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This is to certify that the
dissertation entitled

Three Essays in Industrial Organization

presented by

Sang-Hoo Bae

has been accepted towards fulfillment
of the requirements for the

Ph.D degree in Economics

 

 

 

@J‘ngim.

 

Major ProfeVor’s Signature

5/1 9/03

 

Date

MSU is an Affirmative Action/Equal Opportunity Institution

PLACE IN RHURN BOX to remove this checkout from your record.
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6/01 c:/CIRC/DateDue.p65-p. 15

THREE ESSAYS IN INDUSTRIAL ORGANIZATION
By

Sang-H00 Bae

A DISSERTATION
Submitted to
Michigan State University

In partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2003

ABSTRACT
THREE ESSAYS IN INDUSTRIAL ORGANIZATION
By

Sang-H00 Bae

The first chapter develops a simple model of software piracy to analyze the short-
run effects of piracy on software usage and the long-run effects on development
incentives. I consider two types of costs associated with piracy: the reproduction cost that
is constant across users and the degradation cost that is proportional to consumers’
valuation of the original product. We Show that the effects of piracy depend crucially on
the nature of piracy costs. Policy implications concerning copyright protection are also
discussed.

In the second chapter I analyze a professional Sports league’s Optimal choice Of
the number of franchises in Salop’s (1979) circular city model. I consider two scenarios:
(1) the league operates as a fully collusive cartel in which it controls the number of
franchises and ticket pricing, and (2) the league operates as a semi-collusive cartel in
which it controls only the number of franchises and ticket pricing is left to individual
franchises. I compare the outcomes in both scenarios to the socially optimal and free
entry outcomes. I extend the analysis to the case where the average quality of each
franchise is inversely related to the number of franchises due to diluted talent pool.
Finally, I consider the possibility that the league can play relocation game with local or
state governments. In particular, I examine the strategic advantage of leaving a few cities

vacant, which will be used as a leverage to exploit more consumer surplus.

In the third chapter I develop a simple model of international technology licensing to
study the effect of patent protection policy on the licensor’s endogenous choice of R&D
expenditure and the level of technology transferred. With endowment of two different levels of
technologies the licensor may transfer the old technology when‘the patent protection policy of the
host country is not effective. I present the model in which the effectiveness of protection policy
depends on the quality gap between technologies and the relative magnitude of the licensee.
However, with the licensor’s endogenous choice of R&D expenditure, the strong protection

policy is shown to have a reverse effect on technology innovation.

ACKNOWLEDGEMENTS

For the completion of my dissertation, I am indebted to many people. First of all,
I would like to thank my dissertation committee chair, Professor Jay Pil Choi for his
excellent and invaluable advice throughout the course of writing this dissertation. In
addition to providing much helpful advice about my research itself, he has provided
excellent guidance throughout the entire process. I also thank Professor Carl Davidson

and Thomas Jeitschko for their helpful comments.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................... vi
LIST OF FIGURES ............................................... . ................................. vii
CHAPTER 1

A MODEL OF PIRACY

1. Introduction ....................................................................................... l
2. The Model of Piracy: A Short-Run Analysis ................................................. 6
3. Copyright Protection and Incentives to Create ............................................. 22
4. Concluding Remarks ............................................................................ 30
References ............................................................................................ 32
Appendix A ........................................................................................... 33
Appendix B ........................................................................................... 35
CHAPTER 2

THE OPTIMAL NUMBER OF FRANCHISES WITH APPLICATION TO
PROFESSIONAL SPORTS LEAGUES

1. Introduction ...................................................................................... 46
2. The Optimal Number of Franchises ........................................................... 50
3. Franchise Relocation Game .................................................................... 58
4. ConcludingRemarks...................................................... ...................... 61
References ............................................................................................ 63
Appendix C ........................................................................................... 64
CHAPTER 3

THE QUALITY OF TECHNOLOGY AND PATENT PROTECTION POLICY IN THE
INTERNATIONAL LICENSING OF TECHNOLOGY

1. Introduction ...................................................................................... 76
2. Basic Model without the Licensor’s R&D ................................................... 81
3. The Extended Model with the Licensor’s Endogenous Choice of R&D

Expenditure ...................................................................................... 90
4. Concluding Remarks ............................................................................ 96
References ............................................................................................ 98

LIST OF TABLES

CHAPTER 1
Table 1. Comparative Statics Results in the Short Run ...... , .................................. 39
Table 2.Comparative Statics Results in the Long Run ......................................... 40

vi

LIST OF FIGURES

CHAPTER 1

Figure 1. Consumers’ Choice under Copying Regime... .... .................................. 41
Figure 2. Welfare Effect of the Two Margins of Piracy Costs ................................ 42
Figure 3. The Monopolist’s Optimal Choice .................................................... 43
Figure 4. The Effects of an increase in IPRP with Linear Demand ........................... 44
Figure 5. Welfare Effects in Uniform Distribution Example ................................. 45
CHAPTER 2

Figure 1. The fully league cartel without quality choice ....................................... 72
Figure 2. Comparison of the Number of Franchises under Different Regimes ............. 73
Figure 3. Relationship between quality and number of players ............................... 74
Figure 4. Comparison of the Number of Franchises with Quality ............................ 75
CHAPTER 3

Figure 1. Game structure ............................................................................ 99
Figure 2. The basic model with a strong patent protection .................................... 100
Figure 3. The optimal choice of licensee ....................................................... 101
Figure 4. The basic model with weak protection policy ...................................... 102
Figure 5. The extended model with strong patent protection policy ........................ 103
Figure 6. The extended model with weak patent protection policy ......................... 104

vii

CHAPTER 1

A MODEL OF PIRACY

1. Introduction

As the current controversy surrounding the Napster case testifies, unauthorized
reproduction of intellectual property has been a serious but controversial issue for
copyright holders, consumers, and policy makers alike, especially with the advent of
digital technology. According to a recent study by the Business Software Alliance
(2001), for instance, the piracy rate in 2000 is estimated to be 37%, which can be
translated into $11.75 billion dollar losses for software publishers.1 The piracy rates in
the Far East, especially China, Indonesia and Vietnam, represent in each case over 90%.
The corresponding rates for Western Europe and North America are 34% and 25%,
respectively. Based on these figures, copyright holders claim that piracy is a severe
threat to incentives to develop new products, as well as revenue loss from the developed
software.

This paper develops a self-selection model of software piracy to analyze the short-
run effects of piracy on software usage and the long-run effects on development
incentives. The innovation in this paper is to distinguish two types of costs associated
with piracy — constant and type-proportional — and to show that the effects of piracy
depend crucially on the nature of piracy costs. To comment briefly on the two types of

costs, we first assume that piracy entails reproduction cost, which is assumed to be

 

‘ ‘Sixth Annual BSA Global Software Piracy Study (May 2001)’ conducted by International Planning and
Research Corporation (IPRP) for the Business Software Alliance (BSA) and its member companies.

constant across all consumers. The constant reproduction cost can be treated as the price
of an illegal copy made by piracy retailers. Even with the assumption that actual
reproduction cost is zero, consumers will need to exert efforts to obtain an authorized
copy or may have to spend time to find the software, and then to copy or to download it
for installation purposes. We assume that these costs are the same across all users or at
least independently distributed with the valuation of consumers for the product.

The second type of cost we consider is degradation of product quality associated
with unauthorized copying. The utility loss due to degradation is proportional to each
consumer’s valuation of the software. As examples of degradation of the quality
associated with piracy, for instance, an authorized copy of the software is bundled with
manuals, installation software, online services, as well as discount on future upgrades.
Users who pirate the software, in contrast, may not be able to access the entire
complimentary bundle. In addition, some software publishers strategically include web-
based functions that require personal identification numbers (PIN). Identical PINS cannot
be used on the Web at the same time.2 With an illegal copy, a consumer thus may be able
to use the software off-line, but not able to use online functions, thus experiencing quality
degradation.3 The web-based anti-piracy system is also capable of reducing quality of the
software by blocking the users with a pirated copy from receiving upgrades.4

As another example of policy relevance, consider the Peer to Peer Piracy

Prevention Act (HR. 5211) which was proposed by Rep. Howard Berrnan, D-Califomia,

 

2 With development of high-speed Internet, the new components of game software are online game
services, in which you can play the game with someone through the Internet. With the database for the
registration keys the software publisher is able to prohibit the pirated copies with the duplicated key from
running on the web.

3 For TurboTax software, each authorized copy is designed to file tax returns electronically for only one
customer. Hence, users with an unauthorized copy are only able to do tax returns except electronic filing.

and is being considered by the House Judiciary subcommittee as a way to protect
intellectual property against file-sharing through peer-to-peer (PZP) networks. P2P
networks arose as a response to the shutdown of Napster. Unlike Napster, P2P networks
do not host files on a central server; instead they list available files on individual PCs and
directly connect those computers, which makes the enforcement of copyrights more
difficult. The proposed bill would allow the record industry to “hack” into individuals’
PCS in search of copyright violations. In our model, this type of copyright enforcement
would translate into an increase in the costs of copying that are proportional to user types.
Another response by record labels in face of file-sharing, is to upload the so-called
“spoof” files — containing little or no music — on P2P networks to confuse downloaders.
This practice would increase the expected time of downloading a particular music file
and can be considered as an increase in the uniform copy costs.

The purpose of this study is to construct a model of self-selection with
heterogeneous consumers who choose among three available options: the purchase of
authorized product, the use of an illegal copy with unauthorized reproduction, or no
consumption. In such a framework, we conduct a two-step analysis. In the short-run
analysis, we investigate how the threat of piracy constrains the pricing behavior of the
monopolist. Depending on the relative magnitudes of reproduction and degradation cost,
the monopolist is shown to choose the optimal choice of regimes between limit pricing
and accommodation to copy. We demonstrate that with the threat of piracy the

monopolist’s price is lowered, and usage of an authorized copy is increased in both

 

‘ Responding to piracy of Windows XP operating system, Microsoft announces that Windows XP Service
Pack 1 (and possibly all future updates) will not install with pirated copies.

regimes with positive welfare implications.5 This result provides a sharp contrast to the
common claims of copyright holders, in which the possibility of piracy reduces demand
for a legal copy. We then conduct a comparative statics exercise that analyzes the effects
of increased copyright protection. It is shown that the effects could hinge on how it
affects the two margins of the piracy costs discussed above. The reason is that the
changes in the two margins impact the demand for a legal copy in different ways: the
changes in constant production cost shifts the demand curve in a parallel fashion whereas
the changes in degradation rate induces a pivot change in the demand curve.

In the long-run analysis, we extend the model to allow for an endogenous choice
of the software quality by producer. The existence of piracy creates inefficiently low
quality of the product. Thus, there is potential for increased copyright protection to help
mitigate this inefficiency in quality provision and counterbalance the short-run effects.
Once again, we demonstrate that the effects of increased copyright protection on the
provision of quality depend on how it affects the two margins of the piracy costs.

Earlier papers concerned with the effects of increased copyright protection on
social welfare include Novos and Waldman (1984) and Johnson (1985) among others.
Novos and Waldman (1984) analyze the effects of increased copyright protection in a
model where consumers vary only in terms of their cost of obtaining a copy. They show
that there is no tendency for an increase in copyright protection to increase the social
welfare loss due to underutilization once the cost of obtaining a copy is taken into
account. Our paper, in contrast, allows consumers to vary in terms of their valuations on

the quality of software. In addition, we consider two different types of costs associated

 

5 Choi and Thum (2002) provide a similar framework, if we consider purchasing an authorized copy of the
software as entering the official economy, and making an illegal copy as operating in the shadow economy.

with piracy and shows that the effects of increased copyright protection hinge on how it
affects the two margins of the piracy costs.

Johnson (1985), as in our paper, considers consumers with different tastes, but his
model is of horizontal differentiation and the focus is on the product variety issues. More
importantly, the major difference between his paper and oursr‘is in the long-run analysis:
in Johnson’s analysis software supply responses are modeled along the extensive margin
(the number of software products created), whereas in our analysis supplier responses are
modeled along the intensive margin (the quality of software). In a recent paper,
Belleflamme (2002) analyzes pricing decisions of producers of information goods in the
presence of copying. He assumes a uniform distribution of consumer types in a model of
vertical differentiation and derives similar results as in our paper. Once again, however,
his long-run analysis is along the extensive margin as in Johnson (1985).6

The remainder of the paper is organized in the following way: Section 2 sets up
the basic model and provides a short-run analysis in which we investigate how the
monopolist’s pricing decision is affected by the threat of piracy. We characterize the
pattern of self-selection by consumers and the optimal price for the monopolist. In a
comparative statics exercise, we show that the effects of increased copyright protection

depend crucially on how it affects the two margins of the piracy costs discussed above.

 

6See also Yoon (2002) who considers a similar model in which he derives the optimal level of copyright
protection. Yoon (2002) also assumes that the development cost is fixed in his long-run analysis. The only
measure for the ex ante efficiency with fixed development cost is whether the monopolist develops the new
product or not; the monopolist does not introduce a new product if the development cost can not be
recovered due to weak protection level. With this type of ex ante efficiency measure, the optimal
protection level is characterized by a step function because the incentive for development can be altered
with an infinitesimal change of IPRP. In our model, to have a continuous effect of the increase in IPRP,
we assume that the monopolist’s long-run incentive is to choose the quality of software. Crampes and
Laffont (2002) also analyze the effects of piracy on the pricing policy of a software producer. Their focus,
however, is on the consequences of cost randomness in the decision for piracy and on the risk aversion of
users.

In Section 3, we extend the model to analyze the long-run implications of piracy for

software quality. Section 4 contains concluding remarks.

2. The Model of Piracy: A Short-Run Analysis
Before analyzing the more complex effect of an increase in intellectual property
rights protection (IPRP) on software usage in the short run and development incentive in
the long run, we first develop a simple model of piracy with a monopolistic software
publisher. There is a population of consumers whose total number is normalized to unity.
Consumers are heterogeneous in their value of using the software. Let v denote a
consumer’s gross utility of using the software. The distribution of types is given by the

inverse cumulative distribution fiInction F(v) with continuous density F '(v) S 0 , that is,
F (v) denotes the proportion of consumers whose value of the software is more than v.

To analyze the ex post efficiency effects of piracy, we assume that the software is
already developed and the marginal cost of production is zero. The incentives to develop
new software are considered in section 3. The copyright holder sets the price of the
software p to maximize his revenues. As the consumer’s utility v is private information,

the copyright holder cannot price discriminate and charges a uniform price p.7

Optimal Pricing without Piracy: A Benchmark Case
As a benchmark case, we first consider a situation where the option to pirate copyrighted

work is not available, that is, the consumers’ only choice is whether to purchase or not.

The utility of buying an authorized copy is given by U 3 (v; p) = v — p. We normalize the

consumers’ payoffs from not using the software to zero. Then, consumers whose
valuation of software is more than p will purchase the software.
The purchase behavior of the consumers implies that the copyright holder

maximizes his revenue:

mgx R(p)=p.p(p).

Since the monopolist’s price p is uniquely determined by v, we will find it more

convenient to treat v as the control variable:

max R(v) =v-F(v).

The marginal consumer v * that maximizes the copyright holder’s revenue is implicitly
given by the first order condition:

F(v*)+v*-F'(v*)=0. (1)
We make the standard assumption that the distribution of types satisfies the monotone

hazard rate condition, that is, - F '/ F is increasing:

-F"F+(F')2 > o. (2)
This assumption ensures that the copyright holder’s objective function is quasi-concave

and the second order condition for the maximization problem is satisfied:

2F'(v) + vF'(v) < o .8 (3)

 

7 In a dynamic model, however, the monopolist can price discriminate consumers based on purchase
history. See Fudenberg and Tirole (1998) for such an analysis.
1’Using the first order condition, we can rewrite the second order condition as

2 - F '(v) - F "(v) - F (v) / F '(v) < 0 . The second order condition holds if the distribution F satisfies the

monotone hazard rate condition. This condition is a standard assumption in the incentive literature and is
satisfied by most widely used distributions; see Fudenberg and Tirole (1991, p. 267).

Then, the number of software users is given by F (v*) . The optimal price of the software
for the copyright holder is p* = v*. Note that the optimal price and the marginal
consumer without piracy depends only on the distribution of consumer types F (~) .
Needless to say, the socially optimal price for the software, once it is developed,
is its marginal cost, which is assumed to be zero. Due to monopolistic pricing,
consumers whose types are below v* do not use the software and the deadweight loss is
v..-

given by - deF (x).
0

Optimal Pricing with Piracy

Now we introduce the possibility of using the software through piracy without purchasing
a legal copy. Piracy saves the price of the software for consumers. However, it entails
potentially two types of costs. First, the unauthorized copy may not be a perfect
substitute for the legal copy and typically entail some degree of quality degradation. In
the case of copying with analog technology before the advent of digital technology, for
instance, more iteration of additional copying meant lower quality. Even with digital
copying, the unauthorized copy may lack technical support or access to other resources
offered by the manufacturer. We assume that this cost is proportional to the valuation of
the consumer for the original, that is, the valuation of the type v consumer for the

unauthorized copy is given by (1 —a)-v, where a is the parameter for quality
degradation. Another interpretation is that a represents the enforcement efforts by the

authority. If illegal copiers are caught with the probability of or, in which case the

software is confiscated as punishment, the valuation of using an illegal copy would be

given by (l-a). In addition, we assume that illegal copying entails reproduction cost of c,
which is assumed to be the same across users. Thus, the utility of using an unauthorized
copy is given by UUC(v) = (1 — a) - v —c.9

In order to have a meaningful analysis of unauthorized copying, we restrict our

attention to the parameter regions in which the piracy constraint is binding, that is,

__C <p*:v* (4),
l—a

where v* is defined by (1).10 This condition is satisfied if the degree of quality
degradation 0: and/or the cost of copying c are not too high.

When the piracy condition (4) is binding, the monopolist’s problem is
complicated by the fact that some consumers are better off copying the software given the
monopolist’s price of the software. In response to piracy, the monopolist has two
choices. One option is to limit price the software so that copying is not an attractive
option. The other option is to price the software to sell only to the highest types and

allow copying for intermediate types of customers.

Limit Pricing Regime without Piracy

With the piracy constraint binding (1‘:— < p* = W“), the limit price should satisfy the
— a

following incentive constraint to eliminate the incentives to copy:

 

9 If we let w = a v + c , then UUC (v) = v - W. Hence, we can denote w as the gross copy cost.

'0 If the possibility to copy the software does not constrain the monopolist’s maximization problem, the
marginal type of consumer is given by v“ as defined by (1). The marginal type v* earns zero surplus when
he makes a purchase from the monopolist. If he makes an illegal copy instead, his payoff is
UUC(V*) = (1—a)v*-—c. If c/(l-at) < p* = v*, the surplus from making an illegal copy

exceeds the one from other options. Thus, possibility to copy the software serves as a binding constraint
for the monopolist’s revenue maximization problem.

 

U3(v;p)=v—p2(l—a)v—c =UUC(v) foranyvz (5)

l—a
We observe that U 8 (v; p)— UUC (v) is increasing in v, which implies that if the

constraint above holds for v, then it also holds for any v' such that v' > v. Thus, all we

 

need is that the inequality above be satisfied for v = . This in turn implies that the

l—a

limit price and the marginal type are given by pL = vl‘ = c/(l -—a). Notice that the no

prracy Incentrve constrarnt (5) Is always bIndIng under the assumption 1——— < p* = v *.

Lemma 1. When the piracy constraint is binding, the optimal limit price that prevents

the incentive to copy is given by pl‘ = c/ (1 — a). In this case, the monopolist’s revenue

 

 

is givenby R =pLF(pl‘)= l-ca .Fil—ca)

Copying Regime ( p > pl‘ = c/ (1 - a))
If p > pL = c/ (1 —a) , the no piracy constraint is violated for some v’s that are higher

than but close to vl’ = c/ (1 - a). Each consumer has two different choices for using the
software, which incur two different types of cost. First, when a consumer buys a legal
copy from the monopolist, he has to pay the price (p) and enjoys the full quality of the
software. However, with choice of making an illegal copy, his cost will be the sum of
degradation of quality that is proportional to his own valuation of the software and a
constant reproduction cost. We assume at this time that the parameters of IPRP (or for the

degradation rate and c for the reproduction cost) are fixed.

10

When consumers make their usage decision, they choose the one that yields the

highest net utility. For a given price of a legal copy ( p > pL = c/ (1 — 05)) and the level of

IPRP, consumers’ optimal choices can be divided as follows:

 

 

p - c S v purchase a legal copy
a
—— s v < p _ make an illegal copy
1 — a a
c
v < —— no use.
1 — a

Now the monopolist should take into account that potential consumers have another

option to obtain the software. The monopolist, therefore, maximizes

Max p-F[p—c).
a

 

p—C

 

Once again, we treat the marginal consumer type v = as the control variable:

Max (av + c)F(v).
The first order condition

(av+c)F'(v)+aF(v) =0 (6)
determines the marginal type of consumer i7 , who is indifferent from purchasing an
authorized copy from the monopolist and making an unauthorized copy.11 Therefore,
with the option of making an illegal copy, consumers with low value v < c/ (1 — a) do not
use the software. Those with intermediate value c/(l -a) s v < i7 make illegal copies.

Only consumers with high value v > V purchase legal copies from the monopolist [see

 

“ Variables under the copying regime are denoted by a tilde (t7 ).

ll

figure 1]. We now can compare the monopolist’s pricing behavior with and without

piracy.

Proposition 1. With the possibility of piracy, the price of the software is lowered,
thereby inducing more demand for legal copies. Increase in usage of both legal and
illegal copies under the copying regime brings higher ex post usage for the software.

Proof. Evaluate (6) at v * which is the marginal consumer when no copying is feasible:

a[F(v*)+v*F'(v*)]+cF'(v*) = cF'(v*) <0. Hence, v*>i7.

Under the copying regime, those consumers whose valuation lies between

c/(l —a) and i7 make illegal copies. Therefore, total ex post usage for the software is

unambiguously increased with piracy as shown in figure 1. By being just a threat (limit
pricing regime) or an actual fact (copying regime), piracy has the same effect on the
monopolist’s pricing behavior: the price is lower than the one in the benchmark case. A
more surprising result is that the usage of legal copies increases even in the presence of
copying. Thus, the extent to which legal copies are used is complementary with the
extent of the usage of unauthorized copies.12 The intuition for this result can be found in
the monopolist’s pricing behavior in response to the threat of unauthorized copying. If
there were no price change, that is, at p = p*=v* defined in (1), some of the previous
purchasers of the legal copy will switch to the option of copying with the result of a

lower number of legal copies being sold. Proposition 1, however, shows that the price

 

'2 Our result does not assume network effects between authorized and unauthorized copies as in Shy and
Thisse (1999).

12

reduction by the monopolist (from p* to p = a? + c) not only eliminates the incentives to

switch for the previous buyers but also expands the base of buyers.

Comparative Statics

We now analyze the effects of marginal increase in the intellectual property rights. As
with the previous studies in the literature (Novos and Waldman (1984), Yoon (2002),
etc), we model the increase in the intellectual property rights protection as an increase in
the cost of piracy (w=av+c, see footnote 9), which makes the option of piracy
(U UC (v) = v — w) less attractive. It is shown that the effects can have different
implications depending on which regime the monopolist is operating under and the type

of costs associated with piracy.

Proposition 2. Under the limit pricing regime, both types of an increase in IPRP induces

higher software price and less authorized usage.
Proof. Under the limit pricing regime, we have pL = c/ (1 - a), and qL = F ( pl‘) . If we

take partial derivatives of pL and F(pL ) with respect to c and a respectively, we have

the following results:

ap‘ 1 aFrpL) _ aFtpL) ap‘
— —-—>O, — <0
6c l—a 6c apL 6c

 

L L L L
5” " 2>0,mdM=aF(i)ap <0.
6a (1-0,) 60: 5p 6a

 

 

l3

The intuition underlying Proposition 2 is straightforward. Due to the possibility

of piracy, the monopolist is not able to charge the monopoly price. The maximum price

he can charge under limit pricing is p1” = c/ (1 — a) , which depends on the levels of the
degradation rate (a) and the reproduction cost (c). The marginal increase in IPRP from

either the degradation rate or the reproduction cost provides the monopolist more market

power allowing him to charge a higher price.

Proposition 3. Under the copying regime, as expected, the monopoly price increases
with the strengthening of IPRP. The effects of an increase in IPRP on the usage of
software, however, are ambiguous depending on the types of costs associated with piracy.
Higher degradation rate induces less authorized usage whereas higher reproduction cost
induces more authorized usage [see table 1].
Proof Total differentiation of the first-order condition with respect too:

[20! F '(9’) + a VF"('\7) + cF'(v)]dv = —F'(I7)dc .

Q = - F'(i‘i) < 0
dc IHI

 

where [HI = 2a F '(V) + a VF"('I7) + cF”(v) < 0 by the second-order condition.
Total differentiation of the first-order condition with respect to a :
[2a F '(V) + a VF ”('17) + cF"(v)]dv = —(F('v') + vF’(i7))da .

an? _ -(F(t7)+'r7F'(V)) = L cF'(i7')

_ _ > 0.
da |H| |H| a

 

 

l4

With higher reproduction cost, all consumers face the same increase in the gross
copy cost, which is equivalent to an outward parallel shift in demand for legal copies.
With an increased demand, the monopolist responds with a price hike. The price
increase, however, does not completely offset the initial demand increase with the result
of increased sales. In contrast, if an increase in IPRP is derived from higher degradation
rate, we observe a pivot change in demand that affects the slope of the demand curve for
legal copies. Due to proportional increase in the gross copy cost, higher valuation
consumers are more adversely affected by an increase in the degradation cost. A steeper
demand curve means that elasticity of consumers is lower with more market power.

Thus, the monopolist is more interested in serving only the high valuation consumers.

Welfare Effects of Increase in IPRP in the Short Run

We are now in position to examine the effects of an increase in IPRP on social welfare.
When the monopolist’s optimal choice is limit pricing, it is straightforward to show the
effect of an increase in IPRP on social welfare. As either the degradation or the
reproduction cost increases, making an illegal copy becomes less attractive. In response
to this, the monopolist is able to charge a higher price and fewer consumers use a legal
copy. The increased profit margin is only a monetary transfer from consumers to the

monopolist. Social welfare is reduced as a result of less authorized usage.

Proposition 4. Under the limit pricing regime, both types of increase in IPRP induces

lower social welfare.

15

Proof With limit pricing, the social welfare is identical to the gross consumer surplus

from authorized usage:
00 co
SW(pL) = — j v . F'(v)dv = vLF(vL)+ [F(vwv.
L L
V V

This implies that

2
65W: 0 F'(-—c—)<0and OSW= c F'( c )(0.
ac (l-a)2 1—a 60: (1-003 l—a

 

 

 

If the monopolist’s optimal choice is accommodation of piracy, the welfare

effects of an increase in IPRP depend on the types of costs associated with piracy.

Proposition 5. Under the copying regime, the effects on social welfare of increase in
IPRP depend on the types of costs associated with piracy. Social welfare decreases with
an increase in the degradation rate (a). However, the effects of > an increase in the
reproduction cost (c) on social welfare are ambiguous.

Proof The social welfare can be derived from the sum of the monopolist’s revenue and

the consumer’s surplus:

S W05) = R(5) + (35(5)

= (as + c)F(i‘i) — [(v — a'v’ — c)F'(v)dv - [[(1 - a)v — c]F'(v)dv

C

l-a
= 517(7) + c1:).'F(v)dv - :[[(1 - a)v — c]F'(v)dv .

l-a

16

We examine the effect of an increase of IPRP on social welfare as

 

W = I? -((1- cm7 — curing-’- + ij'(v)dv < 0
6a 60: c
x J a
Y W—j
demand switch (-) copy cost increase (—)
aSW(fn')_~_ _ ~_ mg? V. <0
—dc —[v ((1 a)v C’]F(’)ac+ ch(v)dv>0

 

Y
demand switch (+) copy cost increase (—)
As can be seen from the expressions above, we can separate two different channels
through which an increase in IPRP affects social welfare. The second term in each
equatiOn is always negative and represents social welfare loss due to increase in
consumers gross copy cost caused by an increase in IPRP for consumers who continue to
copy. The first term of each equation represents the demand switch effect between legal
and illegal copies, which induces welfare gain or loss depending on the direction of
demand switches. It decreases social welfare in case of an increase in the degradation
rate (or), since the marginal consumers (7) who were indifferent between the legal and
illegal copies now switch to illegal copies that are produced inefficiently and suffer from
degradation. Taken together, both the demand switch effect and increased gross copy

cost affects social welfare adversely with an increase in the degradation rate (a). In case

of an increase in the reproduction cost (c), however, the demand switch effect is positive

17

since it induces marginal consumers to switch to legal copies as we have demonstrated
earlier. Therefore, the overall effect on social welfare is ambiguous and depends on the

relative magnitude of the two countervailing effects [see figure 2].13

Uniform Distribution Example
We now illustrate our results using a simple uniform distribution that generates a linear
demand curve for the monopolist. This example also allows a closed-form solution for
welfare analysis. Let us assume that consumers’ evaluations for the software are
uniformly distributed over the unit interval as v,- e U [0, 1]. In the benchmark case
without piracy, it easy to verify that the marginal consumer is determined by
v* = p* = 1/2 .14

We now turn to the monopolist’s optimal pricing problem when the piracy
constraint is binding, that is,c S (l—a)/2. The first Option for the monopolist is to

accommodate piracy in which the monopolist sets a higher price and tolerates copying.

In this case, the monopolist’s objective becomes:

Max p(1_p—c).
a

 

p—c
a

as the control variable:

 

Once again, we treat the marginal consumer type v =

 

’3 As can be seen from Figure 2, there is a third effect (total usage change) coming from marginal
consumers c/(l — a) who are indifferent between copying and no consumption. However, these
consumers have zero surplus and the effect on social surplus is of second-order and does not show up in the
equations.

" This would be the case if (1 - (1)/2 < c S l- a . To see this, if we substitute 1!“ = p* =1/2 into the
no piracy condition p < C/ (1 — a ) , the condition is not binding at the monopoly price if we have

(1 - a )/2 < c. If c > 1- a , the gross copy cost exceeds the valuation for the software, which is not a
meaningful case to consider.

18

Max (av+c)(1—v).
The first order condition
a(l—v)—(av+c)= O

. ~ 1 c ....
elds v =—-—— and
yr 2 2a p

=(01+c)

 

, which confirms Proposition 1.

The second option is for the monopolist to eliminate piracy by setting the price

sufficiently low. Since the monopolist should reduce the price until the piracy constraint
is binding, (1 —a )v —c = v — p , the optimal price and revenues are pl” = c/ (1 - a) , and

7:1” = pl” (1 — pL). By comparing profits from each regime, we can conclude that the
monopolist’s optimal choice is to accommodate piracy if 0 < c S a(1-a)/1+a and to
limit price if a(1 —a)/(1+a) < c S (1 -a)/ 2. We can illustrate the monopolist’s

optimal regime change depending on the relative magnitude of IPRP parameters as in
figure 3.

With liner demand and closed form solutions the effect of increased copyright
protection can be shown more clearly in the uniform distribution example. Under the

limit pricing regime, we can verify that both types of increase in IPRP induces higher

software price and less usage. With the optimal choice of price pl“ =[TC—J and
-a

quantity (ql‘ = 1— pl‘) under the limit pricing, we can calculate as follows:

 

 

 

 

L L _
6p ___ 1 >0, aq ___ 1 <0,
6c l-a 6c l—a

L L
61) = c 2>0, and dq = c2<0.
5a (l-a) 6a (l—a)

l9

Under the copying regime, it is observed that the effects of an increase in IPRP depend
on the types of costs associated with piracy [see figure 4]. As we expect, an increase in
both types of costs trigger a higher price but ambiguous effect on demand switch. These

effects are clearly shown as

ip—z-l—>O, 2E]-=-—1—>O,-a£=-l—>O, mdfl=i<0.
6c 2 6c 20:

6a 2 6a 40,2

For the last part of the short-run analysis, we examine welfare effects of an
increase in IPRP. If a(1—a)/(1+a) < c S (1-a)/2, we identify that the monopolist
prefer to eliminate piracy by lowering the price; in other words, the possibility of piracy
enforce the monopolist to set a lower price at p1” = c/ (1 —a). It is straightforward to

show the effect of an increase of IPRP on social welfare. Consumer surplus and the

monopolist’s revenue under the limit pricing are computed as

 

 

 

 

1

follows: CSL = I (x—1 c )dx, and fl'L = pL(l— pl’). Defining social welfare as

—a

C
E
L L L 1—2a+a2—c2

SW =CS +7: = 2 we observe that

2(a—l)

L _ L 2
65W ___ c2<0,and6SW = c 3(0.
56 (a—l) 60: (a-l)

If 0 < c S a(1- a)/1+ a , the monopolist is in the copying regime and the welfare

effects of an increase in IPRP depend on the types of costs associated with piracy. The

consumer surplus and the monopolist’s revenue in the copying regime are given by

20

K2

 

a 1 ~
CS(?5’)= l<<1-a)x—c)dx+ l<x~p>dx.andir‘=fi(I—”;C).

p-c
l-a a

l c.

We then calculate social welfare as SW (25) = CS (p) + E = ————— +

 

With positive demand switch and negative total usage change, the effect of an increase in
IPRP with higher reproduction cost is uncertain. However, with negative demand switch
and negative total usage change we are able to pin down the effect of an increase in IPRP
with higher degradation rate. These results can be illustrated by the following two partial

derivatives [see figure 5].

2 2
=—-1-+ c 2—302<0,and
cisfixed 8 2(1-a) 8a

OS W
6a

 

 

6S W
6c

1 C 3C 15
+—.
4 l-a 4a

 

 

 

a is fixed

 

 

, let 6 be the critical value, which satisfies aSW = 0 and

To determine the sign of aSW 6
c

 

 

 

. a 1— a . . .
we have c = -(———-2 . Hence, If c < c , we have < 0. Otherwrse, we observe
3 + a dc
BS W
> 0.

0c
.5 . . . a (1- a) .

Smce we have parameter region for the copy regime such as c S —-1—- , we can verify that

+ a

OS W
— < 0.

6a

21

3. Copyright Protection and Incentives to Create

Up to now, we have analyzed the effects of an increase in copyright protection on
pricing and the incentives to pirate once the software has been produced. In this section,
we analyze the long-term effects of an increase in IPRP on the incentive to create. To
analyze this issue, we introduce the cost of creating the software and endogenize the
quality of the software. Let 0 measure the quality of software that is created at cost
C(0) (with C'(6) > O, C"(6) > O). The quality of the good enters positively into the
utility of consumers; the utility of consumer of type v is 0 - v.

We consider now the long-term effects of piracy in which the monopolist decides
not only on the pricing of the software but also on the quality of the software. We
continue to assume that the marginal cost of software is fixed at zero regardless of the

quality of the software once it has been developed.

Software Quality without Piracy: A Benchmark Case

Before analyzing the monopolist’s quality provision with the possibility of piracy, we
start with the benchmark case, in which consumers face a monopolistic software
publisher but do not have the opportunity to make an illegal copy. Hence, the
consumers’ only decision is whether to purchase or not. Since the consumers’ payoff
from not using the software is zero, consumers with non-negative net utilities purchase an

official copy: B-v- p 2 0. Given the purchase decision of consumers, the copyright

holder selects a price and a level of quality that maximize his profit:16

max nsdov-F(v)-C(6).
v,0

22

The first order conditions

%=0~F(v)+6-v-F'(v)=0 (7)
91—v-F(v)—C'(0)—0 (8)
aa- _

determines the marginal consumer v * and the monopolist’s optimal level of quality 0 *.

Proposition 6. Given the number of software users F (v*) , the quality of the software is

sub-optimally low.

Proof Given the number of software users F (v*), i.e. all consumers of type v2v*

buying the software, the socially optimal quality of the software can be found by solving
00
max — I6-v-F'(v)dv—C(t9).
0 II
V
The first order condition

00
— v - F'(v)dv - C(eop’ ) = 0

VIII

determines the socially optimal level of quality 00’” . Integration by parts of the first term

co
on the left hand side shows - v-F'(v)dv2v*-F(v*). This implies that
V‘

00901”) 2 own as we have v*-F(v*) = C'(9*) from (8). Therefore, the level of the

software quality provided by the monopolist is sub-optimally low: 6°” 2 6 *.

 

'6 Again, we use v as a control instead of p.

23

The intuition for this result is the following. The choice of 0 "' by the monopolist
is determined by the marginal type v“. An increase in the benefit for the marginal
consumer is captured via higher price of the software by the copyright holder. The effect

on the inframarginal consumers is irrelevant for the monopolist as he cannot price

discriminate among consumers. In contrast, the second-best level 60’” is determined by

the aggregate (or average) benefits for all consumers with values [v*,oo). As the average

consumer’s marginal valuation for the software quality is higher than the one for the
marginal consumer, the second-best level of quality of the software exceeds the one

provided by the monopolist.l7

Software Quality with Piracy

Now we turn to the monopolist’s choice of the software quality when he faces piracy:
how does the potential threat or actual piracy affect the monopolist’s choice of the
software quality? To answer this question, we use the previous optimal pricing
framework with the monopolist’s choice of the software quality. We still assume there
are two different types of cost associated with piracy: the constant reproduction cost and
the proportional degradation rate. The degradation rate now affects the valuation of the

type v consumer for the unauthorized copy as (1 — a) - t9 - v. Thus, the utility of using an
unauthorized copy is given by U UC (v) = (l - a) - 0 - v - c .
In order to have a meaningful analysis of unauthorized copying, we have the same

restriction to the parameter regions, in which the piracy constraint is binding, that is,

 

’7 This point is closely related to a monopolist’s choice on product quality; see Spence (1975) and Tirole
(1988, pp. 100-102).

24

——1 " <p*=6*v* (9).
—a

where 9" and v* are defined by (7) and (8). This condition is satisfied if the degree of

quality degradation (a) and/or the cost of copying (c) are. not too high. Therefore, with
the binding constraint (9), the monopolist practices either limit pricing or accommodation

to piracy.

Software Quality under the Limit Pricing Regime
With the piracy constraint (9) binding, the monopolist faces the following constrained

profit maximization problem:
pL
Max ”L = pLF(—6 )-C(l9)

Subject to

(l-a)0v—cS9v—p

. . . . . . c
SInce the constraint Is always bIndIng under the assumptron -1— < p* = 6 * v* , the
— a

 

optimal price p!“ =1Tcg’ and profit is IZ'L =(fi).F[(1-:z)6)_c(6)°

The monopolist now determines the optimal choice of the software quality with the

optimal limit price as following:

MaxrrL=( c )F[ c J-CW).
a l-a (I—a)e

The first order condition

61L__62_Fr __c__
59 (l—cz)‘262 (1‘609

 

 

)-C'(6)=0 (10)

25

determines the monopolist’s optimal choice of software quality.

Proposition 7. Under the limit pricing regime, the monopolist chooses a lower level of
quality than the one without piracy.
Proof Let us evaluate the first order condition (10) at 0* which is the level of quality

without piracy.

drtL
66

 

=_ c2 F,[ c )_C,(6,)
9.. (1_a)2(9.)2 0-609"

 

We know that

 

_ CZ .F,[___c J < _____c .F[————c J < v * F(v*)
(l—a)2(6*)2 (l-a)6l* (1—a)l9* (l-a)6*

The inequalities above follow from the fact that vF (v) is a concave function which is

 

maximized at v* and our assumption that < p*=6*v*.‘ Thus, we have

l—a

L
2L6 <v*F(v*)—C'(9*)=O,which implies that 61' <0*.
0*

Software Quality under the Copying Regime

Under the copying regime consumers compare the payoffs from buying an authorized
copy [0 - v- p] or making an unauthorized copy [(1—a)-6-v—c ]. Given the purchase
behavior of consumers, the monopolist maximizes his profit:

magt Ff=(a-9-v+c)F(v)-C(0).

)

The first order conditions

26

%=(a0v+c)F'(v)+a6F(v)=0 (11)

~

6n , _
BE—avF(v)—C(6l)—0 , (12)

again determine the marginal consumer V and the software quality 5 .

Proposition 8. Under the copying regime the existence of piracy leads to a further
underprovision of the software quality but more authorized usage.
Proof Evaluating (11) at v = v "‘ yields (a 0 v * +c)F'(v*) + a 0F(v*) = cF'(v*) < 0.

Hence we have? < v*. Also, evaluating (12) at v = v* yields — v* F(v*)(1- a) < 0 and

therefore 5 < 0 * .

The intuition underlying this result is the following. The choice of 5 by the
monopolist is determined by the marginal type '17. At the development stage of the
software the monopolist expects that the marginal consumer is not v * but 7 when there
is piracy. Given this anticipation, the optimal choice of the software quality should be

lower than the one from the benchmark case. As seen from Proposition 6, the software

quality provision by the monopolist is already sub-optimally low (6* < 9019’) even
without the threat of piracy. The existence of piracy aggravates this inefficient provision
of the software quality in both regimes. Our result thus lends theoretical support for the

claim that piracy reduces the incentives to develop new software.

Comparative Statics

27

We now turn to analysis of the effects of marginal increase in IPRP on the monopolist’s

development incentive.

Proposition 9. Under the limit price regime, an increase in IPRP on both margins induce

higher software quality and less authorized usage.

Proof We can rewrite (10) as c2F'(v) + (1 - a )2 9 2C'(6) = 0. By totally differentiating
the first-order condition, we have
2cF’(v)dc +(1— (1)20 2C'(0)d6+ (1 — 00220 C’(6)d6= 0.

d6 _ 2cF'(v)

___ >0.
dc (1— a)2 6[6 0(0) + 20(0 )1

 

By totally differentiating the first-order condition, we have

— 2(1— a )HZC'(6)da + (1 — a)2 62C'(6)d6+ (1 - (1)2 26 c'(e)de= 0
d6 = 2(1— a)6 20(9)

_ _ >0.
da (1— a)2 are 0(0) + 20(6 )1

 

Also we can easily verify that

 

 

 

 

_ >O,and
dc dc (l-a)0
l . i
Q_ (1-a)0 c )0
do: da (l—a)26

28

The intuition underlying Proposition 9 is straightforward. In the limit pricing
regime, the monopolist lowers his price until the constraint (1—a)0v—c S Bv— p is
binding to eliminate piracy. The maximum price he can charge under limit pricing is
pL = c/ (1 — a), which depends on the relative level of the degradation rate (a) and the
reproduction cost (c). Increases in IPRP from either the degradation rate or the

reproduction cost induce less authorized usage, which is equivalent to higher valuation

from the marginal consumer v1”. This induces the monopolist to provide a higher

quality.

Proposition 10. Under the copying regime the effects of increase in IPRP depend on the
types of costs associated with piracy. Higher degradation rate induces higher quality and
less legal usage. In contrast, higher reproduction cost results in lower quality and more
authorized usage.

Proof See Appendix A.

Table 2 summarizes our results. Since the monopolist’s quality provision is
determined by the marginal consumer’s valuation for the software, the effects of increase
in IPRP depend on the change of the marginal consumer, which is different according to
types of costs associated with piracy. With higher reproduction cost, all consumers face
the same increase in the gross copy cost, which is equivalent to overall demand increase
for the monopolist. Hence, the monopolist benefits from higher demand by charging a
higher price, yet increasing sales at the same time. Facing the marginal consumer’s lower
valuation, the monopolist has less incentive to provide higher quality. In contrast, if an

increase in IPRP is derived from higher degradation rate, we observe proportional

29

increase in the gross copy cost and comparatively more market power for the monopolist.
With increase in market power, the monopolist charges a higher price by focusing on
high valuation consumers. Responding to the marginal consumer’s higher valuation, the
monopolist has more incentive to supply higher quality. In the Appendix, we
demonstrate our results by using an example with uniform distribution and quadratic cost

firnction.

4. Concluding Remarks

In this paper, we develop a simple model of piracy to analyze implications of
increased intellectual property rights on the short—run and long-run resource allocations.
In a model of self-selection with heterogeneous users, we show that the consumers’
option to use illegal copies constrains the copyright holder’s ability to charge a monopoly
price. Consequently, the possibility of piracy leads to more usage of legal copies. In this
sense, the presence of unauthorized copies acts as a complement to the usage of legal
copies rather than a substitute.

To analyze the effects of an increase in IPRP more precisely, we consider two
types of costs associated with piracy, the type-independent reproduction cost and the
type-dependent degradation cost. We provide a theoretical framework to show that the
effects of piracy depend crucially on the nature of piracy costs. In particular,
strengthening IPRP in the form of an increase in the degradation cost supports the
conventional wisdom on IPRP. It reduces social welfare in the short-run by providing the
monopolist with more market power, which results in both negative demand switch and

total usage change. In the long-run, the monopolist facing a higher marginal consumer

30

type has more incentive to provide higher quality. Thus, there is a trade-off between
short-run and long-run efficiency. In contrast, an increase in the reproduction cost,
induces more authorized usage of the software in the short-run. Even though an increase
in IPRP with higher reproduction cost reduces the total usage of the software, more
consumers obtain the software from the monopolist with more efficient technology.
Therefore, an increase in the reproduction cost may increase or decrease social welfare in
the short run. Moreover, due to the marginal consumer’s lower valuation for the
software, the monopolist has less incentive to provide higher quality in the long-run.
Thus, we cannot rule out the case where an increase IPRP reduces social welfare both in
the short-run and long-run. The results in the paper thus suggest that any policy
implementation of IPRP should pay more attention to how the policy change will affect

the two margins of piracy costs, not just the overall piracy costs.

31

References

Belleflamme, P., “Pricing Information Goods in the Presence of Copying,” Mimeo,
Department of Economics Queen Mary, University of London, June 2002.

Choi, J .P., Thum, M., “Corruption and The Shadow Economy,” CESifo Working Paper,
No.633 (2), 2002.

Crampes, C., Laffont, J ., “Copying and Software Pricing,” Mirneo. IDEI Working Paper,
June 2002.

F udenberg, D., Tirole, J ., “Upgrades, Tradeins, and Buybacks,” Rand Journal of
Economics, Summer 1998, 29, pp. 235-258.

F udenberg, D., Tirole, J ., Game Theory. Cambridge, MA: MIT Press, 1991.

Johnson, W.R., “The Economics of Copying,” Journal of Political Economy, February
1985, 93, pp. 158-174.

Nordhaus, W.D., Invention, Growth and Welfare: A Theoretical Treatment of
Technological Change. Cambridge, MA: MIT Press, 1969.

Novos, I.E., Waldman, M., “The Effects of Increased Copyright Protection: An Analytic
Approach,” Journal of Political Economy April 1984, 92, pp. 236-246.

Shy, O., Thisse, J .. “A Strategic Approach to Software Protection,” Journal of Economics
and Management Strategy, Summer 1999, 8, pp. 163-190.

Spence, A. M., “Monopoly, Quality and Regulation,” Bell Journal of Economics, 1975,
6, pp. 417-429.

Tirole, J ., The Theory of Industrial Organization, Cambridge, MA: MIT Press, 1988.

Yoon, K., “The Optimal Level of Copyright Protection,” Information Economics and
Policy, September 2002, 14, pp. 327-348.

32

Appendix A: Proof of Proposition 10

By totally differentiating (11) and (12), we have

 

 

921 52” ldv' - 627t-
6v2 avaa F12 Me
627: 62;: 1Q _ 627:
am 592$ch _ aeac]

 

 

 

 

 

By using Crarner’s rule, we have

 

 

 

 

 

 

_a% 52;: 622: 62a
2 __
fé’.__1_ avac magma—La. avac
dc lHl — 62” 5271’ dc IHI 627: — 627:
6966' 502 aeav am
6 7t 62/: 62a 2
where |H|=——2-——2— —— is the determinant of the Hessian matrix with |H|>O
av 69 W69 .

by the second-order condition for maximization.

fl = _1_ r tr 18
dc W (F (v)C (0)) < o.

£2=L[___C(F:"»2]<o.'9

 

 

 

2 2 2
'8 It canbe easily verified that 6—” = F'(v) < 0, _5__7t_ = -C"(9) < 0, a n = 0, and
avac 59 2 696C
2 r
il=avF'(v)+aF(v)=-CF (V) >0.
Oval? 9

33

By totally differentiating the first-order conditions, we have

 

 

 

 

 

6—21 527’ Pdv- P 527! -
5.2 we 21; Ma
62/: 627: 161 _ 627:
am angdal _ 59an

 

 

By using Cramer’s rule, we have

 

 

 

 

 

_ 627: 627: 9:7:
2
fl-ldvdadvad (1112—15,,
da IHI— 627! 627! dd IHI 6271:
696a 602 aeav
391—»in C'(0)+3F(v)]>02°
da |H| t9 '

d6 1 627: c2 2.
da Till??- (—vvF())+a—2—{F(v)} 2]”.

_ddda

627:

 

 

 

 

 

 

 

 

 

 

 

 

 

2 2 2
'9 It canbe also easily verified that, 9—75<0, a It =0, 2—fl;=F'(v)<0,and
6v2 666C dvac
2
-a—”-=avF'(v)+aF(v)=—CF(”)>0
666v
2 _ . 2 2
20Wehave a fl = CFO.) >0 L: —C(9)< <0 6 fl =vF(v)>0,and
6a a 592 666a
2 r
__6 fl =avF'(v)+aF(v)=—CF(V)>0
6v66 6
2 2 2 _ .
21Wehave 6 ”<0, 0 ” =vF(v)>0,—a—fl= CF(v)>0,and
avz 666a avaa a
2 r
a ” =vF'(v)+F(v)=-CF(V)>O
606v a6?

34

Appendix B: Uniform Distribution Example of the Software Quality

We now assume consumers’ valuation for the software is unifonnly distributed as

v,- e U [0, 1]. To make our analysis more tractable, we also suppose that the monopolist’s

2

cost of quality provision is given by C(61) = $6 , where k is a cost parameter.

With uniform distribution we can easily verify Proposition 6 that the monopolist’s
optimal choice of the quality provision under the benchmark case is suboptimally low.
Since the consumers’ only decision is whether to purchase or not, the monopolist has the

marginal consumer whose valuation v* = p /6. Given this arrangement, the monopolist

maximizes his profit:

Maxrr = 0v(l-v)—£t92.
v,6 2

The first order conditions

aEVI-r-=t9—26lv=0 (A1)
67:
5=v(l-v)—k6=0 (A2)
determine v“'=l and 0*=—l—.
2 4k

Socially optimal level of quality can be derived by maximizing the aggregate valuation of

l
consumers between [1/2, 1], which is Max I Bvdv- £02 . We have 60’" = 5;, which
1/2

is 9 OP‘ 2 e * .
Now we turn to the monopolist’s optimal choice of software quality with piracy.

The monopolist’s choice depends on how he responds to the threat of piracy. With two

35

margins of IPRP [degradation rate (a) and copy cost (c)] the monopolist has two

22

different strategies to choose. First, we observe that the monopolist maximizes the

constrained profit under the limit pricing regime as following:

L
Max rrl‘ =pL 1—£—— -£62
6 2

subject to

(l-a)6v-cS9v-p

 

 

The optimal Price pL =—c——, and profit is IIL =( c j l- c ~502. The
l—a l—a (1—a)l9

monopolist then chooses his optimal choice of quality by

MaxrtL=( c )1- c -£62
a l-a (l—a)6 2 '

The first order condition

 

 

arr _ c2

———————k6l=0 (A3)
59 (l—cz)26l2

determines the optimal level of software quality for the monopolist. If we valuate the

first-order condition at 0* = 21; , we can verify that under the limit pricing regime, the

monopolist chooses lower level of quality as the one without piracy.23

 

22 The consumers’ optimal behaviors are the same as the short run case.

 

l 1
2’ With our assumption < p* = 9 * v* =§ , we can verify the sign of (A3) at 9* = E as

l—a
2
16k2 6 —l=16k2[ c +—1-)( c ——1—)<0
(l—a)2 4 1+a 8k l+a 8k

36

 

 

 

For the last case where the monopolist chooses to allow piracy, the marginal

 

consumer who is indifferent between buying and copying is given byv = p :96. With
a

facing demand of 1- 1‘52 , the monopolist’s profit maximization problem is
0:

Max (a6 v+c)(1—v)—1;-02.

The first order conditions

%—:f-=a6(l—v)—(a0v+c)=0 (A4)
?£-ev(1-v)—ka-o (A5)
66' _

a6—c_l_ c
20:6 2 2al9’

av(1 - v)

 

which is '17 < v"‘. Also, if we evaluate 5 =

 

determine 1'7 =

at v*=-1—,wecanverify 5:1«9‘2
2 4k

The effect of increased copyright protection on development incentives can be
shown more clearly in the uniform distribution example. By totally differentiating (A3)
we can show both types of increase in IPRP induces higher software quality and less
authorized usage as the following:

C

 

 

 

 

 

 

d( )
g9” 2ck >0 fl_ (l—a)l9 _ 1 >
dc 6(1-a)29 2 ’ dc dc (1-a)t9 ’
c
d6 26) dv d((1-a)6) c
—— = > 0 , and — = = > 0.
da 3(1— a) da da (1- a)2 g

37

Moreover, we can easily verify the effects of increase in IPRP under the copying regime:
higher quality and less official usage with increased degradation rate, and lower quality
and more authorized usage with increased reproduction cost. By totally differentiating
(A4), (A5) and using Cramer’s Rule we can present a simplified version of proposition
10 as follows:

dv 1 2 d0 1

_.-_—_——— O, —=-— 1—2 0,
d. lHl[ k“ dc IHIW ”’1’
§§=TIII—l(1—2v)[%+av(l—v)]>0,and
5%=fia9[2v(l-v)+(l—2v)2]>0.

38

Table 1.

Comparative Statics Results in the Short Run

 

 

 

 

 

 

Benchmark Limit Pricing Cgpying Regime .
The monopolist’s v * vL (v* > vl‘) V (v* > if)
. . * ~ *
optimal chorce 12 pL ( pL < p”) p (p < p )
L L g: < O and
. . c
Anrncrease In the N/C 5" >0 and 5P >0 ~
reproductron cost ac dc E > 0
6c
An . . th 6 L L B— > O and
‘ncreafe ‘“ 8 MC ——" > o and p > o a ..
degradation rate a a _6_P > 0
6a

 

 

 

 

 

39

 

Table 2.

Comparative Statics Results in the Long Run

 

 

 

 

 

Benchmark Limit Pricing Copying Regime
Th 1' t, v“ vL(v*>vL) 370,537)
e monopo IS 5 ,.. L L ~ ~ < at:
optimal choice Z * p (p < p at) E (5 p3
6L(6L<6..) 9 (6<6)

- - L L 6" d5
Anrncreasernthe N/C 6v >Oand d6 >0 —v<0and—<0
reproductIon cost a c dc a c dc

. . L L "'
Amncmat’e‘“ the MC —a” >0and L9 >0 2[>0 and fl>0

degradation rate a a da 6a da

 

 

 

 

40

 

No use Copy Buy

l—a i

V*

(3.-
<1 _—

 

Figure 1. Consumers’ Choice under Copying Regime

41

total usage change the copy cost increase demand switch
A

 

 

 

 

 

 

 

 

l f—‘r h I
I No use CI I Copy I r Buy I
l — a V
(a) Welfare effect of higher reproduction cost
total usage change coov cost increase demand switch
I I
I No use c I Copy TBuy I
V

l—a

(b) Welfare effect of higher degradation rate

Figure 2. Welfare Effect of the Two Margins of Piracy Costs

42

 

N O
PIRACY

LIMIT
PRICING

COPYIN
REGIME

Figure 3. The Monopolist’s Optimal Choice

 

 

43

 

 

 

 

 

 

 

(b) The effect of the degradation rate increase

Figure 4. The Effects of an increase in IPRP with Linear Demand

SW

 

 

 

 

I
I
I
: SW
I
I I
I I Rm)
I
' I
' I
' I
I J :
Copying 1'1th No piracy C
regime P1101118
(a) The effect of increase in the reproduction cost
SW 4 I
I
I
I
I | SW
l I
I I R(P)
I I
I I I
I | l
I I
I I I

 

 

Limit Copying Limit No piracy
pricing regime pricing

(b) The effect of increase in the degradation rate

Figure 5. Welfare Effects in Uniform Distribution Example

45

H

CHAPTER2

THE OPTIMAL NUMBER OF FRANCHISES WITH APPLICATION TO
PROFESSIONAL SPORTS LEAGUES
1. Introduction

In recent years many issues about professional sport leagues have drawn
economists’ attention; the professional player’s labor market, revenue sharing, relocation
of franchises and public finance of stadiums and increasing ticket prices.“ These
peculiar phenomena are originated from the characteristics of professional sports
industry. One of the most important aspects of the professional Sport leagues is their
monopoly, or cartel status. For decades, since player movement was restricted by the
reserve clause, the leagues enjoyed absolute control over players. Even the control over
the labor market has weakened, the leagues have developed more extraordinary control
over the rest of professional sport leagues.” As the salary of players has been increased,
the leagues are looking for another sources of revenues. They played strategic games
with local governments about relocation of teams unless the local government provides
subsidy for a new stadium or renovation for old stadiums. They increased ticket prices
from new stadiums or renovation of old stadiums with public finance.

This paper constructs a model regarding a league cartel’s optimal choice of the

number of franchises and ticket pricing. The innovation in this paper is to distinguish

 

2‘ See Cairns et al (1986), Fort and Quirk (1995), Kahn (2000), Vrooman (2000) for excellent survey in the
sport literature.

2 Starting in 19705, athletes in the four major sports began to gain some degree of freedom of movement
by inu'oducing some form of free agency. After serving a team for a certain period, a player can be a free
agent, in which he can sell his services to the highest bidder and, as a result, salaries have been increased.
However, even with free agency there remain residual restrictions on player movement and open bidding,

46

two types of cartel associated with its control over franchises’ ticket pricing and to Show
the optimal number of franchises depends crucially on the nature of a cartel. To
comment briefly on the two types of cartel, we first assume there is a cartel with full
collusion in which it has absolute control over the number of franchises as well as ticket
pricing. For example, we can think of an exclusive territorial franchise that is assigned to
the owner of each member team in the league.26 In this case a cartel with full collusion is
able to determine the number of franchises and enforce franchises not to undercut the
ticket price. The second type of cartel we consider is semi-collusive cartel in which it
controls only the number of franchises and ticket pricing is independently determined by
each franchise in non-cooperative behavior. In the first stage the league cartel selects the
number of franchises with consideration there exists trade-off between reduction of
distance cost and increase in fixed cost. On the other hand, if the league cartel is not able
to prevent fi'anchises to cut their ticket below the collusive level, any franchise has an
incentive to deviate. As one of fianchises undercuts ticket price given the rest still stick
to the collusive price, the franchise’s profit will increase by taking customers away from
his neighboring franchises. It is because demand of each franchise is limited by the
league cartel to maximize joint profits. Since the franchise sells his ticket at lower price
to inframarginal consumers to increase ticket sales, for the league cartel it will reduce
joint profit. However, the semi-collusive league cartel is capable of choosing the optimal

number of franchises. It should be the case in which the league cartel increases the

 

such as initial assignments of players to particular teams and required years of service to reach free-agent
Status.

2" In the NFL, for example, a team’s territory is that contained within a seventy-five-mile radius of the
team’s home field.

47

distance between franchises by choosing smaller number of teams until each franchise
becomes a local monopoly.27

The purpose of this study is to analyze the cartel’s optimal choice of the number
of franchises with adaptation of a‘ la Salop’s (1979) circular city model. In such a
framework, we conduct two-step analyses. In the first part of analysis, we investigate
how the degree of control over franchises determines the league cartel’s optimal choice.
Depending on the degree of control, the league is shown to choose different number of
franchises, and we compare the outcomes to the socially optimal and free entry ones.

The second part of analysis examines the league’s strategic advantage of leaving a
few cities vacant, which will be used as a leverage to exploit more consumer surplus. To
serve this purpose, we construct a model with finite number of separated markets. In
each market a franchise operates as a local monopolist and does not compete with one
another to attract consumers from neighboring franchises. With a bidding mechanism
designed to maximize the league’s joint profit, the optimal choice of the number of
franchise is shown that the league does not provide franchises to cover the entire markets
and rather leaves a few cities vacant, which can be used as a leverage to receive subsidy
fi'om state and local governments. Leaving a few cities without a franchise team makes
the vacant cities want to bid for a team.28 In fact, it explains one of the most important
issues in professional sports league; why do local and state governments pay for stadiums
while franchises receive all or almost all of revenues? Beside the fact that the league

already uses the most basic aspect of monopoly, which is to restrict the quantity supplied

 

27 In the case of Korea Baseball Organization (KBO) the ticket price was set by the league until 2002.
However, in the beginning of 2003 season, each franchise is able to determine own ticket price schedule.

48

to increase ticket price, now the league is able to extract more consumer surplus from not
serving the entire markets. By doing this, the league makes teams enable to extract
subsidies from communities that might otherwise enjoy considerable surplus from a
hosting a franchise even they charge monopoly price.

Previous papers concerned with the optimal choice of number of fianchises in
professional sports leagues include Vrooman (1997b) and Fort and Quirk (1995) among
others. Vrooman (1997b) analyzes the optimal size of a league explicitly on analogy of
Buchanan’s (1965) theory of clubs. He Shows that if each franchise has an interest in
maximizing league’s total revenue, franchises should expend to the point in which
average revenue of franchises is maximized. Also, the optimal number of franchises is
smaller than the socially optimal choice, which maximizes total franchises revenue. Our
paper, in contrast, allows two different types of cartel according to the control over
franchises and compares the outcomes in both scenarios to the socially optimal and free
entry outcomes.29

Fort and Quirk (1995) also provide historic evidence of the league’s expansion
choice with the threat of entry of a new league. However, there is no theoretical
framework to explain the mechanism of the expansion choice or the optimal choice of the

league. Our paper, in contrast, is able to provide a theoretical framework by adopting

Salop’s circular city model.

 

2’ In the case of Major League Baseball, the vacant cities would be Washington DC, Las Vegas,
Sacramento and Portland, Oregon even these cities have enough demand for a Major League Baseball
team.

29 Cyrenne (2001), as in our paper, compare the non-cooperative outcome to the socially optimal outcomes.
However, he compares the optimal number of games in a season, not the optimal number of franchises
according to the consumers’ both the absolute and relative quality of game.

49

The remainder of this paper is organized as follows. Section 2 sets up the basic
model and analyzes the two-stage game of the complete and intermediate league cartel, in
which the optimal number of franchises is determined. .1 compare it with the socially
optimal number of franchise and one from the free entry case. In section 3, I provide a
model in which it analyzes the mechanism of relocation game of the league. Section 4
contains concluding remarks. In appendix, I extend the analysis to the case where the
average quality of each franchise is inversely related to the number of franchises due to

diluted talent pool.

2. The Optimal Number of Franchises

To examine the league cartel’s entry decision with differentiated product, we use
the circular city model a‘ la Salop (1979). Fans are located uniformly on a circle with a
perimeter equal to 1. Teams are located equidistant from each other,that is, if there are n
franchises, the distance from one team to the next one is l/n . The location of fans in the
circular city model represents their fan royalties for an ideal team, suffering disutility
from choosing a variant that differs from their ideal. Fans want to buy one unit of the
good, such as a seasonal ticket, and have a cost per unit of distance t. Their reservation
value for the ticket of their ideal team is given by v. They will buy a ticket from the team
that offers the lowest generalized cost (ticket price + transportation cost) if it does not
exceed their reservation value. To analyze the issue of the number of fianchises, we
assume that there is a fixed cost F when a franchise decides to enter the league. In

addition, each franchise faces an identical marginal cost c of serving consumers.

50

Therefore, franchise i’s profit is (p,- —c)q,~ - F if it enters and sells to qi consumers at

the price of p,- , and 0 otherwise.

To facilitate the analysis below, we first consider the optimal pricing problem for
a local monopoly that does not face any competition as a benchmark. If a monopolistic
franchise charges a price of p, the marginal consumers who are indifferent between

buying a ticket and not buying are located at the distance x = (v— p)/t away from the
franchise. Thus, the demand for the local monopoly is given by 2x = 2(v — p)/ t. This

v + c. The demand for

 

implies that the monopoly franchise i sets ticket price as p'" =

2
monopoly is given by q’" =¥ and its profit is It“ = (v 2:) —F . To have a

 

meaningful analysis, we need to make the following assumption to ensure that the local

monopoly is profitable.

Assumption 1. v - c > JZtF

We now analyze two cases depending on the degree of the sports league’s control

over the conduct of franchises.

Cartel with Full Collusion

Consider a situation where the cartel has complete control over franchises, that is, the
cartel chooses the number of franchises in the first stage and franchises coordinate their
prices to maximize their joint profits in the second stage. For analytical simplicity, we

ignore the integer constraint and treat the number of franchises (n) as a continuous

51

variable. With the assumption of continuous n and assumption 1, it is obvious that the

whole market will be covered in the case of full collusion.

Lemma 1. A critical consumer who is indifferent between purchasing from team i and

purchasing i ’S closest neighbor does not get any consumer surplus.

Proof Suppose not. Then, the cartel can increase the prices of both franchises by the
amount of the critical consumer’s surplus and can increase the total profit since there will
be no change in the amount of demand for both franchises.

With the help of Lemma 1, we can easily calculate the optimal number of
franchises for the fully collusive case. We proceed by backward induction. In the
second stage without a threat of price cut by its neighbor fianchises, each franchise

charges the maximum price given the market shares. Since franchise i sets price such

-pf

 

. . ... v . . . .
that an Indifferent consumer xf = rs located at the end of hrs temtory, prrce and

demand for franchise i is

pf =v——t—- and qf =236f =—1-.
2nc nc

Profit of franchise i is given by Irf =(pf —c)q,~c —F =(v——£—;-c)ic—F. Once
2n n

franchises choose their collusive price in the second stage, the cartel select the optimal

number of franchises. The fully collusive cartel chooses n‘ such that

 

Max ncrric =nc[(v— -c)—1——F]. (1)
"C 2nc nc

52

Thus, the optimal number of franchises for the league with full collusion is nc = 1’21}; .

Semi-Collusive Cartel without Price Control
We now consider a semi-collusive league cartel that does not have a complete control
over franchises’ pricing behavior. It is only capable of choosing the optimal number of

franchises in the first stage. By considering the second stage first, given the number of

franchises n“, each franchise faces demand of q,“ = %(pj-c +-Lic—— pic) and profit of
n

franchise i is given by

1 t
are = <pr —c)q.=‘c -F = (pic -c);(pj-" +—,c-— pin-F .3" (2)
n

. . . t .
Therefore, each franchrse sets hrs prIce as p“ = c+—S—c. In the first stage, the semi-
n

collusive league cartel should choose the optimal of franchises n“ so that it maximizes

Its jornt profit, where the jornt profit Is grven by II“ = nrrf’c = 7—nscF . The first
it

order condition with respect to n“, however, is negative for all positive nsc, implying
that reducing the number of franchises increases the joint profit. There are two reasons
for this; it alleviates price competition among franchises and reduces the aggregate fixed
cost. It means that the semi-collusive league cartel is able to increase the joint profit by
reducing the number of franchises. We thus conclude that the semi-collusive league

cartel increases distance between franchises by choosing smaller number of teams until

 

sc . . . .
3° n denotes the number of franchrses In an rntermedrate league cartel case.

53

each franchise becomes local monopoly. More precisely, the semi-collusive league cartel

chooses the optimal number of cartel as —:;— = q'" = VIC; the optimal number of

n

 

. . . . l
franchrses for the semr-collusrve league cartel 18 n” = — .3’

V—C

t I t
> = n“. Thus, we have

2?— 2:1? v—c

 

Under assumption 1, we have nc =

the following proposition.

Proposition 1. Without control over franchises’ ticket pricing, the semi-collusive league

cartel provides a smaller number of franchises than the fully collusive cartel with price ‘

control (nsc < nc).

The intuition for Proposition 1 can be explained in the following way. Each
franchise’s pricing decision is constrained by either the competition margin or the
reservation value margin. That is, the marginal consumers for each franchise are those
who are indifferent between purchasing from it or purchasing from its neighbor
(competitive margin binding) or those who are indifferent between purchasing from it or
not purchasing (reservation margin binding). When the market is covered and the cartel
has no control over individual franchises’ pricing decision, the binding constraint is the
competitive margin. In such a case, reducing the number of franchises relaxes price
competition and saves on fixed costs without affecting the reservation value margin. The

semi-collusive cartel will reduce the number of franchises until the competition margin is

 

3' In this case the semi-collusive league cartel fill the market without market gap. With the assumption of
continuous n, it is never optimal to leave a gap in the market. However, in section 3, we consider the case
where the league strategically leaves some markets vacant to play a strategic game with local governments.

54

not binding. With the optimal number of firms (use ), the competition margin is not
binding and the only constraint is the reservation value margin, which implies that every
franchise is local monopoly under the semi-collusive regime. Under the fully collusive
cartel regime, the league is never bound by the competition margin and does not need to

reduce the number of franchises to relax competition between franchises.

Free entry

Now we consider free entry case in which there is no entry barrier except fixed cost. It
makes any potential franchise enters the league whenever his profit is greater than fixed
cost. Two-stage game is considered. In the first stage potential franchises
simultaneously choose whether or not to enter. AS in Salop’s model, we assume that
franchises do not choose their locations, but they are located the same distance form each
other. By backward induction, each franchise sets ticket price to maximize its profit

f

given distance between franchises. Suppose that franchise i chooses ticket price as p,-

and there exists a fan who is indifferent between buying a ticket form franchise i and

buying a ticket from its neighbor franchise j if v—t'x' —- p,- = v—t(Lf — T) — p j. In this
n

. . . ~ 1 . . . . .
case franchrse 1’s demand IS qif = 2x.f = — and he sets trcket prrce to maxrmrze Its

l nf

profit ”if =(pif—c)qif—F=(pif—c)%(p{+Lf— if)—F. Therefore, each
n

. . t . .
franchrse sets prrce as f = c + —. In the first sta e, otentral fianchrses enter the
P, f g P
n

55

league until trif = (pif — c)—1f- - F = 0. The equilibrium number of franchises with free
n

t
ent is nf= —.
ry VF

Social Optimum

. . 1 . . .
When there are n" franchrses at drstance of 7 apart from Its neighbor franchrse and
n

they all sell products at price of ps , total surplus generated by franchise i is

l

2,15 p‘-’ c v p; l 2 p?’ c
s(n‘)=2 (v—pI—tx)dx+—'——— =———'-—t( )+—'————F (3)
6f 1 n3 n3 n3 n3 2n" n" n3

 

From the above total surplus of one franchise, we have the total surplus in a n5 -franchise

league as S(n“’) = n"s(n“’) = v - LS — c — n" F . Maximization with respect to n3 yields
4n

the socially optimal number of franchises n" = ,l# .

Comparison
We now compare the optimal number of franchises under different regimes to the

socially optimal one and the one that prevails under free entry condition.

56

Proposition 2. With complete control over pricing behavior of franchises, the league

provides a larger number of franchises than the socially optimal one, but a smaller

number of franchises than free entry one (ns < nc < nf ). ,

Proof A simple comparison of expressions for n" =,/; , nc = ,l—t— , and nf = J2 .
4F 2F F

The discrepancy in choices between the fully collusive league cartel and the social
planner can be explained by Spence’s (1975) intuition for the monopolistic provision of
quality, if we interpret the number of franchises as quality since more franchises imply
better match between preferences of consumers and franchise locations. As Spence
(1975, 1976) has pointed out, the fully collusive cartel’s incentive to establish an
additional franchise is related to the marginal increase in gross utility for the marginal
consumer whereas the social planner’s incentive depends on the marginal increase in
gross utility for the average. In our model, the marginal consumers gain more than the

average consumer in gross utilities as the number of franchises increases. More

specifically, by increasing the number of franchises by An , the marginal consumer’s

d(t/2n) = —L. The average transportation cost is

d" 2’12

 

transportation cost decreases by

 

t/2n
jtxdx
given by (18 2”) = Et— , which implies that the average consumer’s transportation cost
n
d(t/4n) _ t

——. Thus, the marginal impact of increasing the number of
d" 4n2

 

decreases by

franchises on gross utility is greater for the marginal consumer than the average

57

consumer. As a result, the firlly collusive cartel supplies more franchises than the
socially optimal level.

When the cartel is semi-collusive and does not. have control over fi'anchises’
pricing, we know that it establishes less number of firms than the fully collusive cartel to
eliminate price competition among franchises. However, the ntnnber of franchises can

be either larger or smaller than the socially optimal choice [see figure 2].

Proposition 3. The comparison between the number of franchises under semi-collusive
cartel (n’c) and socially optimal one (ns ) depends on parameter values. If
v—c> 4tF , n" >nsc. Otherwise, n" <nsc.

Proo. A sim 1e com arison of ex ressions for n3 and n“ roves the ro osition.
P P P P P P

A corollary of Proposition 3 is that if v - c < J4tF , it would be welfare improving not to

allow rice coordination for the lea e since n" < n“ < nc; such a olic would induce
P g“ P y

the cartel to choose the number of franchises more aligned with the socially optimal one.

If v — c > J4tF , however, such a policy would overshoot the target (ns) and its welfare

implication is ambiguous.

3. Franchise Relocation Game
In this section, we extend the analysis to consider the possibility that the league
can play a relocation game with local or state governments. In particular, we examine

the strategic advantage of leaving a few cities vacant, which will be used as a leverage to

58

exploit more consumer surplus. To this end, we depart from the circular model and
assume that there are N separate potential markets where franchises can be located. Each
franchise operates as a local monopolist in each market and does not compete with one
another to attract consumers from other markets. As before, we assume that consumers
with reservation value of v are unifonnly distributed around each franchise in each

market. We assume that the length of each market is assumed to be more than

mv-

q_t

 

c . . .
, which means that the Size of each market does not constrain the

monopolist’s pricing behavior.

Identical Markets

We consider the case where every market is identical in terms of consumers’
reservation value v. With each firm being local monopoly in each market, there is no
distinction between the full and semi-collusive cartels. If the league’sets up franchises in

every market, the joint profit is given by

2
Nrr'" = NFL—7‘)— - F] . (4)

Now consider the possibility that the league vacates some markets with a strategic
motive to extract consumer surplus by playing a relocation game with local government
officials. We assume that a local government maximizes consumer surplus of citizens in

its jurisdiction. Note that the consumer surplus in each market due to the existence of

V’C

2t
franchise is given by cs =2 j (
0

_ _ 2
v c -tx)dx=(v c)
4t

 

This implies that a local

 

59

2
——(v c) to
4!

government without any franchise is willing to provide a subsidy of up to
attract a franchise located elsewhere. Since it takes only one vacant market to extract

such a subsidy, the optimal strategy for playing a relocation game is to install (N—l)

fi'anchises. In such a case, the cartel’s joint profit is given by

_ m _ _ (v—c)2_ (v—c)2
(N 1)[7r +CS]—(N 1)|:——2t F + 4t ] (5)

A comparison of equations (4) and (5) yields the following proposition.

Proposition 4. With identical markets with N 23, the cartel’s optimal strategy is to leave
one market without franchise to extract consumer surplus as a subsidy in the rest of the

markets.

Asymmetric Markets

We now consider the case where markets are asymmetric in terms of consumers’

reservation value vi. Without loss of generality, we assume that v,- is decreasing in i. In

this case, it is possible that the league’s optimal strategy is to leave more than one market
without franchises since the subsidy the league can collect will depend on consumer

surplus in the vacant market with the highest vi. More precisely, when there are m (< N)

franchises, the joint profit is given by

"’ _m ._ "'(vr-c)2_ (van—cf
[an]+m(CS,)—[Z 2t F]+m[ 4t ]. (6)

i=1 i=1

60

Proposition 5. With asymmetric markets, the cartel’s optimal number of franchises n* is
given by

m m ._ 2 _ 2
n* = argmax[ nr]+m(CSi)=[Z£&—é-f)—-F]+ml:g’—"il——c—)—] , where
i=1 i=1

mSN 4t

vm+1 is taken to be c when m = N.

4. Concluding Remarks

In this paper we develop a Simple model of the choice of league cartel about the number
of franchises. I examine the optimal choice of the league cartel with various degree of
control over franchises’ ticket pricing, the socially optimal, and the free entry case based
on Salop’S circular city model. I conclude that the semi-collusive league cartel provides
a smaller number of franchises than the fully collusive cartel. Since the semi-collusive
league cartel cannot control ticket prices, it has to choose a smaller number of franchises
to eliminate price competition. Second, the fully collusive league cartel chooses a larger
number of teams compare to the socially optimal one. The league cartel’s choice is based
on the consideration between the surplus of the marginal fan and the fixed cost. On the
other hand, the social planner’s choice is based on the average surplus of fans. Therefore,
the league cartel oversupplies variety of team to maximize its joint profits.

In the last part of this analysis, we examine the league’s decision of the number of
franchises when relocation game is considered. In this case the league’s choice of the
optimal number of franchises will be smaller than one with covering entire market. The
main force behind this scheme is the league is able to use vacant cities as leverage to

extract more consumer surplus. In addition to the fact that consumers with a franchise

61

face a higher ticket price with a local monopoly, consumer’s who has low valuation for a
team cannot enjoy the benefit from hosting a team in their hometown when we consider

asymmetric markets.

62

References
Buchanan, J ., “An Economic Theory of Clubs,” Economica, 1965, pp.1-l4.
Cairns, J .A, J ennett, N. and Sloane, P.J., “The Economics‘of Professional Team Sports: A
Survey of Theory and Evidence,” Journal of Economic Studies, 1986, 13, pp.3-
80.

Cyrenne, P., “A Quality-of-play Model of a Professional Sports League,” Economic
Inquiry, 2001, 39, pp.444-452.

Fort, R. and Quirk, J., ‘Cross subsidization, Incentives and Outcomes in Professional
Team Sports Leagues,” Journal of Economic Literature, 1995, 33, pp. 1265-1299.

Kahn L., “The Sports Business as a Labor Market Laboratory,” Journal of Economic
Perspectives, 2000, 14, pp. 75-94.

Salop, S, “Monopolistic Competition with Outside Goods,” Bell Journal of
Economics, 1979, 10, pp.141-156.

Spence, A.M., “Monopoly, Quality, and Regulation,” Bell Journal of Economics, 1975,
6, pp. 417-429.

Spence, A.M., “Product Selection, Fixed Costs and Monopolistic Competition,” Review
of Economic Studies, 1976, 43, pp.217-235.

Vrooman, J ., “Franchise Free Agency in Professional Sports Leagues,” Southern
Economic Journal, 1997b, July, pp.19l-219.

Vrooman, J., “The Economics of American Sports Leagues,” Scottish Journal of Political
Economy, 2000, 47, pp.364-398.

63

Appendix C: The Optimal Number of Franchises With Endogenous Quality

In this section, we extend the basic analysis in section 2 by allowing that fans’
reservation value is determined by the average quality of franchises, which is
endogenously determined by the number of teams in the league. More specifically, we
imagine a Situation where franchises use inputs whose supplies are fixed in the economy.
For instance, the talent pools for athletes and prime locations for stores are limited in
supply. If we assume that the best athletes play for the league, increasing the number of
franchises would dilute the talent pool and reduce the average quality of franchises.

To model such a situation, suppose that each franchise’s roster needs a players to
play a game. This implies that the top an players will play in the league if there are n

franchises. Let us assume that the athletic talent/skill in the economy is distributed with a

cumulative distribution G(s) with a support of [ g ,S], where 8 denotes Skill level. We

normalize the population in the economy at 1. Then, all athletics with the Skill level
higher than s* will play for the league, where S“ is defined by G(S“) = 1— am. We
further assume that athletes are randomly assigned to a team and the average quality of a

franchise is given by v = E[s|s 2 3*] = isdG/an, where G(s*) = 1— am. Since the
Sr
critical Skill level s* is decreasing in n, a higher number of franchises imply a lower
average quality of franchises.
To derive a closed form solution, we simplify the analysis by assuming a uniform
distribution of athletic talent/skill. More Specifically, we assume that s is uniformly

l
distributed on [0, 1]. Then, the average quality of franchise is given by v = L Isds.
cm
l-an

64

Therefore, if we have n franchises in the league, the average quality of a franchise is

9232
2

v(n) = —
Quality of Franchise with Fully Collusive Cartel

With consideration of quality of franchises, the league cartel with full collusion chooses
the optimal number of franchises in the first stage, which automatically determines the
average quality of franchises. The second stage follows to maximize their joint profits by
colluding ticket prices. By backward induction, in the second stage each franchise

maximizes its profit given the market Share and the average quality. It is because the

cartel league already chooses nc fianchises, which in turn determine fans’ reservation
value. To maximize the league’s joint profit, each franchise should charge ticket price as

the same manner as without quality choice case. Since fianchise i sets price such that an

 

. . ~c 2_anc -2pf . . . .
Indifferent consruner x,- = 2t rs located at the end of rts territory, prrce and
demand of franchise i is
t 2 1 l
.0 =r—Enc——— and 9‘ =22? =— 1——anc— .c =—.
pr 2 ch ‘11 I t ( 2 pl ) nc
Franchise i ’s profit becomes
xi=(pf—c)qf—F=(1-3n"—#—c>—’——F. (A1)
2 2nc nc

 

’2 Considering the average quality of franchises as the average of the sum of each athlete’s quality such as
1
v = — Isds , the results in the section still hold.
n

l—an

65

As the result of collusive ticket pricing in the second period, the league cartel chooses nc
to maximize its joint profits in the first stage:

Max nczrf =n"(r-%n“- 1 —c)-5-—‘ncF. (A2)

"0 2nc nc

 

Thus, the optimal number of franchises for the league cartel with full collusion is

nc=,/ t .
2F+a

Quality of Franchise with Semi-collusive Cartel

 

We now calculate the optimal number of franchises of the semi-collusive league cartel
that does not have a complete control over ticket pricing: it is only capable of choosing
the number of franchises in the first stage. With the same logic applied for the semi-
collusive cartel without quality of franchises in section 2, we observe that the joint profit
of the semi-collusive cartel increases by reducing the nummr of franchises.
Consequently, the optimal number of franchises in the case of semi-collusive cartel is
determined by increasing each franchise’s territory until it becomes a local monopoly.
To calculate the optimal number of franchises let us start with profit maximization

problem faced by a local monopoly. One additional figure we need to consider with
endogenous quality is q I" decreases as more franchises enter the market. With inverse
relationship between the number and quality of franchises, there is an indifferent

~m 2 — ansc - 26' . , .
consumer, x = 4r , who IS located at the end of local monopoly s temtory.

 

More specifically, by increasing the nrurrber of franchises by An , the indifferent

66

m

consumer decreases by 6 = —% , which implies that the semi-collusive league cartel
n

 

can achieve his maximum level of joint profit by reducing less number of franchises
compared to the choice without quality of franchises.

AS same as the previous local monopoly without quality choice, a monopolistic

franchise charges pm such that his demand is given by qf" = 23,-” = -f—(v(n 5c ) — pf") if

there are n“ local monopolists in the market. After maximizing the monopoly profit, it

_ v(n“) + c

sets ticket price as pf" — ——2—— and its profit is It,“ = —F . Similar to

 

(v(n..)_c)2
2t

assumption 1 the profit of the local monopoly with quality of franchises is nonnegative if
and only if the following profitability condition is satisfied.

Assumption A1. Profitability condition

v(n“) —c 2 JZtF

When assumption A1 is satisfied, we thus conclude that the semi-collusive league cartel

m _ v(nsc)__c

chooses the optimal number of franchises as ——1— = q : the optimal number

nsc t
C . C O t
of franchrses for the semI-collusrve league cartel rs n“ = —————— .33
SC
v(n ) — c
Under assumption Al , we have
t t t
C = "SC .

 

 

t
= _= < >
2F+a VZtF-l-at VZIF v(nSC)-c

67

Proposition A1. Without control over fi'anchises’ ticket pricing, there is possibility that
the semi-collusive league cartel even provides larger number of fianchises compared to
the league cartel’s choice with firll collusion.

One explanation for proposition A1 can be presented as follows. When the
market is covered in the case of the semi-collusive cartel, the binding constraint is still
the competitive margin. However, reducing the number of franchises alleviates price
competition and saves on fixed costs as well as relaxes the reservation value margin. The
semi-collusive cartel will reduce the number of franchises until the competition margin is
not binding in which the reservation value margin, in turn becomes less constraint. At
the market equilibrium, the competition margin is not binding and the only constraint is
the relaxed reservation value margin, which implies that every franchise is local
monopoly. Therefore, the optimal number of franchises in the regime of semi-collusive

cartel with endogenous quality can be larger than the choice without quality of franchises.

Quality of Franchise with Free entry
In this case, we still consider the same case as free entry without quality consideration.

Only difference from the previous free entry case is now fans’ reservation value is
1 . .
v(nf ) = 1 -§cznf . As the same process, two-stage game 18 consrdered. In the first

stage potential franchises simultaneously choose whether or not to enter. By backward

induction, each franchise sets its ticket price to maximize its profit given distance

 

3’ Explicitly, the optimal number of franchises with semi-collusive cartel is
3, (a-c)i\/(1—c)2 —2at
n = .
a

 

 

68

between franchises. Suppose that franchise i chooses its ticket price as pif and there

exists a fan who is indifferent between buying a ticket form franchise i and buying a

ticket from its neighbor franchise j , which satisfies the following:

(rt—5a an -txf-pif =a--2—a znlnf—t( f—Yif)-pif.

. . . . .2 1 . . . . . .
In this case franchrse I ’S demand 1s q, = 2x = — and It sets trcket prrce to maxrmrze rts

"f
profit as follows:

1 t
”if=(p,f-C)q,-f-f=(p,-f-c);(p,[+—f— [)—F. (A3)

n
Therefore, each franchise sets its price as p,f = c+;f. In the first stage, potential

it

franchises enter the league until/r .f = (p,- —c)—7-— F: 0. Therefore, the optimal

number of franchises with free entry is nf = J; .

Socially Optimal Level of Franchise ’3 Quality

When there are ns franchises at distance of is apart from its neighbor and they all sell
it

products at price p" , total surplus generated by franchise i is

l

2ns
s(ns)= 2 j(l—§ans —p;’— —tx)dx+——i—

0 ns ns

69

S
=_1__g__p_,_t(_l_)2+_p_,___c__F. (A4)

Form total surplus of one franchise, we have the total surplus in a n‘ -franchise league is

S(nS) =nss(n") = —%ns —

 

s —c—nSF. (A5)
4n

Maximization with respect to n3 yields the socially optimal ntunber of franchises as
as = /——’—
2(2F + 0:)

Comparison
We now turn to analysis of comparing the optimal number of franchises under different

regimes with quality.

Proposition A2. With quality choice, the league cartel provides a larger number of

fianchises than the socially optimal one, but a smaller number of franchises than free
entry one, it" < nc < nf . The average quality of franchises is v(nf ) < v(nc) < v(a’ ).

Proof For the complete cartel case, we can easily verify that n3 <nc <nf fiom
t t t
/— <,/ < ,l— .
2(F + 2a) 2F + a F

With quality choice, we still adopt Spence (1975, 1976)’s analysis: the incentive

 

to increase the number of franchises is related to the marginal increase in gross utility for

the marginal consumer in the case of the complete cartel and for the average consumer in

70

the case of a social planner. However, Since the consumer’ valuation is affected by
quality of the product and the number of franchises, in which these are also negatively,
the effect of changing the number of franchises will be augmented. More specifically,

avtnC) + er? I

are ancl .Anc by

 

the complete cartel can raise the price by
without qualtiy

increasing the number of franchise by Anc. The choice of the complete cartel will
depend on the marginal increase in valuation and quality of the marginal consumer
against fixed cost. In contrast, the social planner considers marginal increase in valuation

I 1 )

2n"
and quality of average consumers such aS—a—S 2ns “v(n" ) — tx)dx -Ans .
6n
0

 

 

K 1

When the cartel does not have a complete control over fianchises with quality
choice, it is Shown to provide smaller or larger number of franchises compared to the
choice of the complete cartel. Since consumers’ valuation is correlated with the number
of franchises, the outcome is ether fewer fianchises with high quality or many franchises

with low quality.

71

 

xi—l 3} xi 31' xi+l

Figure 1. The fully league cartel without quality choice

72

 

 

A
( l W l I
I I I I I
n s ”c n f The optimal
number of
franchises

Figure 2. Comparison of the Number of Franchises under Different Regimes

73

A
T

Quality of the league

 

 

 

~‘ Ntnnber of players
am

Figure 3. Relationship between quality and number of players

74

SC

 

 

 

A
K I I W J I
I I I I I l
"s "c n f The optimal
number of
franchises

Figure 4. Comparison of the Number of Franchises with Quality

75

CHAPTER 3

THE QUALITY OF TECHNOLOGY AND PATENT PROTECTION POLICY IN
THE INTERNATIONAL LICENSING OF TECHNOLOGY
1. Introduction

Intellectual property rights (IPR) have been controversial policy issue over past
two decades. On one hand, developed countries insist that developing countries should
implement higher standards. However, developing countries view the adaptation of a
strong protection of intellectual property rights as an excessive rent transfer to the high-
income developed countries. Along with policy debate of IPR, licensing as a channel of
technology transfer has been more important for the following reasons. First, recent
empirical evidence suggests that the volume of arm’s length’s contract has been
increased. Mansfield (1995) shows that there has been an increase in recent years in the
extent to which technology is transferred by licensing. Second, a technology transferor
prefers licensing to FDI because of political reasons in a technology recipient country.
For example, in some developing countries government policies traditionally preferred
licensing to equity investment as the model of technology transfer (Contractor and
Sagafi-Negad, 1981).

This paper constructs a model incorporating several of the stylized facts regarding
technology transfer and licensing. In this paper I examine the validity of patent
protection policy in the host country where there exist the licensee’s imitation and R&D
competition between the licensor and the licensee. Its purpose is to address two

interrelated questions: First, are there other concerns except imitation in which the

76

licensor may not transfer the new technology? Second, with endogenous choice of the
licensor’s R&D expenditure, how does the degree of a patent protection policy effect on
the level of technology transferred and the licensor’s R&D efforts?

One of the stylized facts for the technology transfer via licensing is the licensor
may transfer the old technology when the host country’s patent protection policy is not
effective. Since the weak patent protection makes imitation possible, the licensor has to
transfer the old technology to secure future profit. However, the strong patent protection
policy may have a reverse effect on the licensor’s incentive to do R&D. Since imitation
becomes very costly in the strong patent protection policy, the licensor may have less
incentive to develop the next generation technology.

On the other hand, Roberts and Mizouchi (1988) and Davies (1977) Show that if
the licensee may have a potential ability to develop a newer technology, firms are often
reluctant to license their cutting-edge technologies. From the stylized facts, it is possible
that there would be missing parts that explain the validity of patent protection policy and
strategic behaviors of the licensor and the licensee. This paper examines another aspect
of the licensor’s strategic behavior where he faces two different concerns: the licensee’s
imitation and R&D activity.

The effect of the protection of IPR has been studied in a theoretical literature on
technology transfer, where can be divided in two categories. First, Helpman (1990),
Glass and Saggi (1995), Lai (1998), and Yang and Maskus (2001) use a general
equilibrium model with an innovative North and an imitative South to study the effect of
IPR. Helpman (1993) finds that stronger IPR would diminish both the rate of innovation

for the North and welfare of the South when imitation is the only channel of technology

77

transfer. In his model, stronger IPR implies that imitation becomes more costly, so that it
decreases the rate of technology transfer, and reduces incentives to innovate. Glass and
Saggi (1995) Show Similar results with two channels of . technology transfer, such as
imitation and foreign direct investment (FDI). They conclude that a strengthening of IPR
in the South would reduce the rate of innovation in the North and imitation in the South.
The rate of technology transfer also would decrease with stronger IPR. Lai (1998) finds
that the effect depends crucially on the channel of technology transfer. Stronger IPR in
the South would increase the rate of technology transfer, but if only imitation is possible,
then the result would be reversed. Yang and Maskus (2001) analyze the effect of the
stronger IPR by using a dynamic general-equilibrium model of the product cycle. They
have the same results as in previous literature with two channels of the technology
transfer: licensing and imitation.

The second approach for [PR is strategic interactions between a technology
transferor and a technology recipient. Fosfuri (2000) analyzes the decisions about the
entry mode in a foreign country and the quality choices of transferred technology.
Fosfirri studies how these are correlated and how both decisions are influenced by the
degree of patent protection in the host country. In his model, he shows that the licensing
contract is efficient and optimally chosen by the innovator without imitation. Under the
presence of imitation, the optimal behavior of the innovator is to choose different
strategies to deter technology diffusion by using the different mode of entry such as
export or FDI. Although the innovator chooses the licensing mode, he will license the
old version of technology from his technology vintage to reduce the licensee’s incentive

to imitate. Markusen (2001) shows the effect of stronger IPR in the model in which local

78

managers learn the multinational’s technology and can defect to start a rival firm. From
his result, both the multinational’s profit and the host-country’s welfare would be
improved by stronger IPR if the mode of entry changes from exporting to production
within the host country.

This paper takes a different but complementary approach to international
technology licensing. I present a model in which the licensee can choose either to copy
the licensed technology or to do R&D based on the licensed technology. This
consideration reflects a more realistic situation in which the licensor should concern more
about both imitation and leapfrogging fiom the licensee. What it means that the licensor
would choose to transfer the old technology due to either the licensee’s imitation or R&D
activity. To examining these questions I consider the decision of the licensor is examined
under two different regimes, which vary according to the degree of a patent protection
policy. In the basic model, the optimal level of technology transferred is examined
according to the licensee’s decision between imitation and R&D. Here, we assume that
there is no further R&D activity from the licensor. The optimal choice of the licensor’s
R&D expenditure is analyzed in the extended model. With the licensor’s further R&D
ability, we can Show the host country’s patent protection policy does not have a critical
role in determining the quality of technology to transfer. However, the strong patent
protection policy is shown to reduce the licensor’s R&D expenditure which slows down
the innovation.

The basic foundation of this paper is the incomplete licensing contract, which is
analogous to the incomplete contract framework by Grossman and Hart (1986), Hart and

Moore (1990) and Hart (1995). If the licensee’s R&D ability is known to the both

79

parties, then the licensor knows that in the second period there will be either imitation or
R&D. The licensor is able to design the first-period contract, which is contingent on the
licensee’s behavior in the second period according to the licensee’s R&D ability. The
licensor may include a provision, which requires that the licensee should pay for firture
payments depending on the choice of the licensee’s activity. If the licensee chooses to
imitate at the second period, obviously it reveals the licensee has the low ability for
R&D. According to the provision, the licensor will be compensated for the loss fi'om the
licensee’s imitation at the second period. If the licensee decides to do R&D, the licensor
will collect an additional payment from the licensee’s profit when the licensee succeeds
innovation. Since the licensor can extract profit from the licensee because of imitation or
R&D, the licensor does not have any incentive to transfer the old technology in the first
period. He always transfers the new technology with a contract, which includes either
rent from imitation or profit from the success of R&D depending on the licensee’s ability
to do R&D.

However, these activities may be observable to the parties in the relationship but
not verifiable to a third party. Therefore, it may not be enforceable in court. The
incompleteness of licensing contract may be caused by the fact that the licensor cannot
list all the possible future outcomes from imitation or R&D. With weak patent protection
in the host country, which allows the licensee to imitate, the licensee can invent
patentable and not infringing technology around the patent by imitation.

The remainder of this paper is organized as follows. In Section 2 I describe the
basic model and give an example about the quality differentiated market structure and

derive the sub-game perfect Nash equilibrium (SPNE) for the basic licensing game.

80

Section 3 discusses the effect of the licensor’s further R&D activity on the licensing

game and derives the SPNE for the extended licensing game. I conclude in Section 4.

2. Basic Model without the Licensor’s R&D

I construct a two-period model of an international technology transfer via
licensing, where there are two countries: the source and the host countries. In the source
country, there is a firm that has two different levels of patented technologies: the old and
the new technologies. I assume that the innovation process occurred before the licensing
game, so these technologies are considered as exogenous. Also, there is more than one
firm in the host country who are willing to take the license for this technology from the
licensor. AS a result, the licensor has the bargaining power and makes a take-it-or-leave-
it offer to the licensee.

For simplicity, we assume ex ante complete licensing agreement possibly can be
written. With ex ante complete contract, the level of technology transferred is able to
verifiable to a third party, as well as the parties in the relationship, so moral hazard
problem is not considered in this model. In this case the licensor will transfer his
technology only with a lump-sum payment. Also, to maximize the lump-sum payment
from licensing the licensor licenses exclusively, so he can obtain monopoly profit from
the host country’s market at the first period.

We also assume that the licensing contract is only valid for one period. Invalidity
of multi-period contract can be justified as follows. With lump-sum payment the licensor
has no commitment mechanism ensuring no more licensing to potential entrants in host

country in the second period. For instance, the licensee expects the licensor has an

81

incentive to offer another license to any potential entrant at the beginning of the second
period. Therefore, without exclusive licensing commitment in the second period one-
period licensing contract is only valid.

To formalize the idea I assume that there are two types of technology that can be
licensed: the new and the old technologies. The new technology differs fiom the old
technology in two respects. First, the new technology is superior to the old technology in
which it enables the licensee to produce a higher quality product: the quality with the new
technology is ad while the quality with the old technology is 9, where (1 >1. If we

assume that consumers have utility function as U = v— p and valuation v, which is
uniformly distributed over the unit interval as v,- e U [0, 1]. Thus, the quality of the good

enters positively into the utility of consumer. In addition, the transfer of the new
technology may enable the licensee to develop a next-generation technology and make
other technologies obsolete.

I first calculate the licensor’s optimal choice of lump-sum fee in the first period. If
the licensee is transferred with the old technology, he can produce products with quality
level, 6 as a monopolist. Then consumers with non-negative net utilities purchase the

product: 6v — p 2 0 with the old technology. Given the purchase decision of consumers,

the licensee simply chooses a price that maximizes his profit:

M p- 0
”01d =argmax pi(l——9’— =2.
Pt

AS a result the licensor simply charge his lump-sum fee as ”31,, . Similarly, the licensee’s

profit and lump sum fee in the first period with the new technology is shown as:

M a6
”New = —4-

82

When the licensee receives the technology, he has two different options for future
competition at the end of the first period: imitation or R&D. If he decides to imitate the
licensed technology, then he will obtain the same level of technology with certainty. On
the other hand, if he decides to use his research capacity for R&D, he has a chance to

develop one-level higher technology with probability p . For example, the transfer of old

[new] technology endows the licensee with the ability to develop the new [the next
generation] technology with probability p. Therefore, at the end of first period, licensee
has two strategies, either imitation or R&D [see figure 1].

With licensee’s two different options at the end of the first period, we need to
calculate what the optimal lump sum fee will be in the second period. Two different
outcomes will be possible. If the licensor transfers the old technology and the licensee
decides to do imitation at the end of the first period, then the licensor still has the new
technology and the licensee has the old one. Since the licensor has the bargaining power,
he can’make an offer as follows. If there are two firms with different quality, 6 and ad
with new contract with a potential entrant, it will be the duopoly case with two different
levels of quality. When consumers make their purchase decision, they choose the one
that yields the highest utility. For given price for the low and high quality product,

consumers’ optimal choices can be divided by as follows:

PNew " POld S v
9(a—l)

 

purchase the high quality product

p01d Sv < PNew ‘— POld
0 0(a —l)

 

purchase the low quality product

v < POId

no purchase
0

83

Now we can denote the profit of the new entrant with high quality as

 

D _ PNew 'POId _ M

4a(a “'1) 34

where A = 2 .
(4a — 1)

Also, we can represent the profit of the licensee with low quality as

 

D [PNew - pom _ Pozd

M
”(Old, New) = arg max (a -l)0 9 JPOId = AflOld '

AS a result, the licensor’s optimal lump-sum fee in the second period when the licensee

has the old technology is affew — ”(15“, New) .

As another possible outcome, the both parties have the new technology as a result
of either of licensee’s imitation or R&D activity in the first period. We assume that it
leads to Cournot type competition between the licensee and new entrant, then we denote

the prOfit of firm i as

D 4 M
”(New, New) = arg max (16(1- qi _ qj )qi = '9' ”New °
qi

Therefore, the licensor’s optimal lump-sum fee in the second period when the licensee
- M D
has the new technology IS 7: New — 7r( New, New) .

For the last scenario if the licensee with the transferred new technology succeeds

to develop the next generation technology, which makes other technologies obsolete and

brings the quality level of 0:26 into consumer’s valuation. In this case, the licensor no

longer has a dominant position in the second period.

84

Technology transfer without Imitation: A Benchmark case
As a benchmark case, I first consider a situation where the option to imitate the licensed

technology is not available, in which the host government adopts the strong patent
protection policy. Under this policy regime, the licensee cannot imitate the licensed

technology or invent around the patent. Therefore, the licensee’s strategic behavior is

only to do R&D. Let [13(0, R) and H3 (N, R) denote payoffs of the licensee from

R&D activity when the old and the new technology is transferred respectively.”
According to the licensee’s R&D ability, which is denoted by p, we have

3 D a6
H (0’ R)=p°fl(New, New) =p.?’ (1)

l'IB(N R)- M - 333 2
9 -p'7[NG_p° 4 ' ()

Since we assume that the licensee’s ability to do R&D is constant, but expected profits
from R&D increases with respect to the level of transferred technology, the licensee
always prefer the new technology to the old one.

Let IIS (0, R) and IIS (N, R) denote payoffs of the licensor when the old and

the new technology is transferred respectively with licensee’s R&D activity.36

115(0, R)=7rg$d+p-[7rjvew-7t(Il)Vew’New)]+(l—P)'”li’lew
3)
6 Sad a6 (
=_+ — +1- —
4 pl36] ( P)4

a6 a0
rISuv,Ri=nit£w+p-0+<1—p)-niiew=7+(1—p)—4—. (4)

 

3‘ The first cell in the subscript denotes his own technology level and the second one indicates his
opponent’s technology level.

3 Superscript B denotes the licensee (buyer).

’6 Superscript S denotes the licensor (seller).

85

Let p * be the critical value, which satisfies
HS(N,R) —HS(0,R) = 3%(9‘1 —9-5ap) = 0.

Hence, if p < p* , the licensor will choose to transfer the new technology. Otherwise,

the licensor will transfer the old technology. As the licensee’s R&D ability increases, the
licensor gets more cautious in protecting the new technology to maintain his dominant

position in the second period.
Lemma 1. Let define a set P as P: {p|H(p)=I15 (0,R)-1'IS (N,R)>O}. If the

parameter of R&D ability, p , belongs to the set P, then the licensor will choose to

transfer the old technology.

Technology Transfer with Imitation
Now I introduce the possibility of imitation of the transferred technology. With weak

patent protection policy of the host country, the licensee has another option, which is

imitate the transferred technology. Let H3 (0, I ) and H3 (N, 1) denote payoffs of the

licensee from imitation when the old and the new technology is transferred respectively.

Since the licensee’s probability to imitate is given by one, we have

B D
II (0’1)=”(01d,New)=A' . (5)

elm

B D 019
n (N, I) = nmm New) = —9—. (6)

During the first stage, the licensee chooses either to imitate or to do R&D based on
payoffs with different level of technology transferred in the first stage. By comparing the

licensee’s expected payoffs from each outcome, we can conclude that the licensee’s

86

optimal choice is imitate no matter what technology is transferred if p < %I-. Also, if
a

p > 34m the licensee chooses to do R&D regardless of the level of technology
a .

transferred. In the medium range of the licensee’s R&D ability (%/1 < p <51) his
a a

choice will be to do R&D when the old technology is licensed, and vice versa [see figure
3].

We now calculate the licensor’s payoffs with imitation from the licensee. Let
l'Is(0, I ) and ITS (N, 1) denote payoffs of the licensor when the old and the new

technology is transferred respectively with licensee’s imitation activity.

6
TIS(0, 1)=rrg,d Hakim ”gm, 01d))=z(1+a—A), (7)
s M M D 14

Given the licensee’s choices according to R&D ability, the licensor’s optimal choice of
9A . . . . .
the level of technology. If p < 4— , which Induces the lrcensee to rmrtate no matter what
a

level of technology licensed, the licensor will choose the level of technology by
comparing [15(0, I ) and Us (N, I ). The licensor’s optimal choice will be presented in

proposition 1.

Proposition 1. In the regime of weak patent protection policy with low R&D ability of
. 9A .
the lrcensee [ p < T], the level of technology depends on the qualrty gap (or) between
a

the old and the new technologies regardless of the licensee’s R&D ability.

87

Proof By calculating ITS(O, I)—HS(N,I)=%(1—A—%a), we denote a* as the

critical value satisfying IIS (0, I) = US (N ,1 ). If a < a *, the licensor will transfer the

new technology. Otherwise, the old technology is transferred.

The intuition underlying Proposition 1 is straightforward. Due to the licensee’s imitation
activity the licensor faces two different trade-offs: increasing licensing fee in the first
period with licensing of the new technology or securing the future profit by transferring
the old one. If the quality gap between technologies is narrow, the licensor is better off
with licensing the new technology, which increases the licensing fee in the first period.
Since both technologies have little difference with respect to quality of the product, the

licensor has less incentive to secure the firture profit.
. , . . 9A 4 . .
When the lrcensee s R&D abrlrty belongs 4— < p < — Wthh Induces the
a

9a

licensee to imitate the new technology or to do R&D based on the old technology. In this

case the licensor will choose the level of technology by comparing HS (0, R) and

IIS (N, I ) . The licensor’s optimal choice will be presented in proposition 2.

Proposition 2. In the regime of weak patent protection policy with medium R&D ability
. 9A 4 .
of the lrcensee [4— < p < -9—— ], the level of technology depends on the qualrty gap (at)
a a

between the old and the new technologies and the licensee’s R&D ability.

88

Proof By calculating 1'15 (0, R) — I'IS (N, I ) = %[9(1— a) + 4a(1— p)] , we denote

[3(a) as the critical value satisfying IIS (0, R) = l'lS (N, I). If p < [2(a), the licensor
will transfer the old technology. Otherwise, the new technology is transferred.

The intuition underlying Proposition 2 is as follows: Due to the licensee’s two different
response to the level of technology transferred the licensor faces two different trade-offs:
maximizing licensing fee in the first period or securing the future profit. As the quality
gap increases with fixed the licensee’s R&D ability, the licensor puts more emphasis on
maximizing the licensing fee in the first period than maintaining the dominant position in

the future.

As the last case with p > 91 , the licensee chooses to do R&D regardless of the
a

level of technology transferred. With licensee’s only imitation choice, it will be the same
configuration as the benchmark case with strong patent protection policy. To evaluate
the effectiveness of the strong patent protection I Stunmarize the results under weak
patent protection regime in figure 4. We observe change of the level of technology
transferred, which is shown as gray area under the weak protection. Therefore, we can
conclude that the effectiveness of patent policy depends on the quality gap. Moreover, a
surprising result is that the larger quality gap is not a necessary condition for transferring

the old technology.

89

3. The Extended Model with the Licensor’s Endogenous Choice of R&D
Expenditure

We now consider the licensor’s R&D activity at the end of the first period. Given the
quality gap (a) and the licensee’s R&D ability, the licensor decides on how much R&D
expenditure is to be made. For this analysis, we assume that the licensor would be

successful in innovation with probability q(e) depending on the R&D expenditure e. So

the probability of the licensor’s failure to innovate the next-generation technology is

(1—q(e)). Also, q(e) is assumed to be increasing and strictly concave in e with

q(0)=0and q(e)<1forany e<oo.

Technology transfer without Imitation: A Benchmark case

As a benctunark case, I first examine the licensor’s optimal choice of R&D expenditure
when the option to imitate the licensed technology is not available with adaptation of the
strong patent protection policy. Under this policy regime, the licensee cannot imitate the

licensed technology or invent around the patent. Therefore, the licensee’s only strategic

behavior is to do R&D. Let 1'13 (0, R) and H3 (N, R) denote payoffs of the licensee

from R&D activity when the old and the new technology is transferred respectively.
According to the licensee’s R&D ability, which is denoted by p, we have

' 6
H” (0, R) = p(1-q)'7r(‘,)vew, N...) = p(1-q)99- (9)

3' _ D M _ £129 029
H (N,R)—Pq'7r(NG,NG)+P(1-Q)”NG—Pq'—'+P(1"Q)

9 —4—. (10)

90

Since we assume that the licensee’s ability to do R&D is constant, but expected profits
from R&D increases with respect to the level of transferred technology, the licensee

always prefer the new technology to the old one.

Let HS (0, R) and HS (N, R) denote payoffs of the licensor when the old and

the new technology is transferred respectively with licensee’s R&D activity.

I‘IS'(0, R)
= 2:34,, + q(e) . ”its +(1- p)(1- q(e)) - mt... + p(1 — q(e)) - Inf... — ”8..., M...) 1 - e
6 0:26 a6 a0 a6
- 4 + “OT +(1- p)(1-q(e))—4— + P0 "(1(8))(7 -?J ‘3, (11)

HS (N, R) = xii... +(1— p)q<e) - wile + pq(e) - ”5..., NC) +(1- p)<1— q(e))zri’a. - e

2 2
= 3; +(1— p)q(e)g4—6~ + pq(e)39‘—9v +(1- p)(1- q(e))? -e- (12)

Let p * * be the critical value, which satisfies

us (0.1?) —n5 (MR) = £90m)+5a<1—q(e)+aq(e))p**r = 0.
Hence, if p < p ** , the licensor will choose to transfer the new technology. Otherwise,
the licensor will transfer the old one.

Lemma 2. Let define a set P as P:{p|H(p)=I'IS(O,R)—I'IS(N,R)>0}. If the

parameter of R&D ability, p , belongs to the set P, then the licensor will choose to

transfer the old technology.

We now turn to the licensor’s optimal R&D expenditure problem with p < p **

in which the licensor transfers the new technology. The licensor chooses the optimal

level of expenditure by maximizing (12). The first order condition yields

91

36
a0(9(1-— p)(a — 1) + 4ap) '

 

q'(e*(NiR))= (13)

For the other case the licensor will choose to transfer the old technology and the
licensor’s objective becomes maximizing (l l). The first order condition yields

36

q'(eI (0,R)) = a6(9(a — 1) + 4p) '

 

(14)

Proposition 3. With strong patent protection policy, the licensor will engage in R&D

more intensively when the old technology is transferred [e * (O, R) > e * (N, R) ].

Proof Comparing (l3) and (14) we easily conclude that q'(e * (0,R)) < q’(e * (N, R)). It
implies e * (O, R) > e * (N, R).

Technology Transfer with Imitation

Now we consider the possibility when the licensee has another option, which is imitation

with weak patent protection policy of the host country. Since both decisions, which are

the licensor’s R&D expenditure and the licensee’s technology adaptation, will happen

during the first stage, we can denote H3 (0, I) and H3 (N, I) as payoffs of the

licensee from imitation when the old and the new technology is transferred respectively
with given expenditure level e. Since the licensee’s probability to imitate is given by

one, we have

' 6

H3 (0. I)=(1-q)zr£,,d,N,w) = (1 ‘q’A'Z’ (15)
' 6

H” (N. I)=(1-q)n8,,.,, New, =(1—q)“7. (16)

92

During the first stage, the licensee chooses either to imitate or to do R&D based on
payoffs with different level of technology transferred in the first stage. By comparing the

licensee’s expected payoffs from each outcome, we can conclude that the licensee’s

. . . . . . . 9A .
optimal chorce rs Imitate no matter what technology rs transferred If p < T. Also, If
a

> 4(1-q)

(9 5 ), the licensee chooses to do R&D regardless of the level of technology
a ‘ q

4(1 - q)

a(9 — Sq) )

transferred. In the medium range of the licensee’s R&D ability (:—A < p <
a

his choice will be to do R&D when the old technology is licensed, and vice versa.

We now calculate the licensor’s payoffs with imitation from the licensee. Let

IIS (0, I) and IIS (N, 1) denote payoffs of the licensor with choice of R&D

expenditure e when the old or the new technology is transferred respectively with

licensee’s imitation activity.

1.15 (0, I) = ”310, + “err/{,2 + (1 — q(e))(triilew - ”lit... Old))— 6 (17)
=%[1+ q(e)cz2 + (1 - 9(6))(a — A” ' e,

r15 (N, I) = xiv”... + «anti; + (1 — q(e))(zri’t’... - n&,w,N,..)) - e ( 3)
1
= 30590: + q(e)9a2 + (1 — q(e))Sa] — e.

Given the licensee’s choices according to R&D ability, the licensor is now able to choose

the optimal level of R&D expenditure, which induces selection of the level of
9A . . . . .

technology. If p < 4—, which Induces the lrcensee to Imitate no matter what level of
a

technology licensed, the licensor will choose the level of technology by comparing

93

1'15 (0, I) and IIS (N, 1). Suppose that the licensor selects the old technology with

expectation of licensee’s imitation activity to occur, and his optimal level of R&D
expenditure is determined by maximizing (17) with respect to e. The first order
condition yields

4
0(a2—a+A)

 

q'(e*(0J)) = (19)

For the other case the licensor chooses to transfer the old technology expecting imitation
from the licensee. The licensor’s objective becomes maximizing (18). The first order
condition yields

36

q(e*(N, 1))=m-

(20)

Therefore, the licensor’s optimal choice is now comparison of I'IS (e*(0, 1)) and

['1S (e*(N, I))with his optimal choice of R&D expenditure for each case. The

licensor’s optimal choice will be presented in proposition 4.

Proposition 4. In the regime of weak patent protection policy with the low R&D ability
. 9A .
of the lrcensee [p <23], the level of technology depends on the qualrty gap ((1)

between the old and the new technologies regardless of the licensee’s R&D ability.
Moreover, the licensor will engage in R&D more intensively when the new technology is

transferred [e*(O,I) <e*(N,I)].

Proof Since both ITS (e*(O, 1)) and HS (e*(N, 1)) are the function of only quality

gap (a) the optimal level of technology transferred depends on quality gap. Comparing

94

(19) and (20) we easily conclude that q'(e* (0,1)) > q'(e*(N,1)). It implies
e*(0,I) < e*(N,I).

The intuition underlying Proposition 4 is straightforward. Facing the licensee’s imitation,
the licensor’s decision of transferring the new technology depends on how much
monopoly profit increases in the first period and how much he needs to compensate more
to renew the contract in the second period. However, with endogenous choice of his own
R&D expenditure, he has one additional variable to control. If he chooses to license the
new technology, then he engages in R&D more intensively in order to secure the future
profit. In contrast, with licensing the old technology, the licensor has less incentive to put
his effort to develop the next generation technology because he already prevents the

licensee to acquire the new technology in the second period.

When the licensee’s R&D ability belongs Z—A- < p < —4—(I;q—)— which induces the
a

a(9 - Sq)

licensee to imitate the new technology or to do R&D based on the old technology. In this

case the licensor will choose the level of technology by comparing l'IS (e* (0, R)) and

l'lS (e * (N, 1)) . The licensor’s optimal choice will be presented in proposition 5.

Proposition 5. In the regime of with weak patent protection policy with medium level of

4(1 - q)

], the level of technology depends on
a(9-5q)

R&D ability of the licensee [j—A— < p <
a

the quality gap (or) between the old and the new technologies and the licensee’s R&D
ability. Moreover, the licensor will engage in R&D more intensively when the new

technology is transferred [e * (0, R) < e * (N, 1)].

95

Proof Since ITS, (e * (0, R)) is the function of quality gap (or) and the licensee’s R&D
ability the optimal level of technology transferred depends on aand p. Comparing (l4)
and (20) we easily conclude that q'(e* (0,R)) > q'(e* (N , I )) . It implies
e*(O,R) < e*(N,I).

4(1 - q)

, the licensee chooses to do R&D regardless
a(9 - 5(1)

As the last case with p >

of the level of technology transferred. With licensee’s only imitation choice, it will be
the same configuration as the benchmark case with strong patent protection policy. To
evaluate the effectiveness of the strong patent protection I summarize the results under
weak patent protection regime in figure 6. We observe possible change of the level of
technology transferred compared in the regime of strong patent protection policy Shown
in figure. Therefore, we can conclude that the effectiveness of patent policy depends on
the quality gap and the licensee’s R&D ability. Moreover, we conclude that the strong

patent policy has a reverse effect on the licensor’s incentive to engage in innovation.

4. Concluding Remarks
In this paper I develop a simple licensing model of international technology to
study the effect of strong patent protection policy on the choice of level of technology
and ftuther R&D activity. I examine the decision of licensor under four possible regimes,
which vary according to the degree of a patent protection policy and the licensor’s further
R&D activity.
In the basic model without the licensor’s endogenous choice of R&D expenditure,

the level of technology depends on the quality gap and the relative magnitude of the

96

licensee’s R&D with presence of the licensee’s irrritation. Since the level of technology
licensed is only determined by the licensee’s R&D ability in the strong protection regime,
the strong protection policy is shown to be partially effective. Moreover, a surprising
result is that the larger quality gap is not a necessary condition for transferring the old
technology.

In the extended model with the licensor’s endogenous choice of R&D
expenditure, the effectiveness of the strong patent protection policy is partially supported.
In contrast, the licensor’s optimal R&D expenditure level is reduced in the weak
protection regime, which confirms the reverse effect of strong patent protection policy on

the licensor’s innovation efforts.

97

References

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policy response,” Journal of International Business Studies, 1981, 12, pp.113-
135.

Davies, H., “Technology transfer through commercial transactions,” Journal of Industrial
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F osfuri, A., “Patent protection, imitation and the mode of technology transfer,”
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Glass, A.J., Saggi, K., “International technology transfer and the technology gap,”
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Grossman, S.J., Hart, 0., “The costs and benefits of ownership: A theory of vertical and
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Hart, 0., Firms, contracts, and financial structure, New York: Oxford University Press,
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Hart, 0., Moore, J., “Property rights and the nature of the firm,” Journal of Political
Economy, 1990, 98, pp.1119-1159.

Helpman, P., “Innovation, imitation, and intellectual property rights, ” Econometrica,
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Lai, E.L.C., “International intellectual property rights protection and the rate of product
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Markusen, J .R., “Contracts, intellectual property rights, and multinational investment in
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Masfield, E., Innovation, technology and the economy: The selected essays of Edwin
Mansfield, Vol. 11. Edward Elgar, London, 1995.

Massimo, M., “Endogenous quality: price vs. quantity competition,” Journal of Industrial
Economics, 1993, 41, pp.1 13-131.

Roberts, E.B., Mizouchi, R., “Inter-firm technological collaboration: the case of Japanese
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endogenous product-cycle model.” Journal of International Economics, 2001,
53, pp. 169-187.

98

Weak patent protection (imitation is possible)

 
 
    
 
   
 
        

Licensor

Old New

Licensee

Imitation R&D Imitation R&D

   

(0. I) (0. R) (N. I) (N, R)

Figure 1. Game structure

99

{-‘J‘x—Y'K‘,

 

 

Figure 2. The basic model with a strong patent protection

I------------------------------------

 

 

   

 

 

 

 

 

 

(New, R&D)
' (New, Imitation)
:
l
l
l : (Old, R&D)
I
. : : (Old, Imitation)
l ' I
i ' |
I i I
I I I ’
0 9_A _‘L 1 p
4a 9a

Figure 3. The optimal choice of licensee

101

 

 

New

 

 

 

 

 

\ p *
\ 01d
\\ P
\\ /
\
\ /\z
\
\
\
\
\
24 _4_ 1
4a 9a

Figure 4. The basic model with weak protection policy

102

 

e*(O,R)

i e*(N,R)

 

 

 

 

’ P
1

Figure 5. The extended model with strong patent protection policy

103

 

e*(O,R)

NEW

 

e*(N,I)

OLD

e*(O,I) fl

 

 

 

 

 

2A *=4—9a 1

4a ‘1 4 - Sap
Figure 6. The extended model with weak patent protection policy

104

  
 

     

 

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1 93 02548 6071

   

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