0 and dXB/dro. To find the second
equation, we look at borrowers’ optimization subject to the

bond market constraint:

Max EUB(C13,C2*3)=Ua(C13,623,Sch)
Xs,C1B

S.T. C2*3=(W1-013)(1+ro+Xs(;-ro))
8c32= 5r2.X32.(W2-013)2

(1-XA)(W1-CIA)+(1-XB)(W2-C13)20

[EB :01 a -d‘c1 a 2 +02 9 -d'. C: a 2 -d'. 3:: a 2]

The Lagrangian is: L 5U3+qz((1-XA).(W1-CiA)+(1-Xs).(Wz-C1B))

The first order conditions are:
dL/dCi 1: :01 a 5623 . (1+ro +113 (E-ro ))
-2.UaB.X32(Wz-C1B).sr3+qz.(Xe-1)=0

76

dL/dXBeUzB.(W2-C13)(f—ro)+2.U33.Xs[(W21-018).5r12-q2(W1-Cifi):0
dL/dq2=(1-XA).(WI-C15)+(l-XB).(W2-C13)20, q2.dL/dq2=0
Assuming that q2#0, we need one equation from above to solve
for dXs/dro and d(W2-C1B)/dro.
The best strategy is to combine dUh/dC1A and dUB/dXs into
one equation by eliminating qz.
dL/dxaéfiza.(I-ro)+2f§aa.xB(W21-01a).srz-qz =0 (14)
dL/dC132 613-623(1+r0)‘XB.(dUB/XB)+q2.(XB-1) =0
dL/dC1B= U13-Uz3(l+ro)-X3.q2+q2.(XE-1) =0

: Uifl-U23(1+ro)-q2=0 (15)

By combining 14 and 15, we get:

Uza.(E-ro)+2.UaB.xB(W21-C1n).s.2- U1B+Uzn(1+ro)=o

2.UaB.XB(W21-C13).Sr2- U13+U23(1+r) =0

Expanding this equation for a quadratic utility function, we

get:

-4d’.(Wz-C13)2.an.5r3-1+2d’.CiB+
[1-2d’.(Wz-C13)(1+ro+Xs.(f—ro))].(1+;)=0

Totally differentiating this equation with respect to re

gives:

77

d(Wz-Cifi)/dro.[-8d’.(Wz-C1B)2.X32.5r3-2d’-e+
e.2d’.(Wz-C19)(1+ro+Xs.(F—ro))+2d’.e.(W2-C19).(1+;)-
2d’.(1+ro+Xn.(§-ro)).(1+§)] +

an/dro.[-2d’.(Wz-Cia).(;-ro).(1+r)-8d’.(W2-013)2.Xs.5r3]=
2d’.(W2-013)(1+ro+X3.(f—ro)).(-e.d(W1-Cih)/dro)+
e.d(W1-C1A)/dro)+
2d’.(Wz-C1B).(1+;).(1+Xs.(-e.d(W1-C1A)/dro-1)). (16)

Equations 13 and 16 give a system that could be solved for

d(W2-C1B)/dro and dXB/dro

Writing 13 and 16 in matrix form, we have

[ ’ B’] [A’ B’ {d(Wz-C1B)/dro] [H’] 13*
8’:
C’ D' ] G’ 16*

c' D’ ' dXs/dro
We must determine the signs of A’, B’, C’, D’, H’ ,G’ and

IS’I. From equation 13, we know that C’<0, D’<0 and G’<0.
Also Xs>1 , d(W1-C1A)/dr6>0 allow us to claim that BLEQ:
**Sign of A’**
A’: [-ed'.(W2-Czn)2.Xn2.s:3-2d'-e+
e.2d’.(W2-C13)(1+ro+Xs.(;;r0))+2d’.e.(W2-C13).(1+;)-
2d’.(1+ro+Xs.(;-ro)).(1+;)]

78

If e is small enough, we can safely argue that A’ is

negative. A. < 0

**Sign of H’**
H’=(-e.d(W1-C1A)/dro).[-2d’.(Wz-C13)(1+ro+Xs.(P-ro))+1]+
Zd’.(W2-C1B).(1+3).(1+Xs.(-e.d(W1-Cih)/dro-1)).

Since person B is less risk-averse, d’ will be very small.
H’ will be positive if d’ and e are small enough. Assuming a
to be sufficiently small, we claim that 8:29.

The final step is to find the determinant of S’.
IS’le’D’z-(Wz-C1B).A’-(1-Xs).B’
After expanding A’ and B’, we get:

13'): 2d’.(W2-C1B)+ e.[-2d’.(Wz-Cia)(1+ro+Xs.(r-ro))+
1].(Wz-CiB) + 2d’.(Wz-CiB).(1+;).(1+ro)+ 2d’.(W2-
CIB)3.XB.(4Sr3'e.(1+;))

131129

The determinant will be positive for sufficiently small
values of e. Now the system of equations 13 and 16 could be
written as:

[- - d(W2-C13)/dro +
].[ I: J and IS’|>0.
dXs/dro

79

The inverse of S’ is:

Wt w1=1 t)

+
Then: [d(W2-C13)/dro] [- +J [ - I
dXB/dro . + - - +
d(W2-Cifi)/dro<0 and dXs/dro>0

As the interest rate increases (being zero originally),
the borrower’s saving and risk-taking behavior changes in

the following directions:

d(W2-C1B)=d(W2-C1B)/dro.dro = (-)(+)<0
dXs = dXs/dro.dro = (+)(+)>0

,: : c :3"; r. ‘: 0: .2 :.: 1,0 ; ‘. ._qo :_ :._ :_

Next, we will look at the welfare results of Islamic

restriction. For the lender we have:

11611 /dro :31 A .dC1 A/dro +521) .dCzA /dro +3111 .dscn /dro
=U1A.(-1).d(W1 -C1A )/dro +dXA/dr0 . [5211. (W1 -C1A ) . (F-ro )+
2U35.5r3.XA.(W1-C1A)3] +
621 .d(W1 -C1A )/dro . (1+ro +x11+ . (5-1-0 ) )+62A . (W1 -C1 A ). (1+
xA.(d§/aro-1))+201A.sra.xAz.(W1-C1A).a(W1-C1A)/dro

After collecting terms, we get:

80

dUA/droz-d(W1-CiA)/dro.[dUA/dC1]+dXA/dro.[dUA/dXA]+
62A(W1-C1A).(1+Xx.(d§/dro-1))

However, we know that dUA/dC1A=0 and dUA/dXA=0, therefore,

‘

dUA/droz UzA(W1-C1A).(1+XA.(d;/dro-1)) (17.A)
similarly for the borrower we have:

dUB/dro=-d(W2-C1B)/dro.[dUB/d01]+dXs/dro.[dUF/dXs]+
U23(Wz-C1B).(1+Xs.(d;/dro-1)) (17.B)

For the borrower, however, dUB/d01B <0 and dUB/dXs>0.

The direction and size of change in the utilities
depends on dE/dro. We will first expand dE/dro and
determine its sign. From the optimization problem of the
borrower we obtained the system of equations 13 and 16.

Solving this system we get:
d(W2-C13)/dro=[D’H’+B’G’J/IS’I (17.0)
From the bond market constraint equation 13, we get:
6’: (Xx-1).d(W1-C1A)/dro+(W1-Cih).dXA/dro

Putting this in equation 17.0, we will get:

81

d(W2-CIB)/dro={D’H’+B’(XA-l).d(W1-C14)/dro+
B’.dXA/dro(W1-C14)}/IS’I

d(W2-C13)/dro+d(W1-C1A)/dro={D’H’+[B’(XA-1)+
lS’I].d(W1-CIA)/dro+B’.dXA/dro(W1-CIA)}/|S’I (18)

In equation 18, we have added d(W1-C1A)/dro to both
sides of equation 17.0. Further, we have lS’le’D’-B’C’

which gives:

R.H.S. = {D’H’+B’[(XA-l).d(Wl‘ClA)/dr0+dXA/dr0.(Wi-ClA)'
(1-Xs).d(W1-01A)/dro]+ A’D’.d(W1-C1A)/dro}/|S’l

We will use the following breakdown to find the sign.

R.H.S. = {D’H’+A’D’.d(W1-014)/dro+B’(Xa-l).d(W1-C14)/dro+
B’.[dXA/dro.(W1-C1A)-(1-Xs).d(W1-C1A)/dro]/|S’I

The denominator was already shown to be positive. We should
only be concerned with the numerator.

In the numerator, the last term is clearly positive
because B’<0 and dXA/dro.(W1-C1A)-(1-Xs).d(W1-C1A)/dro. The
second inequality is the result of the following
inequalities: d(W1-014)/dro>0, dXA/dro<0 and XA<1. Our next

step is to determine the sign of:

82

D’H’+A’D’.d(W1-C1A)/dro+B’(XA-l).d(W1-CTA)/dro
We have:

H’+A’.d(W1-C1A)/dro=
-8d’(Wz-CTB).X32.sr3.d(W1-C1A)/dro-2d.d(W1-01A)/dro-
e.d(W1-C1A)/dro.[1-2d’.(Wz-CzB)(1+ro+Xs(r-ro))]+
e.d(W1-C1A)/dro.2d’.(Wz-CzB).(1+f).Xs-2d’.(1+ro+
Xs(;-ro)).(1+?).d(W1-C1A)/dro+e.d(W1-CTA)/dro.[1-
2d’.(Wz-C.B)(1+ro+Xs(;-ro))]-e.2d’.(Wz-CTB)(1+
E).Xs.d(W1-CTA)/dro+2d’.(W2-013)(1+;)(1-Xs).

Some of the terms cancel each other out and afterwards we get:
H’+A’.d(W1-C1A)/dro= _

-ea'(W2-C1B).Xn2.513.d(W1-C1A)/dro-2d.d(W1-C1A)/dro

~2d’.(1+ro+Xs(r-ro)).(1+r).d(W1-014)/dro+

2d’.(Wz-C1B)(1+r)(1-Xs)

Also, remember that D’=(W2-C1B).(-1) and

3': 2d'.(Wz-C1a)(1+E)(E-ro)-8a'.(W2-C1B)2;xx.sra

Then, D’H’+A’D’.d(W1-C1A)/dro+B’(Xa-1).d(W1-C1A)/dro =
2d'.(Wz-C1a)(1+?)(}-ro).a(W1-C1A)/dro+
2d’.(Wz-C1B)(1+;)(1+ro).d(W1-C1A)/dro+
Bd’.(W2-013)2.xs.sr3.d(W1-C1A)/dro+
2a'.(W2-C1B).d(W1-C1A)/dro+2d'.(Wz-C1B)2.(1+§).(1-Xn).

 

83

Every term in the above phrase is positive. Therefore,

D’H’+A’D’.d(W1-CTA)/dro+B’(XA-l).d(W1-CiA)/dro>0

Overall, we have shown that the numerator of the fraction in
equation 18 is positive, so the whole fraction is positive

and we have:

d(W1-C1A)/dro+d(Wz-013)/dr020
dE/droz-e.(d(W1-01A)/dro+d(W2-C1B)/dro)<0

We can now estimate the direction of change in net
savings and return to capital when moving away from the zero

interest rate.

d(Net Savings)=d(W1-C1A + Wz-C1B)
=dro.(d(W1-C1A)/dro+d(Wz-CTB)/dro)=(+).(+)>0

The net savings increases.

d(Return to Capital) = d? = [df/dro].dro = (+)(-)<0

The return to capital declines.

We can now elaborate on the welfare effects of Islamic

restriction based on the results of our model. Equations

84

17.A and 17.3 give formulas for dUA/dro and dUB/dro. For
the more risk-averse person, A, the change in utility
depends on the sensitivity of the expected return on risky
assets to changes in the interest rate. If df/dro is a
large negative number, the return to capital (the risky
asset in our model) falls rapidly as the interest rate
rises. This reduction in r will offset part of the welfare
gain from the increased interest payment on the bonds that
person A holds. Compared to the one-period model of 2.A,
the welfare gain of person A will be smaller.

The welfare results for the borrower is undetermined
because, as the interest rises, the cost of borrowing
increases but, at the same time, the quantity of bonds
increases also. If he did not face any quantity

constraints, we would have had:

dUB/dro=UzB.(Wz-Cifi).(1+(d;/dro-1).Xs)
Xs>1 and aE/drow => dUB/dro <0

Therefore dUF=EdU3/dro].dro indicating that the
borrower would have been better off under Islamic regime.
It is the shortage of credit that could change the results.
The net impact on the welfare of the borrower is not clear.

In addition to the above results, we must also point
out that, similar to the one-period model, we observe that

the interest-free system is non-pareto optimal. Under a

85

competitive regime with no restrictions on the interest

charge, we have:

dUA/dCM: U1A-UzA.(1+ro).-.o => U1A/U24=1+ro
dUB/dC1Bz UiB-U23.(1+ro)=0 z: U1B/U23=1+ro
0111/02!) = 018/1328

Equation 19 is the condition of pareto optimality and it no

longer holds under Islamic regime.

Wen

The models that were analyzed in 2-A and 2-B gave us
approximate indications on how the savings and risk-taking
behaviors of the investors changed as a small positive rate
of interest was introduced into an Islamic economy. All
that was needed was to reverse the results that were found
above.

1. For the highly risk-averse individual who was a net
lender, a switch from regular to Islamic regime was welfare
reducing. He saved less and had to take more risk than
before.

2. For the less risk-averse person who was a net
borrower, the welfare impact was not clear. He saved more
and had to take less risk because he couldn’t borrow as much

as he wanted to.

19

86

3. The net saving of the economy declined. As a
result, the rate of return on capital was higher under the
Islamic regime compared to the regular regime (which lead to

less investment).

87

Notes

1) In a recent article, M. Hassan Imam studied the
welfare cost of interest rate ceilings in developing
nations. His study has shown that interest-rate suppression

causes significant distortions in the capital markets of

lesser developed nations.

CHAPTER 3

THE CONSEQUENCES OF ISLAMIC BANKING IN A
MACRO-ECONOMIC FRAMEWORK

In this chapter, we focus on the macro-economic
consequences of the Islamic economic system. We are
primarily interested in three questions:

1) What are the effects of interest-charge elimination

on the volume of real investment and output?

2) How can we conduct monetary and fiscal policy in

the absence of a government bond market?

3) How do policy multipliers compare between regular

and Islamic economies?

The only Islamic regulation which is studied here ,is
the glimingtion of an interest charge on financial
transactions. In Chapter 1, we showed that the other views
of Islam on the economic structure did not substantially
vary from those of a regulated market economy.

The abolition of an interest payment will primarily
affect the financial sector of the economy. Financial
assets in a modern economy can be divided into- debt__and
equity instruments. Equity instruments, such as stock
. shares, do not have a fixed return. They are simply claims

on a certain productive asset and receive a portion of the

88

89

profits as a dividend. Debt instruments such as private and
(government bonds have a pre-assigned rate of interest which
is realized if the debtor does not default on his debt. By
forbidding an interest charge, Islam effectively eliminates
the debt instruments. Consequently, the only financial
instruments available in an Islamic economy are in the form
of equity. The only other remaining asset will be money.

The elimination of an interest charge does not
necessarily lead to the elimination of the depository
institutions such as banks. Instead, it will cause certain
reforms. Banks will provide credit to the public on the
basis of equity arrangements such as the profit- and loss-
sharing contracts. They will raise credit by offering PLS
accounts and demand deposits. (Savings and time deposits
will not be permitted.) Demand deposits will be the only
debt instruments in an Islamic economy. They are tolerated
because no interest charge is involved.

The existence of banks allows the public to divide
their money holdings into currency and demand deposits.
They can also divide the risky portion of their portfolios
between equity stocks and PLS accounts. (For reasons that
were explained in Chapter 2, it is not necessary to
differentiate between direct equity and PLS accounts in our
model.) The Islamic economy, therefore, retains many
features of a regular market economy with the modification
that government and private bonds as well as the interest-

paying bank deposits are eliminated. In the following

90

sections, we introduce a Keynesian macro-economic model

which has been modified to reflect these differences.

Section 1
I] C E I ! ! B ! El° . !' .

The elimination of an interest charge leads to the
elimination of three types of debt assets: private loans,
government bonds and bank savings deposits. It will be too
difficult to study the effect of eliminating all three
assets simultaniously. If the interest rate on bank
deposits are eliminated, they will be transformed into
demand deposits. Similarly, government bonds are
transformed into money. The public will continue to hold
money and demand deposits because, to a large extent, they
trust the government and the banking system. Besides, these
assets provide some utility to the households as stores of
value and means of exchange. Private loans, on the other
hand, will no longer exist if the lender is not allowed to
charge interest. The reason is that these loans carry a
high risk of default and no one will assume this risk when
there is no reward. So the elimination of the interest
charge will eliminate the private loan market altogether.

Since our main analytical method is comparative
statics, we will ignore private loans and government bonds
at first and concentrate on bank deposits. At the end, we
will demonstrate how the results will change if the

elimination of government bonds and private loans are also

91

taken into account.
Our model will consist of the equilibrium conditions
for the real and financial sectors of the economy. _The real

sector will be in equilibrium if the aggregate supply of

real output is equal to the aggregate demand. In the
absence of the government sector, which is the case in this
model, we can show the equilibrium by equating savings and

investment.1 The savings and investment functions of our

___.—
4‘. _—___—..____ __,._1-—-*——'

model are described as follows. ’We_assume that there is a
single homogeneous capital good that is being utilized by
alluhfirms. Firms can increase their capital by investment
in new capital at low cost. But it is more costly to buy or
sell a used capital good. As a result, there are two
separate markets for capital. There is one market for the
newly produced capital good and another market for claims on
the existing stock of capital. The F§?§_S£_iEXE§PmepB wwill
depend on theJ price differentials between these markets.
When the value of equity claims is more than the cost of new
capital, firms are encouraged to invest. On the other hand,
‘if the price of new capital (also called the replacement
cost of capital) increases relative to the equity price of
capital, new investments will decline. This approach to the
investment behavior follows Tobin(69), Tobin-Brainard(17) and
Benavie(15) among others:

- Theappropriate investment function is:

-._._-—q_._

I=(V,P) 11)Ofl and” lg 0

92

I = The rate of real investment.

P = The price of output. (In our one sector model, the
consumer and capital goods are the same commodity.)

V = The value of the equity supply. VzPexE where Pezthe

price of equity and E = the equity claims on the stock
of capital. Since we assume that E is constant, the

choice of V instead of Pa will not affect the results.

The rate of savings by households is assumed to be

\ _# ___,_

positively related to real income and to the rates of return

on financial assets. It is negatively related to the level

of wealth.
+ + -
S= S(q.r.W)xY
q = The rate of return on equity.

The rate of return on saving deposits.

Real wealth.

Real income.
Then Afor the equilibrium condition in the real sector, we
have:
+ + -
S( q ,r , W)x Y = I(V ,P) 1.1
There are three assets in the financial sector of our
model. These are equity ,saving deposits and money. Each
household must allocate its wealth among these three assets.
Savings deposits are offered by the banks. Banks will keep a

portion of these deposits as reserve and invest the rest in

the equity markets. The equilibrium conditions for these

93

markets are given by the following equations:

+ - - +
(1-K).B/P + h1(q.r,Y,W)= V/P Equity (1.2)
- - + +
K.B/P + h2(q,r,Y,W)= M/P High-powered money (1.3)
- + - +
h3(q ,r ,Y ,W)= B/P Savings deposits (1.4)

B = Saving Deposits; M = Money; K = The reserve requirement

ratio on demand deposits

h1,h2,h3 = The household demands for equity, currency and
savings deposits, respectively.

This model has a Keynesian structure where, due to
insufficient demand, the economy is operating at less than
full employment level. As a result, the price level is
assumed to be fixed. Any increase in demand will stimulate
output without putting an upward pressure on prices. We
rely on these (assumptions as well as the static nature of
our model to ignore the question of inflation altogether.

We assume that the interest rate on savings deposits is
fixed below its equilibrium value by the monetary
authorities. As a result, the banks accept all the deposits
that they can get at any level of the interest rate ceiling.
Equation 1.4 indicates that the equilibrium value of the
savings deposits is always the quantity demanded by the
households. The derivative signs of the asset-demand
equations indicate that the demand for each asset is

positively related to its own rate of return and negatively

94

related to the rate of return on other assets.

An increase in income will increase the public demand
for money because of the transaction needs. Since income is
not a component of real wealth, we have h13 + has + h33=0.
We also know that hza implies that the increase in income

must reduce the total demand for other assets:

h13 + haaz-hza <0

Finally, the asset demand functions are positively
related to changes in real wealth.The wealth constraint is
W=V/P + M/P. Since savings deposits are a liability of the
private sector to itself, they do not appear in the wealth
constraint.

We will modify the model further to reflect the
dependence of dividends on the value of equity and income.
While the model itself does not include the supply side of
the economy, we will make a brief reference to the commodity
and labor supplies in order to explain this dependency.

On the supply side of the economy, the production
function is:

Y = F(L,K°) F1>0 & Fz<0

C"
II

Quantity of labor demanded.
K0 = The supply of capital which is assumed to be fixed in
the short run.
Since equity represents claims on the stock of capital,
the return on equity will depend on the share of capital in

national income.

95

q»..—
q=[P. F2(L,K0). KOJ/V

F2(L,K°)=Marginal product of capital. (An increasing
function of labor demanded.)
The demand for labor is a positive function of demand for

Output.
+

L=L(Y)

+..
Replacing for L in F2(L,K0), we get q=[P.H(Y,K°).K°]/V.

Since K0 is fixed, any increase in output will increase the

marginal product of capital. Therefore, we can write the
+'+ -

rate of return to capital asz: q(P, Y, V). The real
q=++q-

wealth could also be written as W = W(V, M, P). Replacing for

q and W in equations 1.1-1.4, we get:

+ + - - + -
S(Y,P,V,M).Y = I(V,P) Commodities (2.1)
? ? - 7 +
(1-K).B/P + f1(Y,P,r,V,M) =V/P Equity (2.2)
?--++
K.B/P + fz(Y,P,r,V,M) = M/P High-powered money (2.3)
- - + + +
f3(Y,P,r,V,M) = B/P Savings deposits (2.4)

As we can see, the dependency of the equity rate of
return on income and the value of equity leads to
indeterminacy in some of the derivative signs.

To study the impact of interest rate control, we will
first combine the asset market equations into a single
equilibrium condition for the financial sector. From 2.4, we
replace for B/P in 2.2 and 2.3. The wealth constraint

allows us to ignore one of the two resulting equations. We

96

will keep the money market equation and drop the other .one.

Then the IS and LM equations of our model are:

+ + + - - + -

S(Y,P,r,V,M).Y = I(V,P) 3.1 IS
- - + + + ? - - + +

K.f3(Y,P,r,V,M) + f2(Y,P,r,V,M) = M/P 3.2 LM

The endogenous variables are Y and V. M and r are
exogenously determined.

Our objective is to see how the endogenous variables
change as the rate of interest is reduced to zero from its
original positive value. Since the method of comparative
statics is only applicable for the study of relatively small
changes in the exogenous variables, we analyze the problem
from a different point of reference. We assume that the
rate of interest is originally fixed at zero, then we
observe the direction of change in the endogenous variables
as the rate of interest is slightly increased. These
changes will approximately reflect the opposite of what will
happen if the interest rate is reduced from an original
small positive value to zero.

The equilibrium conditions 3.1 and 3.2 hold for any
nonnegative rate of interest including zero. Totally

differentiating these equations with respect to V, Y, and r

we have:
Sa.Y-I1 SI.Y+S dV -Sa.Y
'[ = odr 4.1
K.fa4+f24 K.f31+fz1 dY -K.faa-f32

System 4.1 could be written as:

97

, dV
A. = B.dr 4.2

dY
By defining the signs of the elements of A and B, we

would like to determine the signs of dV/dr and dY/dr . From

the derivative signs of 3.1 and 3.2 it is clear that:
A11<0, A12>0, A21>0, Bll<0

A22 and B21 are apriori indeterminate. To determine
their signs, we must make certain assumptions about the
elasticities of asset demands.

If we assume that the demand for money is more
sensitive to variations in income than to variations in
return to equity, then f12 will become positive, and since K
is very small, we would have A22=k.f31+f21>0. Also, we
assume that the savings deposits are the primary substitutes
for money. This assumption implies that fzs is significantly

different from zero and as a result:
Bziz-K.f33-f32>0

These two assumptions could be combined into a single
assumption which says that in a regular economy bonds are
strong substitutes and equity is a weak substitute for
money. This requirement does not weaken the results because
both intuitively and empirically appear to be true. Using

these signs, we write 4.2 as:

98

1.1.1: I] l: :l

det(A)<0

I” H
dY = + . dr 4.3

3;;gil = [; :][;i= [7] : dv/dr>0 , dy/dr:0.

We can now interpret these results to say approximately
the following:

Eganlt_1: The suppression of interest payments on
savings deposits will reduce the value of equity assets and
cause a drop in the rate of investment. The net change in
real output, however, is indeterminate.

The reason for the second result is that the reduction
in the interest rate reduces the size of investment but at
the same time increases the level of consumption. Thus, the
aggregate demand could increase or decrease.

So far, we have seen the impact of Islamic regulation
if the only existing debt instruments were savings deposits.
In most nations, however, we find several other debt
instruments such as private bonds and government bonds. The
regulation will eliminate these instruments as well. We
will now briefly describe what happens when these
instruments are eliminated. First, consider the case of
private bonds that are used for investment. ‘

We assume that firms are originally issuing bonds and
equity. Under Islamic regulation, these bonds must be
liquidated. Whether the liquidation takes place gradually
or suddenly, the net result is that the firms must pay back

the value of bonds or replace them with equity. At the

99

aggregate level, we assume that the entire stock of capital

is owned and employed by the firms. Then it must be the

case that the market value of the stock of capital equals

the value of the equity and bonds that firms have issued.
Pk°.K= Pa .Eo+Bp 1*

Pk0 = The price of physical capital before change.

K = The stock of physical capital (assumed fixed.)
Pa = The price of equity.
E0 = The stock of equity shares before change.

Bp The nominal value of private debt issued by the firms

to the public.

Due to the possibility of default, the private loans
are risky; but since in every firm bonds have the first
claim on earnings, they are less risky than the stocks. When
the interest payment on bonds is eliminated, households will
eventually transfer the funds that were invested in bonds
into money and equity. This transfer will generate a new
demand for equity. At the same time, the firms must raise
funds to pay back the loans and they do so by selling stocks
or by PLS borrowing. Therefore, we would have a rise in the
supply and demand for equity at the same time. If private
bonds and equity were perfect substitutes, households would
have replaced equity for their entire bond holdings and no
funds would have been pulled out of the private securities
markets; but since equities are generally riskier than

bonds, risk-averse investors will not replace each bond with

100

an equal value of equity. Instead, they will replace it with
a combination of equity and money. The allocation will
depend on each person’s degree of risk aversion. In this
case some funds will be pulled out of the private claims
market and held as money. Because the total demand for
securities of private firms has declined, both sides of

equation 1* will decline. We will have:

PR1 . K = Pe1 . E1 2*
Pol . E1 < Pa . E0 3.A*
PR1 . K < PRO . K 1?’ Pk1 < Pko 3.B*

Pkl =Price of capital after the elimination of bonds.

Pal =Price of equity after the elimination of bonds.

Inequalities 3.A* and 3.B* indicate that:

,Besnlt_z: The elimination of private investment bonds,
as a result of the Islamic regulation, will lead to a
decline in the value of physical capital as well as the
value of claims on capital (equities). The drop in value of
capital will reduce people’s incentive to invest.

Next, we consider the removal of the government bonds
market. The Islamic restriction will forbid any interest
payment on these bonds. Under zero interest, the public will
prefer money and demand deposits to the government bonds
because the latter are less liquid while they all pay the
same nominal zero interest and carry the same level of risk.

The government will have to retire all of its debt. The

101

needed funds could be raised either by increased taxation or
by increasing the money supply. Since the effects of tax
increases have already been extensively studied in the
literature, we ignore this option and concentrate on the
case where the government pays back the debt by increasing
the money supply. If the debt is large, this proportional
increase in the money supply could be significant, leading
to an increased demand for commodities and equity. As a
result, the price of equities rises leading to a rise in the
value of equity and encouraging more investment. At the
same time, the price level will also rise; both investment
and consumer goods will be more expensive. These higher
prices, on the other hand, will discourage investment. The
net effect on investment depends on whether the economy is
at full employment or not. If the economy is at full
employment, the price level will rise and the net effect of
this policy will not be clear. 0n the other hand, if there
is unemployment, prices will remain stable and both
investment and output will increase. In brief, we will
have:

,Resnlt__§: To eliminate the interest payment by the
government, all the existing government bonds must be
liquidated. In order to retire its debt, the government
must raise funds by means other than public borrowing. The
remaining options are taxation and increasing the money
supply.

Refinlt_5: If the government prints additional money to

102

buy back its bonds, the money supply will rise leading to an
increase in demand for equities which will in turn stimulate
investment.

We see that elimination of the interest charge will
result in several institutional changes. Each of these
changes has a clear impact on the level of output and the
rate of investment. The direction of change however is not
the same for all of them. Unlike savings deposits and
private investment bonds, the elimination of government
bonds will not necessarily lead to a drop in investment.
Thus, we will arrive at the final result of this section:

Bgsult_5: In the short run, the impact of interest-
charge elimination depends on the existance and relative
magnitude of private loans and government bonds:

a) In the absence of government bonds, the elimination
of interest charges will reduce the aggregate demand for
equities and adversely affect the rate of investment.

b) If government bonds already exist in the economy,
their liquidation (which is assumed to be financed by an
increase in the money supply) will have an opposite effect
on investment. In this case, if the volume of government
bonds is significantly larger than private loans, interest-
rate elimination will lead to an increase in demand for
equity and investment. Otherwise, the net demand for equity

declines and leads to a drop in the rate of investment.

103

Section 2
Wen):-

In this section, we concentrate on developing a macro
model for an interest-free economy in order to study the
conduct of fiscal and monetary policy in such an economy.
With the elimination of the bond market, the remaining
financial assets in the Islamic economy are money and
equity. Thus, any monetary policy must be conducted within
these asset markets. The tools of monetary policy which
depend exclusively on debt instruments such as open-market
operations on government bonds and various interest-rate
controls (such as regulation Q and the discount rate) will
no longer be available. Instead, there will be two major
tools of monetary control. These are open-market operations
on equity markets and control over the reserve requirement
ratio of the demand deposits. The monetary authorities
could intervene in the stock market in the same manner that
the central banks intervene in the bond market in a regular
economy. In priori we expect the open-market sale and
purchase of stocks to be contractionary and expansionary,
respectively. These will be further investigated in the
analytical model that will follow.

The elimination of government bonds implies that the
government can only borrow from the central bank. In
response, the central bank has two options, it can monetize

the deficit by increasing the money supply or it can keep

104

the money supply unchanged and finance the deficit by sale
of equity. The second option is limited to the maximum-
equity ownership of the central bank. If the government
debt continues to grow, eventually the central bank will
have to monetize it. (We have analyzed the debt financed
fiscal policy in appendix A to this chapter.) To study the
impact of these fiscal and monetary policies, we will use
the same model that was developed in section one after

making the necessary modifications.

WW2.

We consider a one-sector economy were the same output
is used for consumption and investment. There are three
sources of demand for the real output of the economy:
private consumption, private investment and government
expenditure. The equilibrium in the real sector is
demonstrated by:

+ - - + + -
C(Y,q,P,W)+I(V,P)+G = Y 5.1
G = The government expenditurea.

There are three assets in the financial sector: High-
powered money, demand deposits, and equity. The banks use
demand deposits to purchase equity after satisfying the
reserve requirements. The equilibrium conditions for the
asset markets are:

+ — +
(1-K).D/P + h1(q,Y,W) + Vg/P = V/P 5.2

105

K.D/P + h2(q.Y,W) = M/P 5.3
h3(q,Y,W) : D/P 5.4
D = The supply of demand deposits.
ha 2 The demand for demand deposits.
K = The reserve requirement ratio on demand deposits.

Vg = The value of equity held by the central bank.

Since the demand deposits do not receive any interest,
banks accept all the demand deposits that they can get and,
thus, equilibrium is given by equation 5.4. Without loss of
any generality we can combine the demands for high-powered
money and demand deposits into a general demand function for
money when analyzing monetary and fiscal policy.4 The
financial sector then will consist of two assets: money and

equity. The complete model of the economy becomes:

+ - — + + -

C(Y,q,P,W)+I(V,P)+ G ; Y 6.1
+ - +

h1(q,Y,W) + Vg/P = V/P 6.2
- + +

h2(q,Y,W) = M/P 6.3

Before starting the comparative static analysis, we
will incorporate the following additions and modifications.

In section one, we already showed that:
+ - +
q: q(Y,V,P) and W=V/P + M/P

Furthermore, we also know that a change in government
equity holding through an open-market operation will change

the money supply. A change in government debt will also

106

change the money supply if the central bank chooses to
monetize it. Therefore, we have:

+ +
M/P= M(Vg,G)/P

Real wealth then will also be a function of V: and G.
The change in Vg, however, does not change the real wealth
of the private sector because we will always have: dW = -
dVg/P + dM/P. Consequently, we have:

+ +:—
W(V,G,P)

i:
ll

After adding these changes to the equilibrium
conditions 6.1-6.3, we will get:

—?++ +- .
C(P,Y,G,V) + I(V,P) + G = Y Commodities 7.1

+?+?
Vg/P + f1(P,Y,G,V) = V/P Equities 7.2
- 7 + + “t +

f2(P,Y,G,V) = M(G,Vg)/P Money 7.3

The asset market equilibrium conditions are connected
together by the wealth constraint and we can ignore one of
the markets in our analysis. To derive the fiscal and
monetary multipliers for the Islamic economy, we totally
differentiate 7.1 and 7.2 with respect to V, Y, G and Vg.
Writing the results in the matrix form we have.

c4 + I1 02-1 dV 03+1 dV¢
[ f14-1/P 112 ]. [dY ] -- li/P 111] [as i8
8.1 could be written as: dV dVg
At[ J =-Bx [ ] 8 2

dY ° dG

107

From 7.1 and 7.2, we can easily see that A11*=04+I1>O

and A12 = C2-1<0. A21 2 f14 - 1/P From the wealth
constraint, we know that f14+f24=1/P. We also know that
f24>0. Combining these two facts, we have f14-1/P=- f24 <0.
So A21<0. A22 is indeterminate.

B* has the following signs:

The determinant of A* is dependent on the sign of A22=f12.

 

 

 

 

 

 

 

 

 

 

 

 

 

‘+ -‘ ? if f12>0
A* = - ? det(A*)=D* = 9
- if f12<0
f12 -A12 ? +
A""1 =1/D*. = 1/D*.
-A21 A11 + +
Solving for dV and dY, we have:
dV dVg ? + 0 + dVg
‘ : - A*-1 , B*'1 : -1/D*. , :
dY dG + + + + dG
+/-D* (?+(+))/-D* st
+/-D* +/-D* dG

 

 

 

 

The multipliers have the following signs:5
dV/dG=?/D* dV/dV¢:-/D*
dY/dG=-/D* dY/dV¢=-/D*

The results depend on the sign of the determinant. We
apply the correspondence theorem to find the sign of D*
which is required for stability. We assume that the time
rates of change in V and Y are increasing functions of
excess demands for equity and commodity.

dV/dt=n(Va-V) n’>0 & n(0)=0
dY/dt=m(C+I+G-Y) m’>0 & m(0)=0

108

Applying a Taylor expansion to these differential

equations around the equilibrium values we get:

 

[dV/dt] [m’.(04+l1) m’.(Cz-1)]. {V- V0]:Q Q{V—Vo
dY/dt n’.(f14-1/P) n’.f12 Y- Yo Y-Yo
The characteristic equation is lQ-z.I|=0. For

stability, the Eigenvalues (the 203) must have negative real

parts: The determinant equation is:

22-(m’.(04+I1)+n’.f12).z + m’.(04+li).n’.(f12)-

n’.(f14-1/P).m’(Cz-1)=0
We must have: m’.(04+11)+n’.f12 <0.
m’.(C4+I1).n’.(f14-1/P) - m’.(Cz-1).n’(f14-1/P) )0

The first inequality implies that f1: <0. Furthermore,
f12<0 is a sufficient condition for |D*l <0. Therefore, we,
see that, for the system to be stable, an increase in income
must lead to a net reduction in demand for equity.
Originally, an increase in income had two offseting effects
on demand for equity. On the one hand, it raised the return
on equity leading to an increase in demand for equity, and
on the other hand, it increased the transaction demand for
money and, since equity is the only substitute asset for

money, the public increased their money holdings at the

109

expense of equity. We require the second effect to be
stronger in magnitude, even if the dividend effect of a
change in income is stronger than the substitution effects,
such that f12 is positive, we will still get the above
results as long as f12 is sufficiently small.7

For the condition that was stated, the open-market
operation multipliers have the expected signs. dV/dVg >0 and
dV/dG<0. The government purchase of equity is expansionary.
It increases the demand for equity leading to a rise in
investment and output.

The fiscal policy multipliers are dY/dG >0 and dV/dG
(>0. A money-financed government deficit increases the real
output but the net impact on investment is not clear. In
algebraic terms, we have: dV/dG = -1/D* .[f12.(03+1) + (1-
02).f13].

By further manipulation of this formula, we will be
able to identify the direct and indirect effects of G- on V.
The bracket could be written as:

' (1-02).[f13 + f12.(Ca+1)/(1-Cz)]

f13 is the direct impact of, increased G on equity
demand via the wealth effect. The indirect effect is given
by the second term inside the bracket. The increased
government spending increases the aggregate demand and Y
will increase to restore equilibrium. The net effect of
these actions is shown by fraction (Ca+1)/(1-02). The
increased income affects the demand for equity f12 but,

unfortunately, the direction of change is not clear.

110

Therefore, the direct and indirect effects could reinforce
or offset each other.

The impact of a monetized deficit on output is
expansionary because the feedback from the equity market
into the real sector reinforces the direct effect.

dY/dG=-1/D*.[(1/P-f14).(03+1) + (C4+I1).f13]
Factoring out (1/P-f151 we get:

dY/dGz-l/D*.(1/P-f14).[03+1+ f13.(C4+I1)/(1/P-f14)]

C3+1 is the direct impact of G on Y and is clearly
positive. The feedback from the equity market is shown by
the second term in the bracket. A rise in G has a wealth
effect on the equity demand, causing an excess demand for
equity. To restore equilibrium, V must rise as shown by
(1/P-f14). The increase in V will further increase the
aggregate demand. Both direct and indirect effects are

positive.

111

Section Three
WWW.

Now that we have developed the tools of monetary and
fiscal policy for an equity-based economy, the next question
is how do these differ from similar policies in a regular
economy in the size and direction of their effects. To
demonstrate a regular economy, we must add two additional
markets to our model of an interest-free economy. These are
the markets for private and government bonds. The policies
that we are concerned with are open-market operations on
government bonds and fiscal policy.

Since none of these require any direct interaction with
the private bond market, we choose to ignore this market as
we did in the model of section 2. Therefore, in the macro
model of the regular economy, there are three assets markets
for government bonds, equity and money. In this model,
government does not hold any equity because the equity
market is not used for monetary intervention. Instead, we
have introduced the conventional method of monetary
intervention that is practiced in the Western economies. The

equilibrium conditions for the regular economy are:

+ - - - + + -
C(Y,q,b,P,W)+I(V,P)+G = Y 10.1 Commodity
+ — - +
f1(q,b,Y,W) : V/P 10.2 Equity
- - + +
f2(q,b,Y,W) = M/P 10.3 Money

f4(q,b,Y,W) = S/(b.P) 10.4 Bonds

112

b = The rate of return on government bonds. (Endogenously

. determined)
S = The nominal supply of government bonds.
f4 = Real demand for government bonds.
The wealth constraint for this model is

W=V/P+M/P+S/(b.P). Changes in government deficit and open-
market Operations by the central bank will change the money
supply and we have: .

M/P=M(S,G)/P

We also have the following function that was explained
in section 2.

+ -
q=q(Y.V.P)

An exchange of bonds for money does not change real
wealth. An open-market operation changes the supplies of
bonds and money by the same magnitude in opposite
directions. When replacing the wealth parameter in model
10.1-10.4, we demonstrated this neutrality by writing:

W=W(G,V,b)

G appears in the wealth function because we have
assumed that the government deficit is monetized.8 Thus, as
G changes, the money supply changes and causes the real

wealth to change.

Replacing for q and W in equations 10.1-10.4, we have:

+—

+I(V,P)+G Y 11.1

t?

3.6.

2.1.3

21+-

"<1-o-

§:1e.
ll

V/P 11.2

113

f2( )

)

?
1Y1 M(G.S)/P 11.3
Y

671-1-04-

4.

1V:
+
V

Cr-OO‘ I

P
f4(P

S/(b.P) 11.4

3 I ’

Since by the virtue of the wealth constraint one of the
equilibrium conditions for the asset markets is redundant,
we choose to ignore the bond market. To analyze the impact
of fiscal policy and open-market operations, we totally

differentiate equations 11.1-11.3 with respect to b,Y,V,S,G.

 

 

'C4+Ii 02-1 05 'dV 0 03+1
l
‘f24 £22 £25 . dY =- -M2/P fza -M1/P .
l
tf14-1/P £12 £15 _db 0 £1
12.1

In matrix form, 12.1 could be written as: A. 3[dY =-B.{

db

 

 

We must determine the signs of the elements of‘x and B
in order to derive the signs of the multipliers. Based on
the derivative signs in system 11.1-11.4, the signs of the

following elements are obvious:

A11=C4+I1 >0 , K12 = 02-1 <0 , X1 = Cs<0
A21 = £24 >0 , A22 = ? , A23 = f25<0
A71 = f14- 1/P(o, £172 2 ? , A. = f15<0

Only two elements of A are a priori undetermined:
Xzz=f22 , Z23=f12.f22 is the derivative of demand for money
with respect to income. The only reason that fzz might be
negative is that an increase in Y will increase the dividend
rate and encourage people to increase the ratio of equity in

their portfolio. We call this the dividend effect. This

114

tendency is in conflict with the transaction demand for
money which rises with income. However, in the presence of
bonds, equity will be a weak substitute for money. Thus, we
assume that the transaction demand for money dominates the
dividend effect and an increase in income raises the demand
for money. A22 = fzz >0.

f12 is the derivative of equity demand with respect to
income.An increase in income will have two opposite impacts
on equity demand, the dividend effect increases the equity
demand while the substitution effect reduces it. In the
equity-based model, we argued that, since equity was the
only substitute for money, the substitution effect was
fairly strong. This leads to the assumption that f12 <0.
In this model of the regular economy, we assume that bonds
are the primary substitutes for money. Therefore, it is
reasonable to assume that the net effect of a change in
income on equity demand is more likely to be positive than
negative. We carry out the analysis conditional on the sign
of £12

In matrix B, the signs of the elements are easily

0 -+
B: + -]
0 +

We have already shown that K has the following signs.

determined.

— + - -
A = [+ + -] F011 021 031
71-1 =1/f). 012 022 012 = 1/1') .0'

 

_01 a 023 033

115

av q dS’
dY =-A-1.B.
db as

D = det(A). O = The matrix of cofactors for matrix A. The
signs of A15 allow us to determine the signs of most of the
elements in 0 under the assumption of f12 >0.

O11 - + '
O’ = + - 023
+ 023 +

The indeterminate elements are:

011 =f12.f15 - f12.f25 13.A
023 =e[(04+I1).f12 - (02-1)(f14-1/P) 13.3
032 =-[(C4+11).f25-Cs.f24] 13.0

The solution to the system is:

 

 

 

av '011 - + ' 'o -' '+/B [(-)-011]/B
_ as _ _ as‘
dY =1/D. + - 032 . - + . l: +/D [(-)-032]/D . J
dG _ _ as
db _+ 023 + ,0 - ,-023/D [(~)+023]/D
The multipliers are:
dV/dS = +/B dV/dG = [(-)-011J/B
_ _ 14
dY/dS = +/D dY/dG = [(-)-01z]/b

The signs of these multipliers depend on the sign of
the determinant which in turn depends on f12. It could be
shown that f12wis a sufficient condition for D < 0. It is
also clear from basic monetary theory that dV/dS and dY/dS
must be negative. This requirement is satisfied when D<0.

Unfortunately, even when f1®0 is given the proper sign, the

116

government deficit multipliers are still indeterminate.

This indeterminacy is caused by two factors: first, the
reaction of equity demand to changes in income is not clear
and second, the presence of a bond market causes a negative
feedback from the financial sector to the real sector.
Consider an initial increase in G which leads to an increase
in income. The rise in Y will cause a drop in demand for
equity which could be partially offset by the wealth effect
£34. Nevertheless, the net effect could very well be
negative causing an excess supply in the bond market. To
restore equilibrium in the bond market, the bond rate must
rise. The rise in bond rate will have a negative impact on
consumption demand.

The initial increase in G will also increase the demand
for equity (increase in money supply will have a wealth
effect on equity demand); but at the same time, the higher
bond rate will have an opposite effect on the equity demand.
As a result, the net change in equity values is not clear.
This indeterminacy causes an indeterminate change in the
investment demand. Consequently, the net change in the
aggregate demand is not clear because the increase in
government spending could be offset by reductions in private
consumption and investment.

Based on the multiplier formulas in 14, we can present
sufficient conditions which, if met, will make the fiscal
policy expansionary. dY/dG would be positive if 031 > 0,
and from 13.c, 032 will be positive if (C4+Ii).f24-05.f24<0.

117

Finally, this last condition will be satisfied if the
aggregate demand for output is more sensitive to changes in
equity return compared to the bond rate9 and, at the same
time, the demand for money is more sensitive to the bond

rate compared to the equity return:

(C4+I1)>Cs & |f25|>lf24|

Both parts of this condition are expected to be true.
The second part, however, depends on the degree of
substitution between money and other assets.

dV/dG will be positive if 011=f22.f15 - f12.f25>0. A
sufficient condition for this inequality to be satisfied is
for the money demand to be less sensitive to income than to
bond rate and the equity demand to be less sensitive to the

bond rate than to income.

f25>f22 and lf12|>|f151

It is not clear if these conditions are satisfied in

the real world.

118

Section Four
0 ' ffect 0 he Re u a and E ‘t -
Wines.

To compare the impact of fiscal and monetary policies
in the regular- and equity-based economies, we have
develOped separate models for each economy. The basic
difference between these models is that the equity-based
economy does not have any bond market. Before going into
the comparison of these two regimes, we must point out that
the macro model of regular economy that is develOped here
differs from the standard textbook macro models. In these
textbook models, money and bonds are the only assets
considered. The implicit assumption is that bonds and
equity are perfect substitutes. They are combined into a
single bond market. The bond rate is the same as the rate
of return on equity.

In this type of two-asset models, there is more
confidence about the impact of fiscal policy. For example,
consider a pure increase in government expenditure which
initially will increase the output. At the same time, it
could cause an excess supply in the bond market leading to
an increase in the bond rate. the rise in bond rate will
feed back into the consumption and investment demand and put
a downward pressure on output. This decline can, at most,
offset the initial increase in output but it cannot cause a

net decline. (If the feedback effect is large enough to

119

cause a net decline in output, the model will be unstable.)
Therefore, a fiscal policy in this case will be expansionary
or at worst neutral.

In a three-asset model like the one that was developed
in this chapter, however, the presence of a third market for
equity could cause a net decline in output in response to a
fiscal policy. The main feature of the three-asset models,
which is partially responsible for this added uncertainty
about the impact of fiscal policy, is the fact that the net
effect of a change in income on demand for equity is not
clear.

We will now turn our attention to comparing the regular
and the equity-based economic systems. The comparative
static analysis of several policy instruments shows that,
while the policies in general have similar effects, there
are some differences in the performance of these two
regimes. As one would expect, these differences are
explained by the fact that one model includes a bond market
and the other one does not. The policies that we studied
are:

1) Open-market operations.

2) Monetized fiscal deficit.

3) Bond (Equity) financed fiscal policy.

In an appendix to this chapter, we have also analyzed
the impact of two other policies: 1) pure fiscal policy and

2) a pure increase in the money supply. Because of the

120

governments’ budget constraint, these policies can never be
implemented alone. They are only analyzed to aid us in
understanding the original three policies. The qualitative

effect of these policies is presented in Table 1.

A. Win):-

This policy consists of an autonomous increase in
government expenditures without any equivalent change in the
supply of bonds or money. Such an increase will increase the
commodity demand but it will not have a wealth effect on the
asset demands:

BESULI_1: A pure fiscal policy will be expansionary

under Islamic and regular regimes.

BESQLI_2: A pure fiscal policy will increase
(decrease) investment if the demand for
equity is positively (negatively) related to
variations in real income, dV/dY>0 and
(dV/dY<0), under both regimes.

The first result comes as no surprise. When the economy
operates at less than full employment, an autonomous
increase in expenditures will stimulate more production.
The explanation for the second result is that an increase in
income has two offsetting effects on the demand for equity.
On one hand, it leads to higher dividends which will
increase demand for equity and on the other hand, it causes
a shift from equity to money because of the increased

transaction demand for money. This second effect might seem

121

Pure

 

 

 

 

 

Pure Increase Bond Money Open
Fiscal In Money Financed Financed Market
Policy Supply Deficit Deficit. Operatign
Equity + + (>0 + +
Based
Economy <>0
Apriori
(>0 ----------- - ()0
+ if f12<0
<>0 <>0
Apriori Apriori
+ --------- (>0 -------- +
+ +
Regular conditional conditional
<>0 <>0
Economy Apriori Apriori
(>0 ----------- (>0 ---------- +
+ +
Conditional Conditional

 

 

 

 

 

 

TABLE 1

122

strange but it is a direct consequence of the fact that
income is not a component of wealth. Therefore, if a change
in income leads to a change in the asset demands, these
changes must offset each other. Since an increase in income
increases the demand for money, it must cause a decline in
all or some of the other asset demands. In the Islamic
economy, equity is the only substitute for money and any
increase in demand for money as a result of rising income is
offset by a decline in equity demand.

Therefore, at the same time that Y increases,
investments could increase or decrease; but investments will
never decline sufficiently enough to cause a net reduction
in aggregate demand. To see this, consider the following
possibilities:

a) If dV/dY<0, the increase in G will increase Y and
cause a drop in V which will reduce I and C, so we have had
a decline in C and I. The net effect on Y could be positive
or negative. A reduction in Y, however, will be
inconsistent. This is because, if Y declines, V will
increase . That will increase 0 and I, then we will have an
increase in Y which is contradictory;

b) If dV/dY>0, the increase in G will increase Y and
that in turn will increase 0 and I. Consequently, Y can

only increase.

123

B) Wank.

BESHLI_3: A pure increase in the money supply under
the Islamic regime will increase output.
Investment will also increase if equity
demand is positively related to income,
dV/dY>0.

BESULI_A: A priori, in a regular economy, the impact
of a pure increase in the money supply on
output and investment is indeterminate. (The
sufficiency conditions for an increase in
output and investment are given in results 6
and 7.)

RESQLI_5: The existance of the bond market in a
regular economy will reduce our confidence
about the impact of an increase in the
supply of money on the aggregate demand.

The explanation for result 3 is same as the one given
for results 1 and 2 with the single difference that this
time the process starts with an increase in the money supply
rather than G. The increase in the money supply will have a
wealth effect on consumption which will increase output. At
the same time, it will have a positive wealth effect on
equity demand, but this might be offset by the income effect
which could be negative.

The lower degree of confidence under the regular regime

compared to the Islamic regime (Results 3 & 4) is due to the

124

feedback from the bond market into the equity and commodity
markets. Consider an initial increase in the money supply
which_ will have a positive wealth effect on the demand for
all three assets. It will cause an excess supply in the
money market and an increase in the consumption demand. The
increased consumption will increase the transaction demand
for money at the expense of a demand for bonds. Therefore,
there are two conflicting forces on the bond market. On one
hand, the increase in money supply will have a positive
wealth effect and, on the other hand, the increased
transaction demand for money will reduce the demand for
bonds. If the net effect of these two forces is a reduction
in bond demand, the bond rate must increase to restore
equilibrium. The rise in the bond rate will then feed back
into the consumption demand and equity demand, offsetting
the initial increase that was brought about by the original
increase in the money supply.

This is only a possibility and the outcome also depends
on how sensitive the consumption and equity demands are to
changes in the bond rate. We can give sufficiency
conditions that will make the increase in the money supply
expansionary:

BESQLI_6;A: Under a regular regime, a pure monetary
policy will be expansionary if the
aggregate demand is more sensitive to
changes in return to equity compared to

the interest rate and, at the same time,

125

the demand for money is more sensitive to
changes in the interest rate compared to
the equity return.

RESQLI_6;B: A second sufficient condition for an
increase in output is the zero-interest
elasticity of consumption.

BESULI_1;A: Under a regular regime, a pure increase in
the money supply will increase investment
if the money demand is less sensitive to
changes in income than changes in the bond
rate and, at the same time, equity demand
is less sensitive to changes in the bond
rate compared to changes in income.

BESULI_Z;B: A second sufficient condition for an
increase in investment is for the
elasticity of the equity demand, with
respect to the bond rate, to be zero.

To explain these results, we refer to the money-supply

multipliers that were developed in Appendix B.

dV/dM=(-011-(-))/B 011=f22.f15 - f12.fzs
dY/dM=((-)-032)/D 032=-[(C4+Ii).f25-Cs.f24]

We have already shown that D <0.

These multipliers will be positive if 011 and 012».
Results 6 and 7 simply present sufficiency conditions for
Ch1>0 and 032>0, respectively. Note that these sufficiency

conditions are independent of the units of measurement. For

126

example, in 011 a change in the unit of measurement for
income will change f12 and fzz by the same proportion

without changing the sign of 011.

C) W91

BESQLI_§: In an equity-based economy, a money-financed
fiscal policy will clearly increase output.
The investment level will increase if equity
demand is positively related to income,
dV/dY>0.

BESQLI_9: The a priori impact of a money-financed
fiscal policy on output and investment in a
regular economy is not clear. The policy
will be expansionary if the conditions that
were listed in results 6 and 7 are met.

This policy is a combination of a pure fiscal policy

and a pure increase in the money supply. Accordingly, the
not impact is a mixture of these two policy effects. Even
though we are less confident about the effects of this
policy in a regular economy, a careful look at the
conditions that were stated in Result 6 reveals that they
are very likely to be met. Recent studies have shown that
consumption in the United States is not significantly
sensitive to the interest rate. Overall, under both
regimes, the response to this policy depends on how changes
in income affect the demand for equity. In case of the

regular regime, another factor is the sensitivity of

127

consumption and equity demands to changes in the interest
rate. If they are insensitive, the policy will be

expansionary.

D) W191.

BESQLI_19: A bond (equity) financed fiscal policy will
have an indeterminate effect on output in a
regular (an equity-based) economy.

BESQLI_11: An equity-financed fiscal policy will
reduce investment in an Islamic regime
while a bond-financed fiscal policy will
have an indeterminate effect on investments
in a regular economy.

The justification for these results is that the
original increase in G could be offset by a possible
reduction in investment and consumption demands. These
reductions are caused by an increase in the interest rate in
the regular economy and a reduction in equity values in the
equity-based economy. Under the equity-based regime, the
added deficit is financed by the sale of government-owned
equity. This sale will reduce the value of equities and
cause a drop in investment. The impact on investment under
a regular regime is not clear because the debt is financed
by the sale of bonds rather than equity. There will be two
opposing pressures on equity demand. The increased bond
rate will have a negative effect while the increase in

government expenditures could have a positive effect. Thus,

128

the net result is not clear.

E) Whigs;-

In an equity-based economy, the open-market operations
are conducted in the equity market instead of the bond
market (which no longer exists).

BESULI_12: The open-market operations are effective
under both regimes, and the policy
multipliers have the expected signs. In
both economies an open-market purchase will
increase both output and investment.

Overall, we see that the elimination of government
bonds does not dramatically alter the ability of the central
bank to conduct monetary and fiscal policy. Both monetary
and fiscal policy are effective. The surprising result is
that in no case did we observe the impact of a policy on the
equity-based economy to be more uncertain than the impact of
the same policy on the regular economy. To the contrary,
for some policies we have more confidence about the response

in the equity-based economy compared to the regular economy.

129

NOTES

In this section, we are not concerned with policy
analysis and as a result, the government sector is not
included.

The reason we ignore the capital gains is that, in this
short term model, expectations are exogenous. Sargent-
Henderson also use this assumption in their model.

Other variables have the same definitions that were
given in Section 1.

With this action, we exclude the banking sector
altogether. Consequently, we can no longer study the
impact of changes in the reserve-requirement ratio, K.
The policy impact of changes in K, however, are straight
forward. An increase in K is contractionary.

The exact formulas for these multipliers are:
dV/dV¢=(-1/D*).(1-Cz)/P

dV/dG =(-1/D*).[f12.(C3+1)+(1-C2).f13]

dY/dG =(-1/D*).[(1/P-f14).(C3+1)+(C4+I1).f13]
dY/dV¢=(-1/D*).[(C4+Ii).1/P]

By dividend and substitution effects, we are referring
to the components of the following derivative:

df1/dY=(df1/dq).(dq/dY) + dfi/dY

We can derive an upper bound for f12 which results in
D*<0.

Another type of fiscal policy involves a debt-financed
government deficit. In an equity-based economy, this
will be equivalent to financing the government deficit
by the sale of equity (that the central bank owns). We
will compare the effects of debt-financed and equity-
financed fiscal policies in a separate appendix.

There is a significant body of evidence that consumpton
in the United States is not sensitive to the rate of
return on financial assets, especially bonds. For a
survey of this evidence, see Chapters 3 and 6 of Evans,
M.K., Macro Economic Activity New York, Harper & Row,
1969.

CEMHER‘Q

ISLAMIC BANKING IN PRACTICE

Currently in the Muslim world, there are two distinct
and parallel approaches to Islamic Banking. Two Muslim
countries, Iran and Pakistan, have eliminated their

conventional banking systems in favor of complete Islamic
banking. In contrast, many other Muslim nations have
introduced individual Islamic banks while allowing the
conventional banking system to continue. We will review the

progress of these competing approaches separately.

4-A. INDEPENDENT ISLAMIC BANKS

The first experiments on Islamic banking began in the
mid-1950’s. Before that time, the post-colonial leaderships
in ‘the Middle East were so preoccupied with secular
modernization that Islamic concerns about the interest
charge were brushed aside. Most 'of_ these nations had
already established Western-style banking institutions. In
addition, foreign banks were also active in more developed
countries of the region. In Egypt, for example, the

British-owned banks began operation as early as 1856. The

130

131

first Egyptian-owned bank (Bank Misr) was established in
1919 by a Cairo financier named Mohammed Talat Harb.1
Similarly, at the same time, financial development was
underway in other nations as well.

The first attempt to create an Islamic bank was made in
Pakistan. Since Pakistan was originally established as an
Islamic nation, the religious leaders called for abolition
of interest in the early years of independence.2 In that
time, the idea was rejected by the leadership because of
economic considerations. After a few years, however, a
small experimental Islamic bank was established in rural
Pakistan. The initial capital was provided by a group of
small local land owners who deposited funds in the
institution primarily for religious reasons. No interest or
profit was paid to these depositors. The bank provided
interest-free loans to the poorer land owners for a small
administrative charge. Unfortunately, this venture did not
survive for long. After a few years, the original
enthusiasm diminished and the bank was closed down. A major
Idifficulty facing the bank from the start was the shortage
of funds. Without paying any interest or profit, it was
difficult for the bank to attract depositors. At the same
time, the low administrative earnings prevented the bank
from paying competitive wages and keeping the staff

motivated.

132

The second initiative towards Islamic banking was taken
in Egypt in 1963. In this case, a small savings bank was
founded by a man named Ahmed Al Nagar in a rural town near
Cairo. Originally, the bank had about 1,000 depositors but

very soon it gained the trust of the conservative local

community and the number of depositors grew to more than
60,000 in three years. While conventional banks were
successful in larger towns, they were received with
suspicion in rural communities. The success of Mitr Ghams
Savings Bank was based on its appeal to the devout Muslim
population of these communities. Persons who were hoarding
funds or accumulating real assets (because they found the
conventional banks un—Islamic) willingly deposited funds in
the Mitr Ghams Savings Bank. The operations of this bank
were similar to the Islamic Savings Bank of Pakistan. The
bank did not charge any interest on loans and did not pay
any interest on deposits either. While a portion of loans
were borrowed for investment purposes, the bank did not
share in the borrowers’ profits. Instead, they only charged
a small administrative fee. The bank operated for almost
three years.3

These two early attempts in Islamic banking were not
investment or profit oriented. Their main objective was to
provide interest-free loans to the low income and poor
individuals. The lack of a clear alternative to the

interest charge was the primary reason for their inability

133

to survive beyond a few years. Their shortcomings were one
of the reasons that Islamic scholars proposed profit and
loss sharing as the basis of Islamic banking.

During the 1970’s, development of Islamic banking took
a different direction. Unlike the two savings banks that
were described above, the new Islamic banks were oriented
toward profitable investments. In 1972, Ahmed Al Nagar, the
founder of Mitr Ghams Savings Bank, established a new
Islamic bank called Nasser Social Bank. This bank continued
to offer many of the services that were offered by the Mitr
Ghams Savings Bank. In addition, the Nasser Social Bank
allocated a portion of its resources to direct equity
investment. While no profit was shared with the depositors,
they enjoyed an implicit benefit by having the privilege to
borrow funds at no interest charge. The initial capital of
nearly 32m was provided by the Egyptian government which has
remained the sole owner of the bank. The state support has
continued and the paid-up capital of the bank is much larger
today.‘

The progress of the Nasser Social Bank was a major
source of encouragement for Islamic banking in other
countries. Through frequent contacts with other Arab
leaders and financiers, Ahmad Al Nagars encouraged them to
establish commercial Islamic banks. Be motivated a group of
Dubai merchants to establish the Dubai Islamic Bank in

1975.6 He also convinced Prince Mohamad Bin Faisal (son of

134

the late King Faisal of Saudi Arabia) to help establish
other Islamic banks in Sudan and Egypt.

In 1977, the Faisal Islamic Bank of Egypt and the
Faisal Islamic Bank of Sudan were established. The Saudi
Arabian private citizens provided 40% of the initial capital

for the Faisal Islamic Bank of Sudan and 49% of the initial
capital for the Faisal Islamic Bank of Egypt.7 The
operations of these banks were much closer to the model of
Islamic banking that was described in Chapter 1. Unlike the
Mitr Ghams and Nasser Social Banks, they distributed a
portion of their profits among depositors and shifted their
lending and investment activities from interest-free
assistance loans to profitable equity investment and PLS
loans. They offered two basic types of accounts: savings
accounts that are fully insured but earn no profits and
investment accounts that share in the profits and losses of
the bank. The investment operations of these banks are very
similar to items that were described in Chapter 1. These
three banks have been able to survive and compete with
regular banks for depositors. The Dubai Islamic Bank has
become the largest national Islamic bank with $13 million in
paid up capital and nearly $100 million in deposits in
1980.8

Ever since 1975, new Islamic banks similar to the Dubai
Islamic Bank have been established in almost every Islamic

country and their presence has been accepted by the

135

financial communities of these nations. As expected,
Islamic banks have appealed to the devout Muslims more than
other groups and their operations have reduced hoarding in
money and jewelry. The operation of independent Islamic
banks along with regular commercial banks has increased the
efficiency of financial systems by adding new and diverse
assets without eliminating any of the already existing
assets. The negative effects of Islamic banking that were
demonstrated in our analysis will only arise when the entire
financial system is modified and all interest-paying assets

are eliminated.

Development ofglgterngtiongl Islamic Banks.

During the 1970’s and 80’s, Saudi Arabia provided moral
and financial support to Islamic banks more than any other
nation. This support went beyond establishing and assisting
the independent Islamic banks. The more important
contribution of Saudi Arabia was the establishment of two
international Islamic banks: The Islamic Development Bank
and Dar al-Mall Al-Islami. The Islamic Development Bank
(IDB) was established in 1975 by the approval of the 38
participating nations of the Islamic conference. The main
objective of this bank was to provide financial capital for
industrial and agricultural projects in Islamic nations. A
second goal was to promote international trade among Muslim

states. The activities of the bank were limited to

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mechanisms that are allowed in Islam, primarily equity
participation and interest-free loans.

The original capital for IDB was provided by several
oil-exporting Islamic nations; Saudi Arabia contributed 25%.

Other major contributers were Libya, United Arab Emirates

and Kuwait. In 1981, IDB had more than $1.5 billion in paid-
in capital. During its first five years of operation, IDB
financed many development and trade projects throughout the
Muslim world. Several nations, including Turkey, Pakistan
and Sudan, received interest-free loans to finance the
import of petroleum products and other commodities (from
other Muslim nations).9

Other activities of the IDB included equity
participation and leasing. To encourage Islamic banking,
IDB invested in national Islamic banks. It also invested in
equity projects in many Islamic nations. Leasing out
industrial machinery was another scheme used by IDB. The
bank leased out refining equipment to Pakistan and machinery
to the Turkish Electrical Company. Overall, the Islamic
Development Bank played a significant role in popularizing
Islamic Banking and providing assistance to low income
Islamic nations.1°

Dar Al-Mall Al-Islami (Islamic House of Funds) is the
second international Islamic bank that was established by
Saudi Initiative in 1981 with a paid-in capital of $300

million. The stated objective of the bank was to support

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development projects in Non-Arab Islamic states such as
Malaysia, Sri Lanka, Turkey, Pakistan and others. Most of
the depositors and shareholders were attracted from the oil-
rich gulf nations. (Nearly 80% of the liabilities of DMI,
Dar al-Mall al-Islami are owned by the Arab nations of the
Persian Gulf area.) DMI has tried to reduce its dependency
on Persian Gulf capital by opening branches in other Muslim
states.

So far, the operations of DMI have been profitable.
The performance of the bank during the 1984-85 financial
year, in particular, was impressive. To achieve further

diversification, DMI targeted the Muslim nations of Africa

and Southeast Asia for future investment. Besides the
Islamic Development Bank and Dar al-Mall al-Islami, there
were several smaller international banks as well. Some of
these banks were headquartered in European capitals,
particularly London and Geneva. They were primarily

involved in equity investment and foreign trade financing
among Arab and European nations.

Overall, there are more than 30 Islamic banks currently
operating throughout the Muslim world. Many of them have
been able to offer attractive profits to their depositors
and compete against conventional banks for people’s savings.
Their operations have pleased a large number of devout
Muslims who were reluctant to use the conventional banks.

However, at the same time, some conservative Muslims have

138

raised concern about the long-term effect of these banks.
According to these critics, the operation of individual
Islamic banks inside the conventional financial system could
delay the total transformation of the financial system from
regular to Islamic. It was for similar fears that plans for

the creation of a pilot Islamic bank in Pakistan (in the

late 1970’s) were rejected in favor of a complete
Islamization of the entire banking system.11 In the
following section, we will review the progress of the

Islamic banking systems (as opposed to independent Islamic

banks).

4-B. ISLAMIC BANKING SYSTEMS

So far only two states, Iran and Pakistan, have
established complete Islamic banking systems. The idea,
however, is popular in the religious circles of many Islamic
states. In Pakistan, the process began in 1981. In the
first phase, special corners for Islamic financial
transactions were established in every bank. This was
followed by the removal of interest-paying assets. The
reforms were completed in 1985. The modification of Iran’s
banking system began in 1984 and it is expected to be
finished within 5 years. Since the Islamic banking systems
of Iran and Pakistan are very similar, it would be redundant
to review both of them here. Several reviews of the

Pakistani Experience have already been published. In

139

contrast, the Islamic banking system of Iran is mostly
unknown; therefore, it would be appropriate to briefly
review the progress and structure of Iran’s Islamic banking

system.

The Islamic Banking System Of Iran.
In the few years before the 1979 revolution, the
Iranian economy was experiencing very rapid growth. The

main reason for this expansion was the sudden increase in

the oil revenues. The financial system was also growing
very rapidly in the same period. The banking institutions
of this era, however, were entirely secular. Despite

religious opposition, banks were issuing loans and accepting
deposits on the basis of interest.

After the 1979 Islamic revolution, the new government
decided to abolish any economic and social institutions that
were unacceptable to Islam. In the economic sector, the
banking system became the first target of this reform. At
the same time, under popular spressure, the government
nationalized the entire banking industry. Having direct
control made it easier for the government to implement any
future reforms. (In Pakistan also the banks are
nationalized.)

With regard to the banking system, the goal was to
abolish any institutions that involved interest charge

and introduce new arrangements that were acceptable to

140

Islam. Since there was no prior experience in Islamic
banking, it was clear that the design and implementation of
the new system would take some time. To avoid any kind of

financial collapse or loss of public confidence in the

banking system, it was decided to continue with the old

banking institutions until the new program was ready for
implementation.

Within the central bank, a special task force was
established to design the new code of banking laws. Because
of the social and political instability that existed in
those early years of the revolution. the work of the task
force was delayed. The first set of Islamic banking laws
were submitted to the Parliament by this task force in 1982.
Gradually, the complete codes of Islamic banking were passed
within two years. The Islamization process began in the
summer of 1984. The interest-paying time and savings
deposits were replaced with investment accounts. On the

investment and lending side, all the new transactions were

based on nonusurious arrangements. Banks continued to
receive interest on long-term loans that were issued
earlier. It is expected that all of these contracts will

and within five years. We will describe the structure of

the Iranian banking system below.

141

Depository Accounts.

Banks offer two types of depository accounts:

1) The interest-free current accounts and interest-

free savings accounts.

2) Short-term and long-term investment accounts.

The interest-free deposit accounts are technically the
same as demand deposit accounts. They are fully insured and
are redeemable upon request. Even though these deposits are
not entitled to any regular interest or profitsharing, the
banks can occasionally offer prizes to the account holders.
The prizes could be cash or durable goods such as radios or
irons. The account holders will also be given priority in
using other banking services such as receiving loans.

The investment accounts are similar to the PLS accounts
that were described in Chapter 1. However, no profitsharing
is specified. Instead, the bank announces a dividend rate
on these accounts. The rate is variable and is supposed to
fluctuate with the overall profits of the banking system in
each period. The same rate of dividends is paid by all
banks. This rate is determined by a special commission
within the central bank. The minimum time for short-term
accounts is three months and for long-term accounts is one
year. In 1984, which was the first year of operation for
Islamic Banks, the short- and long-term accounts paid 7.5%

and 93 dividend rates, respectively.12

142

Even though the investment accounts are fully insured,
the central bank authorities have argued that the return on
these accounts is not interest because no fixed rate of
dividend is declared in advance. The dividend for each six-
month period is declared at the end of that period. The
exact method of dividend measurement is not clear. It is
unlikely that dividends are linked to the banking profits in
the same manner that was described in Chapter 1. It is
interesting to note that the dividend rates offered on these
accounts are very close to the interest rates that were paid
on short- and long-term time deposits by the commercial
banks of Iran in years prior to the revolution. (In 1975,
the interest rates on savings and time deposits were 7% and
9%, respectively.)

On religious grounds, these accounts might be
questionable because the principal is fully insured. It was
explained earlier that these risks face the possibility of
losses. Since the holders of investment accounts do not
face any risk of loss, their dividend is equivalent to a
variable interest. Indeed, if the dividend rate stays above
a certain level for a long period, the public would perceive
it as a safe interest with a minimal rate.

Such accounts may not be Islamic by this standard, but
they would be more efficient than a purely Islamic account
which is not fully insured. Since the principal is insured,

these accounts will be considered riskless. By offering

143

these accounts, banks can attract the savings of risk—averse
individuals. One could expect the public to treat these
accounts in the same way as the savings and time deposits

that existed before.

The Lending ang Investment Activities.

To make the lending operations of Islamic banks
nonusurious, it was necessary to replace the interest-paying
loans with other arrangements. Some of these new mechanisms
are derived from the business customs that were common in
the early years of Islam. Others were developed over the
centuries to circumvent the prohibition of interest. The
lending and investment mechanisms of the Iranian Islamic
banking system are:

l) Interest-Free Loans. These loans are provided to
the needy and poor at no interest for necessary expenses
such as the treatment of illness or repair of damaged
property. These loans are also granted to small businessmen
in small towns and villages. The primary criteria for
interest-free loans is proof of need. There is, however, an
upper limit on the size of these loans. The maximum amount
of interest-free loans for business and industry is
5,000,000 Iranian Rials. The upper limit for personal need
is 500,000 Rials. Another limitation is that, collectively,
the interest-free loans should not constitute more than 10%

of the assets of the banking industry. This sum should also

144

be less than or equal to the interest-free deposit funds
that banks receive from the public. This implies that all
the funds collected by banks from investment accounts will
be invested in profitable projects. No part of these funds
is used for interest-free loans.

2) TheAAgguity Partnership. Banks are allowed to
provide short- and long-term credit to businesses on an
equity basis. There are three different types of equity
arrangements available to the banks:

a) Direct partnership between bank and businesses.
b) Equity stock ownership in corporations.
c) Direct investment by banks without any partners.

The partnership between the bank and businesses is
specially designed for short-term projects. It could only
be used in cases where the project is expected to be
completed within one year. Only in special cases could the
time limit be extended to three years. Under a partnership,
the bank can at most provide 80% of the capital that is
needed for a project. The equity stock partnership is
designed for longer term projects of existing corporations.
Banks can provide capital to these corporations by
purchasing up to 49% of their total outstanding stocks. The
49% upper limit is designed to curtail any bank control of
corporations. The banks can sell the stocks to the public
at a future date. In this function; Islamic banks are

operating similarly to the investment banks in the West.

145

They purchase the newly issued stocks of corporations and
then gradually sell them to the public.

3) Advance Purchase. In this arrangement, the bank
purchases the product of a productive unit before it is
ready. The unit then can use the funds to pay for the
required working capital. The bank can resell the product
after receiving it.

4) Price Mark-up Resale. If an industrial unit needs
funds for the purchase of machinery and equipment, the price
mark-up mechanism is used. In this scheme, the bank
purchases a particular tool that was requested by the unit
and resells it to that unit at a higher price. In exchange
for the profit, the bank allows the unit to pay the cost on
an installment basis. A similar mechanism could be applied
to the sale of existing houses where the bank buys a house
on behalf of a costumer and resells it to him for a higher
price on an installment basis.

5) gent To Own. Banks can buy productive equipment and
structures and rent them to the public on the condition that
the renter will assume ownership of the item after paying
rent for a certain period.

6) Crop Sharing. In the area of agriculture, besides
the above-mentioned financing schemes, banks can own land
and enter into crop-sharing agreements with peasants. In

addition to land, banks can provide other items (such as

146

fertilizers and transportation) which are needed for
farming.

Overall, the profit-oriented lending operations of
Islamic banks fall under two categories.

a) The equity arrangements (Items 2 and 6 in above

list)

b) Price mark-up schemes (Items 3,4 and 5)

The equity-based arrangements are truly nonusurious.
In these schemes, the bank does assume some degree of risk
as required by religion. In practice, both profits and
losses are possible. However, to avoid bad investments,
banks can only invest in projects that are expected to
generate profits above a minimum rate that is determined by
the central bank. While encouraging the banks to be
efficient, this law ignores the possibility that more
profitable projects might also carry higher risks. If the
minimum profitability rate is too high, the bank might be
forced to acquire a highly risky portfolio. A better
approach would be to put limits on an expected risk as well
as the expected profit rate of acceptable projects.

While no explicit interest charge is involved in the
price mark-up schemes, they are implicitly usurious. The
mark-up on the resale price of a tool, when it is resold by
the bank to a buyer, can only be explained as the financing
cost which is equivalent to the interest charge. The

difference between the purchase and resale price will

147

determine the implicit rate of interest. Therefore, from a
religious point of view, these schemes will be questionable.

On one hand, trade is permited in Islam and the exchange

price is a matter of agreement among parties involved. This
view makes the price mark-up mechanism acceptable. But, on
the other hand, if the interest charge is forbidden, one

might expect the price of a commodity to be the same
regardless of the method of payment. The price mark—up
mechanism contradicts this principle by charging a higher
price for deferred payment. Thus, it could be seen as a
usurious act. This conflict, however, is purely religious.
From an economic efficiency point of view, the mark-up price
is justified because the financial capital is productive and
there is an opportunity cost to receiving the payment in the
future. The availability of price mark-up options will make
the Iranian Islamic banks more productive by offering risk-
free and low-risk investment channels. Banks can use these
options to offset their high-risk equity investments and
create diversified portfolios. Indeed, some banks might
even prefer these low-risk options to equity investments.15
The experience of Islamic banks in Pakistan reveals that
most banks prefer price mark-up schemes to equity-based
investments. This has led some officials to question the

Islamic nature of that country’s banking system.16

1)

2)

3)

4)

5)

6)

7)

8)

9)

148

NOTES
(Chapter 4)

This bank was owned by a small group of wealthy
merchants and land owners in Cairo. It attracted
a large group of depositors from middle and low
income classes as well. (See Rodney Wilson page
29.)

There was a debate in Pakistan in that time on
whether the banning of interest charge should be
included in state constitution or not. The
proposal was not included. (Maxime Rudinson page
154.)

One major reason for its failure was the low
salaries that bank employees recieved. The rural
location of the bank was also a disincentive to
the staff members who prefered to live in larger
cities.

By 1980 the paid-in capital was $14.3 million. The
total assets for the same year were $330.0 million.
Source: Wohlers-Scharf, table 12, page 164.

The founder and first general manager of Nasser
Social Bank.

Dubai is a small Arab nation in the Persian Gulf
area.

See Rodney Wilson page 85.

The multinational Islamic banks such as Islamic
Development Bank and Dar Al-Mall Al-Islami have
much larger financial resources. Islamic
Development Bank, for example, has more than $1.5
billion in Paid-in capital. (Wohler5*Scharf, Table
12, page 164.)

Islamic Development Bank, Fourth Anual Report,
Jaddah 1979, Page 34.

10)

11)

12)

13)

14)

15)

16)

149

In recent years IDB has paid special attention
to the African developing nations. Actvities
include a leasing conract with a Tunisian-Saudi
company for Small projects in Tunisia. The country
of Benin has also recieved $5 million in loan and

technical assistance from IDB (Source: Arabia, June
1985 page 76.)

See ”Report of the Council of Islamic Ideology
(Pakistan) in Money and Banking in Islam by Ziauddin
Ahmed, Munawar Iqbal, and F. Fahim Khan.

Reported in Keyhan Havai, "Negahi-Be Vaz-iatt-e
Faaliatha-E Banki" Page 14, July 12, 1985.
Ibid.

Source: Banking Structure and Sources of Finance
in the Middle East, page 15.

During the first year of Islamic Banking in Iran
(1984) almost 44% of the resources of Islamic Banks
were invested in Hire Purchase and Price Mrak-Up

contracts while 37% were allocated to various equity
arrangements. (Keyhan Havai July 12, 1985, page 14.)

Arabia, September 1984 pages 48-49.

CONCLUSION

In this concluding section, the analytical findings of
the previous chapters will be put into perspective, then the
implications of these findings for the field of Islamic
Economics in practice will be analyzed. Finally, several
suggestions for further research on Islamic banking will be
offered.

The objectives of this research project were two fold.
The first goal was to analytically study the consequences of
switching from a conventional to an Islamic banking system.
This investigation was conducted within two distinct models:
one macro-economic model and one micro-economic model. The
basic results of these analyses were that at the micro-level
elimination of the interest charge will adversely affect the
welfare and resource allocation of households. In
particular, the more risk-averse persons are forced to
assume more risk while the less risk-averse persons are not
able to take as much risk as before.

The reason behind these adverse developments is that
clearly money and risky assets are weak substitutes for the

interest-paying riskless asset. So when the interest rate

150

151

is reduced to zero, the risk-averse investor will transfer a
fraction of his funds from the riskless to the risky asset.
Thus, his total investment in risky assets will increase. At
the same time, since the more risk~averse investor will lend

a smaller amount at zero interest, the borrower cannot

borrow (and consequently take risk) as much as before.

The analysis shows that the relatively more risk-averse
persons will save less while the less risk-averse
individuals will do the opposite. Since each expected rate
of return is associated with a higher level of risk under
the zero interest rule, for the more risk-averse individual,
the opportunity cost of consumption is smaller. Therefore,
he is expected to increase his consumption at the expense of
savings. The less risk-averse person is not as concerned
about risk and under zero interest rate, his borrowing cost
will be smaller so, to him, savings and investments will be
more attractive under the zero rate of interest.

While the savings of the lender and the borrower change
in different directions, the net effect on aggregate savings
is negative. When switching from positive to the zero
interest rate, the net savings is expected to decline. This
decline will increase the marginal productivity of capital
which leads to a higher rate of return on capital.

Similarly, in the macro economic analysis, we were able
to demonstrate that aggregate real investment will decline

as the interest rate is reduced to zero. In the absence of

152

government bonds, it was assumed that banks invested the
funds available to them in the equity market. At the zero
interest rate, the savings deposits will become demand
deposits. When the interest payments on savings deposits

are stopped, people will transfer a portion of their funds

from the original savings deposits to equity and money. The
total demand for equity declines by the amount of funds that
have been transferred from savings deposits into money. The
bank demand for equity declines while the direct demand for
equity increases. The net effect, however, is a decline in
the total demand for equity. Consequently, the level of
aggregate investment will decline.

The second objective was to gain some insights on the
structure and the performance of the Islamic economy itself.
The institutions of Islamic banking were described in
Chapter 1. We demonstrated that in the absence of the
interest charge, Islamic banks will operate similar to
mutual funds. The new banking institution to replace
interest-based lending is profit and loss sharing. Using
Mean/Variance analysis and portfolio theory, we have shown
that PLS lending was inferior to lending at zero interest
and PLS borrowing was preferred to borrowing at zero
interest. 'These findings indicate that, even though there
will be many investors who like to borrow PLS loans, they
would face a severe shortage of credit because savers are

reluctant to lend on the PLS basis. Therefore, with the

153

regular bonds prohibited and the PLS loans rejected by the
lenders, the only mode of transaction remaining is equity.
Even if banks choose to operate based on the PLS mechanism,
the competitive pressure will make these arrangements very
similar to equity contracts.

Therefore, based on the above reasoning, we did not
find it necessary to include the PLS account as an
independent asset in the macromodel of the Islamic economy.
Also, since all types of bonds are eliminated, the model
does not include any bond markets either. The three
financial assets included in our model are equity, high-
powered money and demand deposits. A unique feature of this
model is that the central bank is allowed to hold equity and
use equity transactions to alter the supply of credit in the
same manner that Western central banks use open-market
operations in the bond market.

We introduced several tools of monetary and fiscal
policy for an Islamic economy. The three basic tools are:

l) Open-market intervention in the equity markets by

the central bank.

2) The control of the required reserve ratio on demand

deposits.

3) A monetized and equity-financed fiscal policy.

We have assumed that government debt in an Islamic
economy is either monetized or financed by the sale of

government-held equity. The reason is that government

154

cannot pay any interest on its debt and the public will be
reluctant to purchase the bond at no interest. The only
remaining option is for the government to borrow interest-
free loans from the central bank.

To analyze the effect of these policy instruments, we

have applied the method of comparative statics. First, the
equations of the model are reduced into two equations
representing equilibrium in real and financial sectors, then
we totally differentiate these equations with respect to the
policy instruments and the endogenous variables. The
endogenous variables of our model are real output and the
value of equity stocks. The results of the analysis were as
expected, the purchase of equity and the reduction in
reserve requirements are both expansionary and they increase
the level of output and investment. An increase in
monetized debt is also expansionary but the effect on equity
values is unclear.

To further understand the nature of the economic policy
in an Islamic economy, we developed a similar model for a
regular economy by adding an additional equation for
government bonds to our original model of the Islamic
economy. After applying a similar comparative static
analysis to this model, we were able to compare the effects
of these policy instruments on regular and Islamic
economies. The results were summarized at the end of

Chapter 3. We observed that open-market operations had the

155

expected effects under both regimes (an open—market purchase
will increase investment and aggregate demand). A money-
financed deficit will be expansionary under Islamic regime.
The impact of the same policy under a regular regime will

depend on the interaction between the bond market and other

markets. If the sensitivity of commodity and equiy markets
to the interest rate is relatively small, the policy will be
expansionary. A bond-financed deficit will have an
indeterminate effect on output under both regimes. Overall,
it appears that open-market operations in the equity market
are the most effective tools of monetary policy in an
Islamic economy.

Under an Islamic banking system, the equity market is
used for open-market intervention. In practice, however, the
central bank could use the PLS accounts of Islamic banks for
intervention. As was described earlier, these accounts are
similar to mutual fund shares in the Western world. One
advantage of using PLS accounts instead of direct
involvement in the stock market is that bank portfolios are
highly diversified and any change in demand for the PLS
accounts (which are related to these portfolios) will have
minimal effect on the relative prices of different equity
assets. Therefore, using PLS accounts allows the government
to control the money supply without any distributional

effect in favor of any particular industries or stocks.

156

The welfare effects of interest-charge elimination
could be deduced from a basic knowledge of optimization. At
the micro level, we know that in a utility maximization
problem, imposition of a new restriction will either reduce

the maximum utility available or give the same result as

before. Since Islamic restriction primarily affects the
lenders by eliminating the interest they can receive on
loans, they will be clearly worse off. The welfare effect
on the borrowers is not clear because, on one hand, they
face a quantity restriction on loans and, on the other hand,
the rate of return on their investments will be higher.

When talking about the welfare effects of Islamic
banking however, we must not ignore the impact of religious
faith on the preferences of individuals. It could very well
be the case that, to the believers the existance of
interest-paying assets is disturbing because it indicates
disobedience from the commands of Islam. In that case, the
elimination of these assets could even increase the utility
of this group of Muslims.

Some authors such as Rafi Khan have indicated that,
under a regular banking regime, some devout Muslims might
shy away from the banks which are considered usurious
institutions. Be estimates that devout Muslims are hoarding
as much as $80 billion in Saudi Arabia. Once an Islamic
system is established, these funds will be deposited in

banks and channeled into productive investment projects.

157

Therefore, he argues that the level of savings and
investment might actually be higher under an Islamic banking
regime.

This argument could be criticized on several grounds.

First of all, there has never been a formal scientific

investigation on this issue. Secondly, there is evidence
that the majority of people in Muslim nations use the
services of the conventional banks without any hesitation.
As demonstrated in Rudney Wilson’s book on Middle Eastern
Banking, conventional banking in the Arab middle east has
been expanding more rapidly than any other region in the
world during the past two decades. This growth indicates
that a substantial number of people find it acceptable to
interact with commercial banks. Most likely, therefore, the
number of investors who shy away from regular banks and the
size of funds that are hoarded this way is minimal.
Besides, the act of hoarding currency and precious metals is
a portfolio allocation decision, not an intertemporal one.
The monetary authorities could easily offset the effects of
hoarding by increasing the supply of credit to the
commercial banks. It is the intertemporal decisions of
households that affect the rate of investment most
significantly. Nevertheless, the issue of religiously
motivated hoarding could be an interesting topic for further

research in the field of Islamic banking.

158

Our theoretical analysis has led to a number of
predictions about the consequences of Islamic banking which
were reviewed earlier. How closely these predictions apply
to the operation of Islamic banks throughout the Muslim
world depends on how similar they are to our theoretical
model. The basic assumption of our model is that, under an
Islamic banking system, all of the interest-paying assets
are eliminated and the remaining financial assets are risky.
The negative impact of Islamic banking in our model was a
direct result of this assumption. Obviously, in those
nations that have established independent Islamic banks
without eliminating their regular financial systems, the
predictions of our model will not be applicable. This rules
out all nations accept for Iran and Pakistan.

Iran and Pakistan are the only nations that have
modified their entire banking system. The banking systems
of these countries, however, do not operate according to the
basic assumptions of our model. In these countries, banks
can insure the principles of investment accounts (PLS
accounts). They also have the right to request insurance
and guarantees from their loan customers. In addition, the
price mark-up schemes are, to a large extent, risk free. The
result is that the Islamic banks of these nations are
similar to the conventional banks in many aspects.

In contrast to the assumptions of my model, the Islamic

banks of Iran and Pakistan are able to arbitrage risk.

159

Consequently, these banking systems are not as inefficient
as predicted in our model. The closer they comply with the
Islamic requirement, the greater would be the level of
inefficiency. This inefficiency, however, might appear

tolerable to an extremely religious people. To them it

would be a small price to be paid for obedience to Islam.
Alternatively, a Muslim people (or their leadership) might
be concerned about efficiency in the financial markets and
choose a semi-Islamic banking system.

Finally, the single most important policy
recommendation of this dissertation is that establishing
independent Islamic banks without the elimination of
conventional banks is more efficient than switching to a
complete Islamic banking system. The direction of Islamic
banking in the future depends on the performance of these
experiments with Islamic banking which are currently
underway in Iran and Pakistan. It is also dependent on the
political will of the Muslim population in each nation.
While certain reforms in the furture are likely, there is no
doubt that the notion of Islamic banking itself enjoys
considerable support. There are still many unresolved

issues and additional research will surely be welcomed.

Suggestions For Future Research.
Clearly, the volume of research on Islamic economic

systems has significantly increased over the past six years.

160

However, there are still many important questions to be
analytically investigated. With regard to the impact of
Islamic banking on savings and investment, which was the

main topic of my research, there is more work to be done.

First of all, my research was limited to theoretical
analysis. It must be followed by empirical tests. Within a
few years, sufficient volume of data on the banking systems
of Iran and Pakistan will be available, making such tests
feasible.

My micro-economic analysis could be improved by replacing
the quadratic utility functions with more general,
functional forms which do not suffer from the weaknesses
attributed to quadratic functions. The results of my model
might be sensitive to the choice of the utility function
because the quadratic utility function leads to increasing
degrees of absolute risk aversion. It must be noted,
however, that if a general utility function is used, the
comparative static method will be fruitless. The reason is
that we will not be able to determine the signs of the
parameters which are needed to indicate the direction of
change in savings and risk taking. Therefore, with general
utility functions, a different method of analysis is
required.

One possible direction for improving the macro model is
to specify the equity and bond markets in more detail in

order to capture their differences better. We have already

161

shown some of these differences by specifying the dividend

as a function of income while the interest rate is
independent of income. Another major difference that could
be included is the risk structure. Bondholders have the

first claim on a firm’s earnings, thus they are less risky
compared to equity. To capture this difference, we must
formally incorporate uncertainty in our model. Doing so,
however, will make the model more complex.

Aside from the topic of this dissertation, there are
other issues which are worthy of consideration. The large
scale use of PLS arrangements will lead to a number of
difficulties. If the lender and the borrower have assymetric
information about the concerned project, the borrower might
under-report his profits to minimize the lender’s
profitshare, Also, one could perceive a situation where a
borrower conceals the actual risks of a project in order to
make it look more attractive. These questions of moral
hazard and adverse selection should be studied empirically
to see how Islamic banks deal with these issues.

A second interesting topic is the difference between
economic stability of a regular and an Islamic economy.
Some authors (M. Khan for example) have argued that an
Islamic economy would be more stable than a regular economy
because savings and investment would be better synchronized.
This important issue could be a rich area for further

research.

APPENDIX A

(CHAPTER 2)

The Impact of Zero Interest When the Loan Market Fails

In this appendix, we study the impact of interest-
charge elimination under the assumption of complete loan
market failure. The microeconomic analysis of Chapter 4 is
based on the assumption that even at zero interest the
savings of risk-averse investors are transferred to the less
risk-averse individuals by the intermediaries. Therefore,
the bond market still exists even though it is in
disequilibrium.

While I believe that this assumption of partial lending
is a realistic description of how the financial system of
the Islamic nations will operate, the total failure of the
loan market is also worth considering as a possible
alternative outcome. We will briefly review the outcomes of
the certainty and uncertainty models of Chapter 4 under the
assumption that at zero interest no one will agree to lend.
The public will keep their savings in the form of idle cash
in the safe boxes and there would be a strong demand for

loans but no supply.

162

163

A) The Loan Market Failure in the Certainty Framework.

The failure of the loan market imposes no new
constraints on the risk-averse savers. They will simply
keep their savings in a safety box instead of placing it in
a bank deposit (which will no longer pay any interest). The
failure of the loan market will change the constraint that
the borrowers face. The two-person models of sections l-c
and l-d will be modified to reflect the no—lending
constraint.

In model l-C (where no investment option is included),
each person must maximize his utility subject to no

interest-charge and no borrowing.

For person A: Max UA(Ci‘,Cz‘)
S.T. C1‘+C2A = C1°A+C2°A

01mm“

For person B: Max U°(C13,Cza)
S.T. 013+02° = C1°3+CZ°B

C133C1°B

Figure A-l shows the allocation under regular regime and the
Islamic regime (with no lending). Persons A and B are
lender and borrower, respectively. Point E is the
equilibrium under regular regime. When the interest rate is

suppressed to zero, the optimal allocations must lie on

164

$132. The lender chooses point F. Person B (the borrower) is
deprived of any loans so he remains at his original position
at point H. He is obviously worse off as is the lender.
(Under the partial lending assumption of l-C, the welfare

impact on the borrower is indeterminate.)

 

B
S! R.‘ ‘- CI B
Cl
1
+
6?

 

 

 

 

Figure A-l

When the investment opportunities exist but the loan
market fails at zero interest, the optimization problem of
the saver is the same as the one given in section l—D, but

for the borrower, we would have:

Max 03(013,C23)
S.T. 013+023 = C1°3+K13+K2B

C13_<_C1°3+K1B

165

 

 

 

c,B

Fig A-Z

In figure A-2, the borrower chooses the consumption and
investment pattern shown by points E and J. Under zero
interest, he wishes to borrow up to point G and invest at
point K; but since no borrowing is allowed, he is forced to
produce and consume at point F. In this case, the borrower

is clearly worse off (compared to a regular capital market).

B) The Loan Mgrketgfigilurgggnder Uncertainty Framework.

To analyze the general uncertainty model which allows
for investment as well as consumption, we will look at the
behavior of the risk-averse saver in more detail. In the
partial lending model of Chapter 4 (section 2-B), we assume
that the risk-averse investors will deposit their savings in
the bank even when the interest rate is zero. The banks, in

turn, invest these funds or lend them to other investors. In

166

other words, the total savings of both persons is eventually
invested. There are no idle savings in this model as
demonstrated by the loan market clearing condition (equation
12).

Here, we assume an alternative behavior by the savers.
They can now put their riskless savings in money or bank
deposits which are both risk free (inflation is ignored).
As the interest rate on bank deposits declines, the demand
for these deposits diminishes until it reaches zero at a
zero rate of interest. (This implies that the loan market
fails completely at a zero rate of interest.) These
investors will substitute money and risky assets for the

bank deposits. Figure A-3 compares the supply of loanable

funds under partial lending and complete loan market
failure.
Suer 03>
LOANS

ro

 

 

 

Fig. A-3

167

g1 is the supply of loanable funds when all savings is

kept in banks. There is a positive supply of loans at zero
interest. g2 is the supply of loanable funds under the
alternative assumption. In this case, the loanable funds
are not the same as savings. At zero interest rate, the

riskless savings of original lenders is positive but the
supply of loanable funds is zero.
We define two types of savings: idle and active. The

portion of savings that is placed in banks is active and the

rest which is kept in currency is idle. The active savings
are:

ZA(W1-Ci‘)
Zx = The fraction of total savings kept in the bank

deposits. ZA=ZA(FO). This fraction falls to zero as the
rate of interest goes to zero. Now the bond market

constraint facing the borrowers is:

ZA(W1-Ci*)=-(l-Xs)(Wz-C13) 12*

The maximization problem of the lender that was given in

section 2-B still holds. For the borrower, we have:

168

3’“ ' ’
Max EU9(C1,C23)=Max UB(013,023,3c2)
-8 _—
S.T. C2=(W2’Cla)(1+FO+XB(P‘FO))
Sc2= (Wz-C13)2.st.5r2

ZA(W1‘CIA)+(1‘XB)(Wz-CIB)Zo

When the constraint is binding, ZA=0 and Xa=l.

To study the impact of interest-free banking on the
behavior of the borrower, we must go through the same
procedure that led to the derivation of equations 13 and 14
in section 2-B. Equation 14 will essentially be the same,
but since the bond market constraint has been changed, we
must derive a replacement for equation 13. Then we will
have a two-equation, two-variable system to solve for d(Wz-
C1°)/dro and an/dro

Totally differentiating equation 12* with respect to

re, we get:

(l-Xa).d(W2-C13)/dro- (Wz-Cis).dXs/dro=

-dZA/dro.(Wi-Ci‘)-ZA.d(W1-C1*)/dro 13‘
From the lender’s behavior, we know that:

dZA/dro>0 and d("l‘ClA)/dl‘0>°

 

169

Therefore, the right hand side of this equation is negative.
Then we get: (l-Xs).d(W2-C13)/dro-(W2-C13).an/dro= K’.
Since K’<l, this equation has the same signs as equation 13.
Therefore, the results obtained from the system of equations
13 and 16 in section 2-B remains valid in this case as well.
Even under complete market failure at zero interest, we

still have:

d(Wz-C13)/dro(oand dXs/dro)0
d(Wz-Cia) = d(Wz-C13)/dro. dro=(-)(+)<0

dXs=dXB/dro . ro=(+) (+)>0

Moving away from zero interest (in a positive direction)
will encourage the (less risk-averse) borrowers to take more
risk and reduce total savings.

In section 2-B, it was shown that the lender will have
lower utility under a zero interest rate. The same result
is valid when the loan market fails at zero interest because
for him the financial opportunities have not changed. We
also saw that the direction of change in the utility of the
borrower was unclear. One expects that, under loan market
failure at zero interest, the borrower will be worse off
compared to the regular loan market. This, however, is not
true because there are still two conflicting forces in

action. The change in the utility of the borrower is:

170

dUB/dro=an/dro.[dUB/an]- d(Wz—C1B)/dro.[dUB/dC13]+

Eza.(w2-CIB).dF/dro

We know that dUB/dC13=0 but dUB/an>0 because X3 is

constrained below its optimum value.

dUB/dro=an/dro.[dUB/dxa]+U23.(W2-C13).[dF/dro]

dUB/an>0, dXs/dro>0 and dFVdro<o => dUB/dro = (+)+(—)=?

The direction of change in the utility is unknown because,
on one hand, the investor can no longer borrow any funds
and, on the other hand, the rate of return on the risky
assets is higher. We can only argue that because the
borrowing restriction is stronger under the assumption of
total market failure, the borrower is more likely to be

worse off in this case.

APPENDIX B
(CHAPTER 2)

The P.L.S. Arrangement

According to Muslim economists, the Islamic banks will
use profit- and loss-sharing arrangements as their main mode
of financial transactions. In this appendix, the reaction
of lenders and borrowers to the P.L.S. arrangement will be
briefly analyzed.

As an investment asset, a PLS loan is very similar to
equity and the two could be close substitutes for each
other. Indeed, every PLS loan is borrowed for investment in
a risky project (or a portfolio that consists of several
risky projects). As a result, the expected return and
variance of a PLS loan is linked to the risk/return
characteristics of the project for which it is borrowed.

Let’s assume a PLS borrower has 3W of his own and
wishes to borrow 3B on a PLS basis to invest in project A
that is risky. The expected return and risk of A are K’ and
ox, respectively. Let 0<q<1 be the profit-sharing ratio
(the lender receives (l-fié of the joint profits), then the

share of the lender and the borrower from total profits will

171

172

be (W+qB)/(W+B) and (1-q)B/(W+B), respectively. However, if
a loss occurs, the lender assumes the entire loss on the
funds that he has landed.

Given that X is the random rate of return on asset A,
the borrower faces the random return X’ on his investment.

X’ will be related to X by the following equation:
[(W+qB)/W].X if X; 0
X if X< 0

Equation B.1 indicates that, with PLS borrowing, the
investor can expect a higher return when a profit is
realized. However, the probability and the size of his
losses remain unchanged. In order to understand the
advantages of PLS borrowing, we must derive the expected
return and risk of X’. From equation B.1, we can see that X’
has the same distribution as X. Assuming the distribution
function of X, f(X), to be discrete we have:

x =zx£ .ws) + zn‘fln)
n; x.<o

X =2X1.f(Xl)+ 2X1.f(X1)+ 2[qB/W].Xi.f(X1)
X110 X1 (0 X120

And finally we have:

x =i+ch/w1.e where: e: 2n.£(m)>o 3.2
X120

173

(The results will not change if a continuous function is
used.) Equation B.2 shows that the expected return with PLS
borrowing will be larger than without it. The degree of
increase in an expected return depends on the profit share
of the borrower, q .

We must also derive the variance of X. Var(X6 )=2(X1-
X)Z.f(X;). After expanding this equation and collecting

terms, we get:

Var(x')= Var(X)+(qB/W)2.(2X21.f(Xi)-e2)+
[2qB/W].[ZX21.f(Xi)-eX] 3.3
Xi>0

Now we can compare the expected return and risk of PLS
borrowing to regular borrowing at zero interest. When
borrowing at PLS, the investor is entitled to q% of the
profits on the borrowed funds. Therefore, an equivalent
portion of profits is obtained by borrowing qB$ from a
regular bond market at zero interest. Then the expected
return and risk on his profit will be:

Xo=(1+qB/W).X and oo=(1+qB/W).ax 3.4
Comparing expected returns, we can see that: e=2X1.f(X1) :9
.2i.
Therefore, since X’=X+[qB/W].e and X0=X+[qB/W].X
iizfi 3.5

174

To compare the standard deviations, we note the following

inequalities:
N-
2X21.f(X1) g 2X21.f(Xi) B.6
szo i=1
‘e>)—( :> e2 > i2 B.7
N -
Therefore: 2Xl.f(Xl)-e2 < [2X21f(X1)-X2] = Var(X) B.8
X1>0 F)
Similarly:
.2 g i2 => zxzi-ei 5 [zxzif(xi)-izj = Var(X) 3.9
From B.4, we have:
020=ozx + [quz/Wz].ozx + [2qB/W].ozx B.10

Using inequalities B.6 and B.7, we can compare the variances
of X and X as given by equations B.3 and B.10 . Clearly, we

can see that:

Var(X')5Var(Xo) 3.11

Inequalities B.5 and B.11 demonstrate that PLS borrowing is
more advantageous to regular borrowing at any rate of
interest even Zero.

Using similar procedures, we can compare the
characteristics of PLS lending and regular lending. As
explained before, the way PLS loan transactions work is
that, if there is a loss, it will be born by the lender; but
if there is a profit, it is shared between the lender and

the borrower. If Y is the random rate of return on the

175

lended funds and those funds are invested by the borrower in
portfolio A which was described earlier, then Y and X will

be related by the following equation.

(l-q).X if X>0

X if X50
Let T and 0y denote the expected return and risk of random
variable Y, respectively. Then we have:
- N _
Y: 2Yi.f(Xi) = X-qe B.12
i=1
After rearranging terms and simplification, the variance of
Y could be written as:
day = Var(x)+q2.[ZX21f(X1)-e2]-2q.[EX21f(X1)-e.X] B.13
X120 10,0
For sake of comparison, assume that the investor wants
to use an alternative portfolio which would have the same
expected rate of return as PLS lending. If this portfolio
consists of dividing the original funds between direct
investment in portfolio A and safe cash which does not pay
any interest, then his expected return will be ‘T*=(l-p).X
where p is the portion kept in cash. With the expected
return being the same under both cases, we have:
X“ = "Y- => (1-p).X = X‘ 15

and we get szqe => p)q and p=qe/X B.14

176

The variance of Y* is (1-p)202x. We like to compare the
variances of Y and Y*.

02y*=02x+p2.02x-2p02x 8.15
To compare 02y* and day as given in equations B.13 and B.15,

we use inequalities B.8, B.9 and B.13.

Let: H: [ZXzif(Xi)-ez], G: [ZXzif(Xi)-6.X] X<e => G>H

02y* - oz, =q2H-2qG-p2.ozx+2pozx
Ozy* - oz, =q2H-2qG+2q(e/X).azx-q2(e/X).02x

02,. - ozy =qz[H-(e/i).02x1+2q[<e/i>.on-G)1

We know that HgGgon, leading to: l(e/X).ozx-G))g IH-

(e/X).ozx| and q2<2q. We conclude:
02" - 03! 5 0

Therefore, PLS lending is an inferior strategy.

The above analysis indicates that, under conditions of
perfect capital markets, the market for PLS loan
transactions will fail. The PLS lender can always do better
by investing a portion of PLS loans in the same project for
which the funds were borrowed and keeping the rest in cash.
Only when small investors face prohibitive transaction and

information costs will the PLS loans appear attractive.

APPENDIX A
(CHAPTER THREE)

Debt (Equity) Financed Fiscal Policy in a Regular

(Islamic) Economy

In this chapter, we studied the fully monetized fiscal
deficit. Another option available to the policy makers is
to finance the increased government expenditure without
increasing the money supply. In a regular economy, the
government can finance its deficit by the sale of bonds. In
an Islamic economy, the government can borrow from the
central bank. The central bank, in turn, could raise the
needed funds by the sale of equity. In this appendix, we
will derive the multipliers of a debt-financed fiscal policy
in a regular economy and an equity-financed fiscal policy in
an Islamic economy, respectively.

In an equity-based economy, an increase in the deficit
without any change in the money supply will require an
equivalent sale of government-held equity. Therefore, we
will have dG=(-dV¢/P). V; will change every time that G
changes: V¢=Vg(G). Since G is measured in real output and

V: is measured in nominal money value, we have dVg/dG = P,

177

178

or for every 1 unit increase in equity, $P worth of equity
must be sold.

An equity-financed deficit will have a wealth effect
because at the same time that public equity holdings rise,
the central bank gives the money that is raised by the sale
of equity to the government for spending, and the money
supply stays the same. We will have: W = W($,G,P).

Incorporating these changes in the original model of an

equity-based economy that was given by equations 6.1-6.3, we

get:
-?++ +-
C(P,Y,G,V) + I(V,P) = Y
+?+?
V¢(G)/P + f1(P,Y,G,V) = V/P
-7...
f2(P,Y,G,V) = M/P

Totally differentiating the first two equations of this
model with respect to Y, V and G gives:

dV Ca + 1
A*. dY = -1+f13 . dG

A* was given in equation 8.2. We showed that A*'1 had
the following signs:

7 +'
A*'1 = (l/D*). + +

We claim that f13-1<0 because: f13+f23 = 1, f23>0. Then we

will have:
( )(?)+
( )+

dY =1/D*. (+)

?+
G = 1/D*.

   

 

 

( + )
(+)(+)

179

D*<O if f12<0. At the same time, dV/dG<0 if f12<0. In
Section 2, we showed that f12<0 was a required condition for
the stability of this model. Unfortunately, even when f12
is assumed to be negative, we still don’t know the sign of
dY/dG.

The initial increase in G will increase the private
demand for equity, but the sale of equity by the central
bank will more than offset the initial increase leading to
excess supply of equity. To restore equilibrium, the value
of equity must fall, . thus, we have dV/dG<0. The
indeterminacy of dY/dG is due to the fact that the decline
in V leads to a reduction in investment and consumption
demand which could offset the increased government
expenditure.

For a regular economy, a debt-financed fiscal policy
implies that an increase in government expenditure is
associated with an increase in the supply of bonds. We will
always have dG=dS/(b.P). The money supply will remain
constant M/PzMo/P. This policy will have a wealth effect
because the‘ supply of bonds changes while the supply of
other assets remains unchanged, therefore, we have:

++—
W=W(G,V,P)

Taking these modifications into account, model 11.1-11.4

could be written as:

- ? + + - + -
C(P,Y,G,V,b)+I(V,P)+G = Y 11.1A

180

7 7 + 9 -
f1(P Y,G,V,b) = V/P 11.2A
-9++_.
f2(P,Y,G,V,b) = Mo/P 11.3A
--++’7

f4(P,Y,G,V,b) S/(b.P) 11.4A
To derive the multiplier, we totally differentiate

equations 11.1-11.3 with respect to V,Y,b,G.

_ dV C3+1 Ca+1>0
A. dY ‘ - f13 .dG f13>0
db f2: f23>0

 

 

 

 

A is given in the left hand side of equation 12.1. In

section 3, we showed that:

+ - ..
+ + -
- f12 -

IA}.-

 

 

A was found to be dependent on f12. We have already
developed ALI in Section 3. Solving for the endogenous

values, we have:

 

dV C3+1 011 - + +
dY = -A-1 £13 .dG= -1/5. + — 032 + .dG
db £23 + 023 + +

dV _ 011 + (-) + (+)

dY = -1/D . (+) + (—) + 032 .dG

db (+)+023+()

 

As we can see, both dY/dG and dV/dG are indeterminate
and, even when 011 and 032 are determined, the multipliers
will still remain undetermined. In the case of a pure bond-
financed deficit, the impact on investment is not clear

because the policy does not directly affect the equity

181

market. An increase in the supply of bonds increases the
real wealth and the rate of interest on bonds at the same
time. These two will have offsetting effects on the demand
for equity and the net change in the equity values is not
clear.

The net change in the aggregate demand for output is
also unclear because, at the same time that G rises, the
bond rate also rises. The higher bond rate will reduce the
demand for investment and private consumption. Comparing
the results of a debt-financed and equity-financed deficit,
we see that there is more certainty about the impact in the
case of the equity-financed deficit. We at least know that

the investment will decline.

 

APPENDIX B
(CHAPTER THREE)

A Study of Pure Fiscal Policy and a Pure Increase

in the Supply of Money

The government’s budget constraint requires that any
increase in a government deficit be accompanied by an
equivalent increase in the supply of bonds or money.
Similarly, an increase in the money supply is always
accompanied by an equivalent increase in bonds or government
deficit. While a pure increase in money supply or a pure
increase in government deficit can never happen without
something else also increasing, their study will help us
improve our understanding of the feasible policies that were

described in this chapter.

B-l. E E E. J E 1. . E °I ‘E 1 E

Working with the model of an equity-based economy that
was developed in section 2, we modify the model to show that
an increase in G, in this case, does not change the supplies
of money or bonds and, therefore, has no wealth effect. The

model becomes:

182

183

? - + + + -
C(Y,P,M,V)+I(V,P)+G:Y 15.A
- ? + ?
Vg/P+f1( ,Y,M,V) :V/P 15.B
- ? + +
f2(P,Y,M,V) :M/P 15.0

Totally differentiating the first two equations of the model

W.R.T. Y,V,G, we get:
C4+Il Cz-l dV -1
. = .dG
f14-1/P f12 dY .0
dV f12 1-Cz -1 -f12
= 1/D*. : 1/D*. .dG
dY

1/P-f14 C4+I1 0 f14-1/P
We have already shown that for this model to be stable,

 

f12 must be negative. f12 is a sufficient condition for
D*<0. Therefore, we have:
dY/dG=(-)/(-)>0
dV/dGz-fiz/(-) <> 0
If the system is stable, then f12<0 and dV/dG<0.
B-Z. WW
We repeat the same exercise with the model in section 3
for a regular economy. Since there is no wealth effect, G

will no longer appear in the asset-demand functions. The

modified model is:

184

+—

_?++-

C(P,Y,M,V,b)+1(V,P)+G=Y 16.A
_?+?_

£1 (P, Y,M,V,b) :V/P 16.B
—?++-

f2 (P, Y,M,V,b) =M/P 16.C
--++?

f4(P, Y,M,V,b) =S/(bP) 16.D

Totally differentiating the first three equations

W.R.T. V,Y,b,G, we get:

C4+Il Cz-l C5 dV +1
f24 £22 £25 . dY : - 0 .dG
f14-1/P f12 f15 db 0

 

 

 

 

The multipliers will be:

dV 011 - + -1 011
dY = 1/5 + - 022 0 = -1/5 + 3<0
db + 023 + 0 +

dV/dG ()0 , dY/dG>0 and db/dG>0

Appendix C
(CHAPTER THREE)

The Stability of the Macro Models

In this appendix, we will use Samuelson’s
Correspondence theorem to investigate the stability of the
macro models that were developed in this chapter. This
investigation shows that, within acceptable range of the

parameters, all three models are stable.

C-l- We
We define the time rate of changes in V and Y as
increasing functions of excess money supply and excess

demand for output, respectively.

dV/dt= 0(M-Md) dY/dt = I’(I-s.Y)
0’ >0 F’>O

After replacing Mk, 5 and I from 3.1 and 3.2, we apply
a Taylor expansion to these equations and write them in the

matrix form:

185

186

 

 

 

 

 

[dV/dt [o’(K.f34 + f24)(-1) o’(K.f31 + f12)(-1) {V—Vo
dY/dt F’(11-s4.Y) F’(-s1.Y-s) ' Y-Yo
C.1
The characteristic equation of this system is:
~o’A12-n -o’A22
=0 0.2
-F’A11 -F’.A12-u
We have:
A11 = s4.Y- I1 A21 = K.f34 + £24
A12 = 51.Y + S A22 = K.f31 + £21
- +
A11 A12
+ + is the Jacobian of system 4.1 and u’s are
A21 A22

 

 

the eigenvalues of equation 0.2.
Expanding equation C.2, we get:
112 - u(-a’A11 - I"A12) + F’o’(A21.A12 - A11.A22) =0 0.3
For the system to be stable, the roots of this equation
must have negative real parts. The necessary and sufficient
conditions for having negative real parts are:
(-a’A21 - F’A12) <0 C.4
(A21.A12 - A11.A22)>0 C.5
Since A21 and A12 are both positive, the first
inequality is satisfied. The second inequality implies that
the determinant of A must be negative.
Furthermore, we can give a different interpretation for
inequality, C.5. The slopes of IS and LM equations (3.1 and
3.2) are:

nylrm -1:1_._LL1+ =-A1_z.
dY 15 dIS/dV s4.Y-Ii A11

dil|=-dLM2dI -1.K.121_m_1+ =-122
dY LM dLM/dV K.f34+f24 A21

187

Manipulating inequality C.5, we have:
A21.A12 > A11.A22 :: -A12/A11>-A22/A21
In other words, for stability, the IS curve must be steeper

than the LM curve.

C-Z, =.'_' ._ ,- on: O, 1, o ’ -:a ‘q - .,o

For the model that was developed in section two, we
define the time rates of change of the endogenous variables,
V and Y, as increasing functions of excess demands for

equities and commodities, respectively.

dV/dt o(Vd-V) o’>0 0(0)

0
dY/dt

F(C+I+G-Y) F’>0 I(O) 0

Applying Taylor expansion to these differential equations

around the equilibrium values, we get:

 

dV/dt o’(f14 - l/P) o’fiz V—Vo
[dY/dt} - [r’(04+11) r'(02-1)] Y-Yo]
The characteristic equation is
dV/dt c’(f14 - 1/P)-u a’fiz V-Vo
[dY/dt] _ [F’(C4+Il) F’(Cz-1)-u] Y-Yo] - 0

 

or
uz-(a’(f14-1/P)+F’(Ca-1)).u +
a’(f14-1/P).F’(Cz-1) - a’F’(C4+Ii).f12=0
The roots of this equation must have negative real
parts in order for the system to be stable. The necessary

and sufficient conditions for having negative real roots

are:

188

1) o’(f14-1/P)+F’(Cz-1)<O

2) (f14-1/P).(C2-1) - (C4+I1).f12>0

We have already shown in section 2 that (f14-1/P)<0 and
(Cz-l)<0, so the first equation is satisfied. f12<0 is a
sufficient condition for the second inequality to hold. In
general, we can write the second condition as:

'(C2-1)/(C4+Il) > -f12/(f14-1/P)

From equations 7.1 and 7.2, we can drive the lepes of the

IS and LM equations:

fig, : - d|§£dx : - - >0
dY IS dIS/dV C4+Il

01 =-0mmx =-_f1_2_ <>0
dY LM dLM/dV f14'l/P

Therefore, a necessary condition for stability is for
the IS curve to be steeper than the LM curve in a (Y,V)
graph. Finally, it must be noted that an equivalent
condition for stability is that the determinant must be

negative.

C-3. WW
For the regular model in section 3, we investigate

stability by defining the following three ‘differential

equations.
dV/dt = d(Vn-V) o'>0 6(0) = 0
dY/dt = T(C+I+G-Y) T’>0 I(O) = 0
db/dt = t(-M/P + f2) t’>0 t(0) = 0

Applying Taylor expansion, we get:

189

dV/dt f14-1/P f12 f15' V-Vo V-Vo
dY/dt = C4+I1 C2-1 Cs Y-Yo = A* Y-Yo C.4
db/dt £24 £22 f25 M-Mo M-Mo

The characteristic equation of C.4 is:

0’(f14-1/P)-n o’fzz o’.f25
(A*-nII = T’(C4+Ii) T’(Cz-1)-n T’.Cs = 0
t’.£24 t’.f22 t’.f25-n

According to Samuelson’s correspondence theorem, the
model will be stable if the principle minors of matrix A*

alternate in sign as follows.

£14-1/P f12
(f14-1/P|<0 , >0
C4+I1 Cz-l
f14-1/P f12 f15
C4+I1 C2-1 Cs <0
£24 £22 £25

The last determinant is the same as D*; therefore, D*<0

is a necessary condition for stability of the model.

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