CAPITAL FLOWS AND INTERNATIONAL ADJUSTMENT Thesis for the Degree of Ph. DE MICHIGAN STATE UNIVERSITY THAI VAN CAN 1 9 7 2 v.1. ...... 3' ‘61 LIBRARY 5 . ‘ . ' .7 O" '.. Mldngm ... “we :1. University rl E? anfihnc av ‘? HUM} & SUNS’ ‘2, IBM 3mm mc. T. LT 'BINDERS n “Inlflfill ABSTRACT CAPITAL FLows AND INTERNATIONAL ADJUSTMENT By Thai Van Can This thesis uses a one-country model similar to Patinkin's as well as a two-country model to investigate the effectiveness of fiscal and monetary policy (consisting of changing outside and inside money) under the hypothesis that international capital flows influence aggregate demand by changing the level of real balances. Fiscal and monetary policy are generally found to be effective in each of the models. CAPITAL FLOWS AND INTERNATIONAL ADJUSTMENT By Thai Van Can A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1972 G7%%S€3 aé’Ngay Mai Mgi’xt Tm"; mu ch. .. ACKNOWLEDGMENTS I wish to express my gratitude to Professor Anthony Koo who suggested the t0pic and provided freely of his time and patient guidance. Special thanks are due to Professor Mark.Ladenson and Professor Maurice Weinrobe whose concise criticisms and invaluable assistances helped me see the way through many dark tunnels. Appreciation is also due to Professor Warren Samuels whose advice and understanding added another spicy touch to my graduate- study expreience. To all my friends and colleagues and especially to those in the Third World Study Center: M. Allal, W. Barnett, S. Behdah, Huynh Cong Hiep, J. Palmer, 8. Sheer, Nguyen Thi Bich Thuy, Vu Quoc Thuy, Ron Tracy, I extend my sincere thanks for their help, encouragement, and willingness to discuss economic as well as non economic problems whenever requested. To the members of my family who have given so much and asked so little I can only say that words will never be able to convey my feeling for their unstinting support of this as of all my other endeavors. They make everything worthwhile. ii TABLE OF CONTENTS List of Tables .. ..... . ........... ...... .......... . ......... List of Figures ..... ................. .... .................. INTRODmT I ON 0 O . O O O . O . O O . . . . . O . O O O O . O . . . O O . O ...... . ......... PART I: ONE-COUNTRY MODEL Chapter I DESCRIPTION OF THE MODEL .... ............. .. ..... 1.1 Assumptions ...... .......................... 1.2 Formal Description of the Model ............ II INTERNAL EQUILIBRIUM AND COMPLETE STERILIZATION . 2.1 Monetary Policy .................. .......... 2.2 FiscalPOIicy ......................... ..... 2.3 Comparison between Fiscal and Monetary POIicy ............O........................ conCIUSion ...........................O........OO III INTERNAL AND EXTERNAL EQUILIBRIUM ...... ......... 3.1 Monetary Policy .................... ...... O. 3.2 Fiscal-Policy ...................... ........ 3.3 Comparison between Fiscal and Monetary Policy .0.............................. ..... Conclusion ... ......... .... ............ .... ...... Iv GENERMJ GEE 0.... ..... ...... .................... 4.1 Eight Different Cases .... .................. 4.2 Determinant and Stability Conditions ....... 4.3 Analysis of Cases VI and VII ............... conclusion .......................... ...... ...... PART II: TWO-COUNTRY MODEL V FORMULATION OF THE TWO-COUNTRY MODEL ............ iii Page vi VO‘ 20 20 25 29 31 33 34 38 40 46 48 49 49 53 61 62 VI VII VIII IX X INTERNAL EQUILIBRIUM AND COMPLETE STERILIZATION . 6.1 Monetary Policy ............................ 6.2 FiscalPOIicy ..................... ..... .... conCIUSi-on ........................O.......OOOOOO INTERNAL AND EXTERNAL EQUILIBRIUM ..... .......... 7.1 Monetary Policy ... ......................... 7.2 Fiscal Policy .............................. Conclusion ........ ............. . ................ GENERfllcwE .... ..... ......O....... ............. 8.1 Determination of Different Cases ........... 8.2 Determinants and Stability Conditions ...... 8.3 Fiscal Policy ................... ........... 8.4 Monetary POIicy ......O.........O.....O..OO. Conclusion ........................ ..... ......... SENSITIVITY ANALYSIS FOR THE GENERAL CASE ....... 9.1 Constraints and Choices of Values for the Parmeters ......O.......................... 9.2 Elimination of the Improbably Cases ........ 9.3 Analysis of the Results .................... 9.4 Sensitivity of the System to Changes in the Parameters ............................ ..... SUMMARY AND CONCLUSIONS .................... ..... SEECEDBIBLIOGRMW ....................................OO APPENDIX A ................ ........ ...... .......... ......... MPENDIX B . . . . . O . ..... . ...... . . . O Q . . O ........ . O O . . . ........ APPENDIX C ........................ ......... .. ..... . ........ MPENDIXD..........O....00.00.00.00000......OOOOOOOOOOO... APPENDIX E iv 66 67 72 78 79 80 83 85 87 87 94 100 108 110 110 114 115 118 122 140 145 146 156 '162 165 Table 4.1 4.3 4.4 8.2 8.3 8.4 8.5 9.1 9.2 LIST OF TABLES Sign Relations among the Entries of Matrix A ....... Eight Different Sign Patterns for Matrix A ......... Changes in the Sizes of Income and Interest Multipliers following Changes in the Values of Ki and Ky, Cases VI and VII .............. ............. Effects of an Increase in M, MI, and G on the Balance of Payments Position with Different Values Ofxy andxi ...... .......... ......... ..... O ........ Sign Relations Among the First Two Column Entries OfMatrixA..... ..... ......O.... ........ . 0000000000 Ten Different Sign Patterns for Matrix A ........... Changes in Incomes and Interest Rates for a Payment Deficit and a Payment Surplus Country under a Fiscal Expansion ............. ..... . ..... . .......... Effects of an Increase in the Money Supply (M) and the Monetization of the Debt on Incomes and Interest Rates ofCountriesIand II, Under Hypotheses I and II Effects of an Increase in Inside Money on Incomes and Interest Rates of Countries I and II, Under HypotheseSIand II ......O....... ....... 00......000 Relations Among Ky, Ly, M, E1, and K1.. for Cases IX andx......0.0......000.........O.........O.. ...... Values Used for the Sensitivity Analysis Cases IX andx................ ...... ......... ........ O ...... Page 50 50 55 89 90 99 104 107 112 113 Figure 3.1 8.1 LIST OF FIGURES Fiscal and Monetary Policy for Internal and External Balances .......O...........O..... ......... Fiscal Expansion Under Hypothesis I ....... . ........ Monetary Expansion in Outside Money for Country I Under Hypotheses I and II .................... ...... ‘Monetary Expansion.in Inside Money for Country I Under HypotheSiSI ..................... ........ .... The BF Curve, Surplus and Deficit Regions .......... Relative Positions of BP, EE, and LM Curves ........ Relative Positions of BP, EE, and LM Curves and stability Of the system .................0.00. ...... vi Page 44 95 102 106 149 150 154 INTRODUCTION This dissertation is concerned with the effectiveness of fiscal and monetary policy in Open as well as interdependent economies where capital flows receive a particular interest. They will depend not only on the interest rate but also on income and they will be allowed to influence the level of aggregate demand. To investigate the impacts of fiscal and monetary policies on Open economies which do not only exchange goods and services but also capital movements, economists have conducted several studies that we may conveniently review according to the assumption whether the country is small or large. The latter allows for foreign reprecussions whereas the former ignores them. hi Section 0.1. The Small Country Assumption: No Foreign Reprecussions This is the most wideSpread assumption in international economics literature. This assumption, to borrow from A. Krueger's words, implies that: ... the rest of the world is unaffected by any develOpment within the country: in particular that foreign interest rates are constant and that the terms of trade and foreign prices are unaffected by the level of domestic real income or prices. L27, p. 199] Therefore, the level of exports of a small country may be treated as a completely exogenous variable, while its fiscal and monetary policies cannot influence either the levels of income, 1 price or the interest rate in the rest of the world. This assumption has led to the development of a series of one-countrydmodel studies. They were based mostly on a constant price level within a two~market economy: commodity and money markets and where the impacts of fiscal and monetary policies were examined under the conditions of fixed as well as flexible exchange rates. See for instance, Johnson [20], Krueger [27], Mundell [40], Ott and Ott [44], Sohmen [59]. The wealth effect in such a model was studied by McKinnon [32] and by McKinnon and Oates [33] and Takayama [63]. In some of those studies, for instance, Mundell [40], Sohmen [59], Takayama [63] capital flows are made to influence the money supply, whereas in some others, e.g. Johnson [23], 0tt and Ott [44] they are not. But in most of them, when capital flows are considered, they are made a function of the small-country interest rate while the rest-of-the-world interest rate is assumed constant. However, in 1966 Johnson wrote his capital function as dependent on the domestic interest rate and income. In 1969, the argument income of the capital function was included by Takayama in his study [63] where the wealth effect as well as the possibility of variations in the price level were considered. At the end of their analyses, Johnson [23, pp. 358-59] and Takayama [63, p. 209] admitted that their studies had a major limitation that we may extend to the others as well eSpecially inasmuch as they treated international capital movements as a variable which did not affect the level of aggregate expenditures. This limitation, we will attempt to remedy in our study. Section 0.11 The Large Country Assumption: Foreign Repercussions The studies conducted under the small country assumption are partial equilibrium in character, since they pay no attention to the feedback of domestic policy through changes in the economic variables of the rest of the world. Any policy taken by any country, however small its size may be, but especially for a large country like the United States, is expected to cause some reper- cussions on other countries. To account for this interdependence in any model dealing with international adjustment, it is desirable to include a second country representing the rest of the world. The first of such analyses are to be found in the pioneering works of F. Machlup [31] and L. Metzler [34, 35, 36, 37]. The former was more concerned with the foreign multiplier, while the latter with the transfer problem and its adjustment mechanism through income. But, both of them dealt with two or more countries which were supposed to be Open and interdependent, i.e. the exports of a country depended on the level of incomes of the countries from which it imports. In their models, they focused their analyses on the commodity market equilibrium condition and assumed price, the interest and exchange rates to be constant. In subsequent studies, those restrictive assumptions were dropped. In 1964, Mundell [40] examined the effectiveness of fiscal and monetary policies under the asswmptions of fixed and flexible exchange rates and perfect mobility Of capital. In 1965, Kemp [25] went a step farther to study the cases of immobility and imperfect mObility of capital. In 1969, COOper [14] with a fixed- exchange-rate model made the international capital movements between two countries depend on the interest rate differential. But, Cooper was particularly interested in the gains derived from the coordination of the instruments of economic policy and how those gains vary with the degree of economic interdependence between countries. In 1970, ROper [55] was interested in the same problem but within the context of a constant world money supply. In his work capital movements depended on the interest rate differential as well as the change in the differential itself. In the same year Eeckhoudt in an unpublished Ph.D. dissertation [16] studied the effects of different economic policies on Open and inter- dependent economies, where investment and saving were the result of the difference between the desired and actual level of wealth. The capital flows between countries were a component of wealth and depended merely on their interest rates. From those studies one may single out three points: 1-The economies in question consist of two markets only: commodity and money markets; 2-As in the one-country models, the two-country models do not allow international capital move- ments to affect aggregate demand; 3-Capita1 movements depend only on the interest rates of the countries involved but not on their reSpective incomes. Our contribution consists of the remedy to the above limitations undertaken in a three market economy a la Patinkin: commodity, bond, and money markets, where the wealth effect and inside money are also considered. In Part I, the analysis will be conducted under the small- country assumption, in Part II that assumption will be relaxed, permitting the feedback mechanism to Operate. In each Part three different cases will be considered. A-The authorities of the country or countries desire that the internal goals of increasing income and employment should not be disturbed by the international conditions. They may realize this by completely sterilizing their balance of payments. This is the case of complete sterilization (or CS). B-The authorities are not only concerned with the above internal goals but also with maintaining the equilibrium in the balance of payments. This is the case of internal and external equilibrium (Balance of Payments = R = 0, or R0). C-While they can continue to use fiscal and monetary policies to pursue the internal goals they may not either actively seek the equilibrium in the balance of payments or completely sterilize it. We will call this the general case (or GC). we will assume throughout this study that the price level is constant and the exchange rate is fixed between countries. PART I ONE -COUNTRY MODEL CHAPTER I DESCRIPTION OF THE MODEL Dividing the economy into three markets, i.e., commodity, bonds, and money markets, a la Patinkin, we propose to investigate the effectiveness of fiscal and monetary policies on the level of income, the rate of interest, when foreign trade as well as inter- . 1 . . national capital movements are included in the model. Section 1.1 Assumptions l-This study will be conducted under Keynesian conditions. The economy is functioning at less than full employment level, the price level is assumed to be constant. Employment is directly proportionate to income. 2-The rate of exchange between the countries is fixed. 3-The home country is small. Thus, its economic policy cannot influence incomes and interest rates in other countries. 4-The total wealth of the country is composed of its out- side money, the surplus in its balance of trade, and human and non- human capital. Since both forms of capital are assumed constant during the period of our analysis, only outside money or its equivalence from the foreign sector remains in the model. This study only deals with financial capital flows. S-In fact, outside money is issued by the central bank against either government deficits, surpluses in the balance of trade, or net inflows of foreign capital. 'The amount of foreign reserves representing the surpluses are repatriated and bought by the central bank with an equivalent amount of newly issued out- side money (BT). The central bank may neutralize this new increase in the money supply by an equal decrease in the amount of outside money (M) already existing in the economy. As for the net inflow of capital (K), it may create an amount of outside money smaller or greater than K. The ratio of the newly created outside money to the net capital inflow is represented by v, or coefficient of sterilization. If v = 0, the central bank does not create any outside money for a given inflow of capital; if v = 1, it creates an amount of outside money exactly equal to the capital inflow. As a consequence, the central bank may change the total supply of money by changing either M or v (the amount of outside money and the coefficient of sterilization). 6-Capital is neither perfectly mobile nor perfectly immobile. If perfect mobility exists, the interest rates prevailing at home and abroad are equal. If there is a complete immobility no capital flows will take place. Section 1.2 Formal Description of the Model The main characteristics of this model may be found in Patinkin's study [46]. We will examine the production function for the supply side; the commodity, bond, and money markets, and the balance of payments for the demand side. A - Supph Side: The Production Function The aggregate production function relating output Y to the total input of labor N and to the total fixed capital equip- ment of the economy K0 is (1.1) Y = f(N,Ko) Since within the short run, changes in capital stocks are dis- regarded, the production may be written as (1.2) Y= f(N) where f' =-->0 . Under the assumption of profit maximization and perfect competition, the scale of production is adjusted so that the marginal product of labor is equal to the real wage rate 3' and the demand function for labor is (1.3) f' =§ The labor supply takes the form W0 + $01) (1.4) §= P SUbject to ¢(N)=0 if O 0 ll - 0 I . dY . . since f is negative, f positive 3P. must also be pos1t1ve. Thus, an increase in P will increase Y. We may ask what is the sign of £2? From (1.13), we get d¢ ' =§— N, P is variable. We will be concerned with the case of constant price only. As a result, all variables in our model will be expressed in real terms, unless otherwise stipulated. B - Demand Side For the demand side, we will describe the commodity, bond, and the money markets, and the balance of payments. 1 - Commodity Market The basic equilibrium condition for this market is the traditional one: (1.16) Y=C+I+X~IM+G where C, I, and G represent consumption, investment, and 11 government expenditures respectively, whereas X = exports and IM 8 imports. Consumption and investment can be lumped into total expenditures E, (1.17) E=C+I where C is consumption out of disposable income and investment is dependent on the interest rate i, and taking into account the real balance in the economy, the behavorial equation for E may be expresses as: (1.18) E = E[(l - t)Y, i, M + BT + vK] where t = the rate of taxation, a positive constant and less than one; M = the amount of outside money; v = the coefficient of sterilization; K = the net capital inflow; BT = the equivalent amount in outside money of the surplus in the balance of trade. Let (1 - t) = a where O s a < 1, equation (1.3) can be rewritten as: (1.19) E = E(qY, i, M +-BT + vK) where the partial derivatives of E with reSpect to Y, i, M, and R have the following signs: Ey = e > 0; Ei < 0; E > O; E > 0; E > O . M BT R The total amount of tax is assumed to be proportionate to Y (1.20) T = tY 12 and the government expenditures are set at (1.21) G = C0 The level Of exports is assumed to be constant (1.22) X = X and the level of imports a constant prOportion Of income (1.23) IN = mY where m is the marginal prOpensity to import, a positive con- stant, less than one. 2 - Bond Market By assumption, bonds are traded under the form of consols paying one monetary unit (say one dollar) per period. Households decide on the total stock of bonds they wish to hold; firms on the total stock they wish to supply3. For the households, changes in those stocks represent their net lendings during the period; for the firms, their net borrowings during the period. Net lendings and net borrowings represent net savings and net investments reSpectively for the period under consideration. The initial bonds holdings and redistribution effects are assumed away. Bonds supplied by firms (BS 5 BF) are demanded by households (BH) and the banking sector (BB) which issues inside money 0M1) to make the purchase. Patinkin [46, pp. 213-21]. 13 (1.24) BB = MI . The total demand function for bonds is (1.25) BDEBH+BB =H(aY, i,MH+BTH+vKH) +MI The supply function is (1.26) BS E BF = J( Y, 1, MP + BTF + vKH) where MH the amount of M held by households; MF = the amount of M held by firms; BTH = the amount of M issued against a trade surplus and held by households; BTF = the amount of M issued against a trade surplus and held by firms; KH = the amount of M issued against a net inflow of capital and held by households; KF = the amount of M issued against a net inflow of capital and held by firms. It is to be noted that a does not appear in the supply function. It is more realistic to think that firms base their decisions to increase their activities, thus to supply more bonds, on the level of economic activity represented by Y rather than on income after tax. The partial derivatives BDy, BSY’ BDi’ BDMH’ BDBTPDK’ are positive while BSMF’ BSKF’ BSBT’ BSi, are negative. Since MF +'MH = M, BTF + BTH = BT, and KP + KH = K, the excess-demand equation for the bond market may be written as: (1.27) BD - BS 5 B(dY, i, M + BT + vK) + MI 14 where Bi’ BM, BBT’ and BK are positive, except that BY 18 equal to zero by assumption4. Equilibrium exists when (1.28) B(aY, 1, M + BT + vK) + MI = o . 3 - Money Market As in the case of bonds, the supply and demand in this market are for stocks. If MI is net wealth then M* will repre- sent the sum of M and M15. On the contrary, if MI is not net wealth (throughout this study we will adOpt this concept) then following Patinkin6 the equation for the supply of money is (1.29) M8 = M,+ BT + vK +‘MI and the equation for the demand for money is (1.30) MD = L( Y, i, M + BT + vK) where LY’ LBT’ LK are positive and L negative. It is to be i noted that a does not figure in the demand for money. Since money is demanded by households and firms to meet their expenditures as well as the payment of their taxes, therefore, it appears more realistic to make the demand for money depend on income before tax rather than after tax. 4 Ibid. p. 510. Pesek and Saving [49] and Saving [57]. Patinkin [46, pp. 296-97]. 15 The equilibrium condition for this market is (1.31) MD = MS 4 - Balance of Payments The balance of payments R is defined as R = EXports - Imports + Net Capital Inflow or (1.32) R = x - 1M + K where (1.33) BT = x - IM and capital K is not only responsive to the interest rate but also to income, since according to H. Johnson an increase in economic activity may attract international capita17. More pre- cisely international capital movements are supposed to reSpond to the incomes differential and the interest rates differential between the home country and the rest of the worlds. More formally (1.34) K=K(Y-Y', i-i') . Since the rest-of—the-world income Y' and the interest rate i' have been assumed to be constnat, by virtue of the small-country assumption, then equation (1.17) becomes (1.35) K = K( Y,i) where the income-sensitivity of capital (K ) and the interest- y 7 It would be more realistic to think that capital flows depend on the rate of growth dY/Ydt rather than on the absolute level of Y. The first specification would make the model too complex to solve. Following Johnson [23], we shall adopt the second one. 8 Patrick [48, p. 281]. 16 sensitivity Of capital (Ki) are both positive. After these preliminary explanations, the complete one- country model with trade and capital movements can be rewritten more clearly as follows. 1 - Commodity Market (I) Y=E+X-IM+G (11) E =E((yY, i,M+BT+vK)[0 0 di _ -2q(h+m) + qu > (2.5) KM— — A < o . If (2.5.1) Ly > 2(h+m) then g— > 0 di (2.5.2) Ly < 2mm) then 8M < o . From the above expressions, it can be concluded that an increase in M, like in Johnson's model [23, p. 349], will increase income thus, employment will unambiguously rise. But contrary to that model change in the interest rate is indeterminate. The difference 22 may be attributed to the presence of the wealth effect in our model. The interest rate is in fact, subject to conflicting forces: the increase in the amount of outside money tends to drive the interest rate down, while at the same time through its real-balance effects, it tends to drive the interest rate up. The outcome depends on which force is stronger. 2 - Effects on theigglance of Payments Although by decision, the balance of payments has been completely sterilized in order not to influence the pursuit of internal goals, we may still ask whether an increase in the amount of outside money, improves or worsens its position. Taking equation (XVI ) and totally differentiating it, we obtain (2.6) dR = ~de +'Kde +~Kidi dividing (2.6) by dM and regrouping the terms we have “...—6— _ 1 (TM idM (2.7) $- = (Ky - m) replacing dY/dM and di/dM by their values from (2.4) and (2.5), expression (2.7) becomes dR (Ky-m)[-qlai - (l-q)Ei] + Ki[2q(-h-m) + qu] > (2.8) EM'= A < 0 . The impact on the balance of payments in indeterminate. This is due to the indeterminancy in the direction Of change of the interest rate and to conflicting forces resulting from the in- crease in income. In fact, the increase in income tends to 23 improve the capital account by attracting international capital flows, and worsen the current account by inducing more imports. The final position of the balance of payments depends on the result of the above forces. Hence, the balance of payments may improve of deteriorate. However, the necessary and sufficient con- dition for its improvement is given by (2.9) 1 ml’_-qLi - (l-q)Ei] + Kil: 2q (+h+m)] . From the above expression, while nothing can be said about the influence of the interest sensitivity of capital Ki on the balance of payments, it can be seen that the higher the income sensitivity of capital Ky the greater is the likelihood for the balance of payments to improve. These results are precisely those obtained by Johnson [23, pp. 345-50] except that, instead of being indeterminate as in our model, the balance of payments tends to deteriorate more and more with increasing values of Ki' B - Increase in Inside Money For an increase in inside money the structural matrix re- mains the same, while the policy vector B becomes (2.10) BMI = [0 dMI]' . Using Cramer's rule, the effects of an increase in inside money on income and the interest rate can be found as (2.11) -—=—>O 24 di -h-m (2.12) dMi A < 0 . Thus, an increase in inside money will raise income and lower the interest rate unambiguously. If we compare inside and outside money, we can see that both increase income when they are increased. However, their magnitudes are not equal, they depend on the relative value of Li and Ei' From (2.4) and (2.11) we can see that if the absolute value of Li is greater (smaller) than that of Ei then the in- crease in income is larger (smaller) with an increase in outside money than with an increase in inside money. The effect of an increase in inside money on the balance of payments may be expressed by (2.13) 31-31— = (Ry - m)(-Ei) - Ki(h+m) 2 o the sign of which is indeterminate. If Ky < m, i.e. the increase in the capital inflow is less than the increase in imports resulting from an increase in income, then it is with a decrease in the interest rate, the balance of payments must deteriorate and the expression (2.13) is then definitively negative. However, in the most general setting, the necessary and sufficient condition for dR/dMI to be positive is (2.14) «yr-:i > -mEi + Ki(h-41n) . This expression shows that the higher K.y the greater is the likelihood for the balance of payments to improve and that the 25 higher K1 the better the chance for the balance of payments to deteriorate. These qualitative results are the same as those obtained by Johnson with an increase in M [23, p. 350] since by ignoring the wealth effect of M, he make it implicitly equivalent to our MI. l-The main difference between an increase in outside money and inside money is that the latter will lower the interest rate while the former may decrease or increase it. 2-The higher Ky is the more likely is that an increase in the money supply will bring about an improvement in the balance of payments. 3-The indeterminacy of the sign of the balance of payments resulted from an increase in the money supply conflicts with the common view that a monetary expansion will worsen the balance of payments. Section 2.2 Fiscal Policy The impacts of fiscal policy may be examined for the following cases: A - An increase in government expenditures is not accompanied by an increase in the money supply, this is the tradi- tional fiscal policy; B - An increase in government expenditures is in fact accompanied by an increase in the money supply, more precisely in the supply of outside money. This is the case of the monetiza- tion of the debt; C - A change in the amount of tax; 26 D - The increase in government expenditures is matched by an equal increase in the amount of tax collected. This is the traditional balanced-budget change. A - Deficit Financing With Constant Money Supply The government, through its Treasury, can finance the budget deficit without affecting the money supply. The Treasury, for instance, may sell bonds to the public and use the proceeds to finance the increase in G. As a result, the size of the money supply does not change. The structural matrix A remains the same, but the policy vector B now becomes (2.15) BG = [-dG 01' . Using Cramer's rule, it is found that dY a 1 (2.16) —dG _A > 0 di _ LY (2.17) dG - _A > 0 . An increase in government expenditures will increase both income and the interest rate. §_;;Change in Tax The authorities may choose to stimulate income and employ- ment by decreasing taxes, i.e. changing the tax rate. In this case the structural matrix A and the policy vector B become respectively 27 Fedm-l ETA 1 (2.18) AT = L L. Ly U whose determinant AT is (2.19) AT = (e~m-1)Li - EiLy which is always positive. (2.20) BT = [edT 0]' . As previously, the use of Cramer's rule yields eL. (2.21) %-__1 < o . -eL (2.22) 11,4 <0 . dT AT We find the usual result: a decrease in tax will increase income and the interest rate. C - Balanced-Budget The authorities may decide that an increase in expenditures should be matched by an equal increase in tax, i.e. d0 = dT. The structural matrix A for this case is the same as in (2.18), therefore, AT = AGB' The policy vector B becomes (2.23) BGB = [(e-l)dGB 03' Then, (2.24) 51-3- = SEE—Li- > o dGB AT 28 di (l-e)L (2.25) fi=-—AT1>O . A balanced-budget will increase income as well as the interest rate. It can be seen that if the value of the marginal prOpensity to spend out of gross income is greater than 0.5, which is the most likely in reality, then the increases in income and the interest rate are greater with a tax reduction than with a balanced budget. D - Deficit Financigg with Change in the Money Supply: The. Manetigation of the Debt Another way to finance the deficit is for the Treasury to sell bonds to the central bank in exchange for its deposits. This is equivalent to the Treasury printing of money. This method of financing is frequently referred to as the monetization of the debt . Thus, an increase in government expenditures is accompanied by an increase in the money supply, more precisely by an increase in outside money, i.e. dG = dM = dGM. The structural matrix A is the same as in (2.1), while the policy vector B becomes (2.26) BGM= [(4-11)ch (l-q)dGM]' . Then, (2.27) 3%}; = -(1+q)LiA- EiO-q) > 0 (2.28) 93- = (l-qH-hm) + Lqu) 3 o . dGM A ‘ If 29 (2.28.1) 2Ly > h+m then 361; > 0 di (2.28.2) 21y < h+m then dGm < o The monetization of the debt will increase income, whereas its impact on the interest rate is indeterminate. The interest rate is subject to conflicting forces: the increase in outside money tends to drive it down, while the concomitant increase in expenditures tends to drive it up. Without knowledge of the magnitudes of the parameters involved, it is not possible to know the direction of change of interest rate. Section 2.3 Comparison Between Fiscal and Monetary Policy We will take the case of an increase in government expenditures without changing the money supply and the increase in the amount of outside money as the representative types for fiscal policy and monetary policy, unless otherwise Specified. An increase in M and G (except the case Of monetiza- tion of the debt) will bring about an unambiguous rise in the level of income. The interest rate will increase with dG, while it may increase or decrease with M. Because of this indeterminancy the comparison of the interest changes will not be made. However, for income it is obvious from (2.4) and (2.27) that the increase in income resulting from an increase in 'M is smaller than that from the monetization of the debt, i.e. dy/dM is smaller than dY/dGM. The ranking of dY/dG and dY/dM cannot be as clearly determined. For their comparison, the expression (dY/dM - dY/dG) must be formed from (2.4) and (2.16) 30 (W 91 _ L1 - qLi - (140Ei _ (1-<1)(Li - 13,) (2.29) FM- - dG — A — A , From the above expression it can be seen that the income increase resulting from an increase in G is greater (smaller) than that resulting from an increase in M whenever the absolute value of L1 is greater (smaller) than that of Ei' More formally, dY > dY >'—‘ . (2.30) IL1I < [Ed at E< dM For the impact of fiscal policy on the balance of payments we will take the case of the increase in government expenditures with constant money supply as the representative case. Then, the equation for change in the balance of payments is cm- 91. 11 (2.31) dG (Ky m) dG +Ki dG replacing dY/dG and di/dG by their values from (2.16) and (2.17), expression (2.31) becomes (2.32) 3% = (Ry - m)(-L1) + KiLy It is clear that if K.y >~m, dR/dG will be positive and the balance of payments will certainly improve, but if Ky'< m, then its sign is ambiguous. However, the necessary and sufficient con- dition for the balance of payments to improve is (2.33) KiLy - KyI‘i > -mLi . Referring to (2.9), we may conclude that for an increase in M and G, the higher the income sensitivity of capital is the greater is the likelihood for dR/dM and dR/dG to be positive. But, 31 while nothing can be said about the influences of K1 on the balance of payments fo an increase in M, we may say that the higher the interest sensitivity of capital the more likely is for dR/dG to be positive. It is to be noted that these conclusions concerning the impacts of an increase in G on Y, i, and R are the same as those obtained by Johnson [23, pp. 349-51].- In sum, when Ky > m, fiscal policy, with the exception of the case Of monetization of the debt, will raise income and improve the balance of payments. When Ky < m both fiscal and monetary policies will increase in- come, but their effects on the balance of payments are altogether uncertain. Conclusion In an Open economy where international capital flows and the real balance effect are taken into consideration and where the authorities attempt to pursue their internal goals without being concerned with the external factors by completely sterilizing the balance of payments, the following main features may be pointed out: l-The income and interest multipliers depend only on the marginal prOpensity to import 'm and not on the income and interest sensitivity of international capital flows (Ky and Ki)' [See e.g. equations (2.1), (2.18)] 2-Both fiscal and monetary policies are effective to in- crease income and employment. [See e.g., (2.4), (2.16)] 3-Any fiscal policy which tends to raise income and employ- ment with a constant money supply M will result in an increase 32 in income and interest rate; 4-Any policy which tends to stimulate the economy and which is accompanied by a change in the amount of outside money will re- sult in a rise in income, but its effect on the interest rate is indeterminate; 5-With a high Ky it is easier for a fiscal expansion and a monetary expansion to improve the balance of payments than with a low KY; 6-With a high K it is easier for a fiscal expansion 1 to improve the balance of payments, whose change, however, is indeterminate with an increase in M; 7-With an increase in outside money (M) the effect on the interest rate is indeterminate, but with an increase in inside money (M1), the interest rate decreases unambiguously. Further- more, if KY is smaller than ‘m, the effect of an increase in M on the balance of payments is uncertain, while an increase in MI deteriorates it. 8-The qualitative impacts of an increase in inside money and government expenditures on the level of income, the interest rate, and the balance of payments are similar to those obtained by Johnson [23] where instead of an increase in inside money there is simply an increase in the money supply. CHAPTER III INTERNAL AND EXTERNAL EQUILIBRIUM Instead of completely sterilizing the international balance of payments as we have examined in Chapter II, the authorities choose not only to pursue the internal goal of in- creasing income and employment but also the external goal of equilibrating the balance of payments. we intend to show that, except under highly improbably circumstances, fiscal or monetary policy alone is incapable of reaching the internal and external goals simultaneously. In order to achieve those goals there must be at least two policy instruments. Thus, proving in this particular context, the validity of Tinbergen's principle of the equality between the number of instruments and the number of targets. The external equilibrium requires that (3.1) R = x0 - IM + K(Y,i) = o 01' (3.2) xo - IM = -K(Y,1) . Replacing those two equations in the system on page 13, with v = l and after performing the usual transformations we obtain 33 r n ‘ -h-K E. - KIN ANY r:dG - qu y 1 1 (3 .3) e + L Ly Li J ndi LdMI (l -q)dMJ or more compactly (3.4) AX=Bl . The determinant A of A is equal to (3.5) A = (--h-l(y)Li - (‘Ei - Ki)Ly > 0 which is always positive. As it can easily be seen the only difference between (3.3) and (2.1) is to be found in the structural matrix A, where m in the CS case has been replaced by K.y and E1 by (E1 - Ki). In this chapter, the same Operations will be performed as before to investigate the effects of fiscal and monetary policies on the level of income and the interest rate. Section 3.1 Monetarnyolicy A - Increase in Outside Money An increase in outside money brings about the following results: -qL. -(1-q)(E -K) (3.6) QY-s 1 i 1 >0 dM A . -2q(h+K ) +’qL 93., 1, ty,> (3.7) an A < 0 . For each chapter, when A, X, B, or A are mentioned, they refer only to the matrices and determinant defined in that chapter, unless otherwise specified. 35 If (3.7.1) LY > 2(h + 1%) then gin-‘- > 0 (3.7.2) 1.Y < 2(h + 1(1) then %< o . Like the CSI case, an increase in outside money will bring about an increase in income, while the interest rate may decrease or increase. 1 become greater and greater? For convenience sake, we will use the What happens to income and interest rate if KY and K notation (« m) to translate the concept "becoming greater and greater". Then, if £1!“ 11ng (3.8) 1840:): (TM 0 and (1M L1<0 9}. 1:1 21,, (3.9) KiawndM-D IY>O and M 0 dY di (3'10) 1% and Ki-OooadM-o-hp and m...” L - (l-q)E le. 'qi 1 (3.11) KY and Ki~0=m~_hL -EL >0 and 1 1 Y gidQ(ly'2h)zo dM -h-E£LY From the above expressions we may make the following remarks: 1-When the authorities are concerned with maintaining equilibrium in the balance of payments, the higher Ky is the smaller is the increase in income and the more likely it is that the interest rate will decrease; 2-The higher K1 is the more likely it is that the interest rate will remain constant, while income will increase; 36 3-In the absence of international capital movements, i.e. K.y and K1 tending to zero, income will increase, while the interest rate remains indetenminate; 4-In the presence of perfect capital mobility, i.e. Ky and K tending to infinity, income will increase and the interest i rate will decrease indefinitely. This result is at Variance with that reached by Mundell [40, p. 261], McKinnon and Oates [33, pp. 13-17] and Sohmen [59, p. 519]: an increase in the money supply has no impact on income and the interest rate. The difference stems from the constraint of the equilibrium of the balance of pay- ments in our model, while it is absent from their studies. The behavior of income and the interest rate seems strange indeed, when K.y or Ki becomes greater and greater, yet, an explanation can be found in the external equilibrium constraint. Take a value of Ky’ say (Ky)1 sufficiently large in the neighbor- hood of infinity in order to make di/dM close to its limit 2q/Li and dY/dM still positive. From the external constraint, one knows that the balance of payments will deteriorate due to the increase in imports and an outflow of capital due to the de- crease in the interest rate. In order to counterbalance this deterioration, there must be an inflow of capital due to the in- crease in income. Now suppose there was an increase of de in the income sensitivity of capital to (Ky)2 which is equal to (Ky)1 + de, since di/dM has practically decreased to its lower limit, there would be no more capital outflow due to Ki or an increase in imports, while there would be an inflow of capital due to the increase in the value of Ky. This would produce a 37 disequilibrium in the balance of payments. Since the exchange rate is fixed the only way to reestablish the equilibrium in the balance of payments is for income to decline. Thus, if Ky becomes greater and greater in value and.after the initial change following the increase in. M, the limit of the decline in income approaches zero. Following the same line of reasoning, the result for K tending i to greater and greater values can be easily established. B - Increase in Inside Money An increase in inside money will raise income and decrease the interest rate. More formally, K - E (3.12) dMI A > 0 (3.13) EM? 3 ——1A < 0 . An increase in outside money and inside money will lead to an increase in income, however, their magnitudes are not equal. i’ and Ki' From (3.6) and (3.12) one concludes that if the absolute value L1 is greater (smaller) than that of (E1 - K1) then the rise in income They depend on the relative values of L1, E is larger (smaller) with an increase in outside money than with an increase in inside money. When K.y or Ki tend to infinity, dY/dMI and di/dMI become respectively dY di 1 (3.14) Ky-ocondMI-io and dMIflLi0 and 93—40 i dMI Ly dMI 38 (3.16) Ky and Ki-ocoag-MX-faoo and iii-few . On the contrary, when they tend to zero, we obtain (3.17) K and K. -oO==—"-—o y 1. di -h dMI " -hL.-E.L < O ' . 1 1 y By comparing the results obtained for the outsidedmoney case and the insidedmoney case, we see that the conclusions thus far reached for the former apply to the latter. There is only one main difference, the interest rate decreases with an increase in the amount of inside money while it remains indeterminate with an increase in the amount of outside money. Section 3.2 Fiscal—Policy A - Deficit Financing with Constant Money Supply The results of this policy on income and interest are -L d_Y.=__i. (3.18) dG A > 0 di 1:1 (3.19) E=A >0. From the above two expressions, it is obvious that if K.y or Ki tends to infinity, both dY/dG and di/dG will tend to zero, and if Ky or Ki tends to zero they are still both positive. The conclusion is that the higher the value of Ky or Ki - or the greater the mobility of capital movements - the less effective will be an increase in government expenditures with a constant money supply in increaseing income and employment. A corollary to 39 this is that the existence of perfect capital mobility will leave income and interest rate unchanged when there is an increase in government expenditures with constant money supply. This result is contrary to that reached by Mundell [40, p. 261] and Sohmen [59, p. 518]: when there is perfect capital mobility an increase in G is capable of increasing the level of income and employment. The difference is due to the balance-of-payments constraint which is present in our study but absent in their models. B - Change in Tax The structural matrix becomes: r3-K -l E. - K? Y 1 1 Ar = L Li L y I and its determinant is (3.20) AT = (e-Ky-1)Li - (Ei - Ki)Ly > 0 and eL dY 1 (3.21) —-=--<0 dT AT . -eL (3.22) 9—1-=-1>0. dT AT C - Balanced Budget (e-1)L. (3.23) E6? = —-ZT——1- > 0 51}... (l-e)L (3.24) = dGB Ar 40 D - Monetigation of the Debt d, («i-m, - (E11 - K1) (l-q) (3.25) m= A > 0 d, = <1-q) (-h-Ky) + (mm.Y > (3.26) BE— A < 0 If (3.26.1) L > h + K then £1-i'--->10 y y dGM di (3.26.2) LY < h + KY then dGM < 0 For each above case, the directions of changes in income and interest rate are the same as in the 031 case in Chapter II. The conclusions concerning the influences of the extreme values of Ky and K1 on income and interest rate reached for the case of an increase in government expenditures with constant money supply apply to the above varieties of fiscal policy except the case of monetization of the debt where the conclusions are the same as for the case-of an increase in the amount of outside money. Section 3.3 Comparison between Fiscal and Monetary Policies The comparison between positive and negative changes in the interest rate cannot be made, as was shown in Chapter II. Only the income multipliers resulted from an increase in M and G will be compared. Let form the difference between dY/dM and dY/dG d3 11... - (3.27) dM dG 2q(Li Ei + Ki) We can see that if 41 dY dY (3.27.1) Ki - Ei > 4L1 then dM >rdc dY dY Nothing more can be said about the relative magnitudes of the multipliers. They depend crucially on the relative magnitudes of the absolute values of Li and (K1 - Ei)° As for the balance of payments, we need not be concerned whether the effect of a policy will result in an improvement or deterioration, since by imposing the constraint R = 0, we know that at the end of all adjustments the net sum of the capital flows and the balance of trade must equal zero. But we can legitimately ask the question is this constraint of external equilibrium feasible under any condition? Since R = Xo - IM + K ( Y,i) = 0 then (3.28) dR = ~de + 1(de + Kidi = 0 or (3.29) (m - Igl)dY = Kidi . For an increase in government expenditures with money constant, the combination of (3.18), (3.19) and (3.29) yields (3.30) -Li(m - KY) = KiLy . Since the right hand side of the above equation is definitely positive, the left hand side must be also positive, which implies that (3.31) KY < m . 42 Therefore, if K,y is greater than the marginal prOpensity to import, it is impossible for the external equilibrium constraint to be achieved when an expansionary fiscal policy is adapted. The necessary and sufficient condition for 3%.: 0 is (3.31.1) ~mL. = K.L - L.K . For an increase in M equation (3.29) becomes (3.32) (m - Xy)[—qLi - (1-q)(13i - 1(1)] = Ki[-2q(h + Ky) + qu1 . We can see that if Ky >Im the necessary condition for an increase in M to achieve the external equilibrium constraint is 3.33 L < 2(h+K ) ( ) Y Y and the necessary and sufficient condition for dR/dM = 0 is o o - - = - + (3 34) 2m(2K1 Ei) mLi KiLy Ky(2Ei Li) For an increase in M1, the constraint R = 0 is satisfied when (3.35) (m - Ky)(Ki - Ei) + Ki(-h - Ky) = 0 . Since the second term is always negative, the first term must be positive for the expression (3.34) to be equal to zero. This can be achieved if (3.36) Ky < m . This is exactly the condition (3.31) when there is an in- crease in G. The necessary and sufficient condition for dR/dMI = 0 is 43 (3.37) m(Ki - E1) = Ki(h + Ky) + Ky(Ki - Ei) From the three necessary and sufficient conditions for dR/dG, dR/dM, and dR/dMI equal zero we can see that given the values of all other parameters, there is only one value of the marginal prOpensity to import (m) which can satisfy each relation (3.31.1), (3.34), and (3.37). Thus, the reader should not be surprised when he sees that m does not appear in the multipliers of this chapter. It does not mean that these multipliers are independent of m in the sense that with any value of m their values do not change. In fact, m does figure in the eXpressions of the multipliers implicitly by satisfying the above necessary and sufficient conditions for R to be zero and by substituting m by its value determined precisely by the above conditions. If m no longer satisfies those conditions, equilibrium in the balance of payments cannot be Obtained, and then the expressions for the multipliers would have to contain m as well. The complexity of those relations raises doubt about the feasibility of increasing income and achieving the equilibrium in the balance of payments simultaneously by using either an increase in G, M, or MI alone. To achieve those goals, two policies must be used. Consider Figure3.1 where the EE, 1M, and BP curves represent the equilibrium in the commodity market, money market, and the balance of payments (See Appendix B). Suppose initially we were in equilibrium at (io, Y0), under the constraint R = 0, and that the authorities decided to increase income by increasing G. EE would shift to the right to EE Since R = 0, BP would 1. Y0 Y2 Y1 FIGURE 3.1 FISCAL AND PDNETARY POLICY FOR INTERNAL AND EXTERNAL BALANCES 45 remain invariant. Income would increase to Y1 and the interest rate to i At I where EE1 and LM intersect, the balance 1' l of payments is in a deficit position. To close the deficit and achieve the external equilibrium, the authorities must choose one of two policies. The first policy would be to alter m. How can the authorities achieve this? By imposing quotas or increasing tariffs such that the resulting surplus in the balance of trade makes the BP curve move down to GP1 and pass through 11 where the constraint R = 0 is definitely satisfied at a higher level of income (Y2). An alternative policy would be to reduce the money supply. Then the LM curve would shift to LM1 which would raise the interest rate stimulating capital inflow. Of course, the authorities would have to reduce the money supply further to neutralize the effect of capital inflow on the money supply such that LM pass 1 through 12 where the constraint R = 0 is satisfied at a higher level of income (Y2). Thus, in this particular context, we have proved the necessity of having at least two policy instruments in order to attain two objectives, hence corroborating Tinbergen's principle of the equality between the number of instruments and the number of targets. Having established the above conclusion, we may ask which combination of policy instruments G and M, or G and MI is preferable to attain those goals. If G and M are used then in addition to condition (3.31) and from (3.32) we derive the complementary condition 46 (3 .38) 1Y > 20mg!) On the contrary if G and MI are used instead, then the only requirement is that (3.39) 1% < m . From the viewpoint of a policy-maker, it is preferable to change G and MI rather than M in order to achieve both internal and external balances, since the only condition for this to happen is Ky < 111. On the contrary, the use of G and M, in addition to condition Ky < m the existence of condition (3.34) or condition (3.38). Conclusion l-Both fiscal and monetary policies are effective in raising income and employment. Z-Any policy which tends to raise income with a constant money supply M will result in an increase in income and the interest rate. 3-Any policy which tends to stimulate the economy and which is accompanied by an increase in the amount of outside money M will result in an increase in income, but its effect on the interest rate is indeterminate. 4-A high K militates against the use of the fiscal 1 expansion - except the case of the monetization of the debt - and in favor of the use of the monetary expansion to achieve the internal balance. A low Ki favors the use of fiscal and monetary expansion to achieve the internal balance. 47 5-With either a high or low K1 the effectiveness of fiscal and monetary policies to achieve the equilibrium in the balance of payments cannot be clearly determined. 6-In the absence of capital movements, i.e. Ky and K1 tending to zero, both fiscal and monetary expansion are equally efficient to increase income and employment. 7-When there is perfect capital mobility, i.e. Ky and K1 tending to infinity, monetary expansion is very effective and fiscal expansion is completely ineffective in increasing income and employment. These results are at variance with those obtained by Mundell, Sohmen: monetary expansion is ineffective while fiscal eXpansion is effective to raise income and employment. 8-Unless by chance, the use of either G, M, or M1 to increase income under the constraint of the equilibrium in the balance of payments, is not feasible. There must be at least two policy instruments, e.g. G and M to reach those two goals. Thus, this instance corroborates Tinbergen's principle of the necessity of the equality between the number of instruments and the number of goals. 9-If K.y is smaller than m, to achieve internal and external balances, the use of G and MI is preferred to that of G and M. CHAPTER IV GENERAL CASE In Chapter II and Chapter III we have examined the situa- tions where v = 0 and R = 0 respectively, in this chapter the case of v positive and R different from zero will be analyzed. Under that hypothesis, the system is represented by (1.24) which is reproduced below: r' -I F‘] F 1 -h-qm-m+vq1(y Ei+qui dy -dG-qu (4.1) g L +2qm-2qu L.-2qu. di dMI+(l-q)dM [Y Y 1 1] L; I. J or more compactly by (4.2) AX = B . The structural matrix A may be more conveniently rewritten as q F811 al12 (4.3) A = 821 822 I. J the Sign of which cannot be calculated because all’ 312, and a21 are indeterminate in sign. We are left with the alternative of counting all possible combinations of signs in the matrix A and analyzing the ones we are most interested in. 48 49 Section 4.1 Eight Different Cases We know 811’ 812’ and a21 may take on either a positive, negative, or a zero value. There are 33 possible different combinations of A. Since the value zero is highly improbable and accidental, it can be ruled out, only 23 cases remain. Table 4.1 presents the tree indicating the relations of signs among the elements of matrix A. Table 4.2 shows their sign patterns. Among those eight possible combinations of matrix A, we will be interested in the cases which exhibit stability. Section 4.2 Determinant and Stability Conditions Up to this point, the comparative statics analysis has yielded the equilibrium values for the level of incomes and the interest rate in response to various changes in fiscal and monetary policies. The results of Chapter II and Chapter III are of limited usefulness, however, unless equilibrium positions are also stable. If there is no guarantee of stability, a change in an exogenous variable, e.g. M or G, can lead to a time path for an endogenous variable, e.g. Y or i, which does not approach an equilibrium position. As a consequence, the predictive value of the comparative statics results derived without attention paid to stability is severely limitedl. Taking account of this consideration, an investigation will be made as to which of the eight cases are likely to be locally stable 2 for a particular dynamic adjustment, i.e. a tatonnement mechanism . Quirk and Ruppert [50, pp. 311-12]. 2 This is Samuelson's "stability of the first kind in the small". See Samuelson [56, pp. 263 and 334-35]. 50 TABLE 4.1 SIGN RELATIONS AMONG THE ENTRIES 0F MATRIX A 8121< 0 II 11 ‘ > 0 III 812 < 0 IV a >10 V ‘ 12 a21 > 0 812 < 0 VI > 0 VII a11<0 12 | a21 < 0 ,n____a12 < 0 VIII Source: System (4.1), p. 48. TABLE 4.2 EIGHT DIFFERENT SIGN PATTERNS FOR MATRIX A Case I Case II Case III Case IV + + + - + + + - + - + - - - - - Case V Case VI Case VII Case VIII - +7 - - - + - - + - + - - - - - Source: Table 4.1, p. 50. 51 Only those cases will be retained for further analysis. Incidentally, we will examine whether the case of Complete Sterilization in Chapter II and the case of Internal and External Equilibrium in Chapter III fulfill the requirements for stability. In a sufficiently small neighborhood of equilibrium, for instance Y0 and 10, the adjustment process can be approximate by the linear terms of a Taylor series expansion, so that the system may be written as3 P F’ ‘1 r 1 $ Y1 0 -h-qm-m-I'quy Ei-l-qui-I [Y - Yo di -- 0 L +2 m-Z K L,-2 K i - i r A z where Yl’ V2 are constants assumed to be positive and representing the speeds of adjustment in each market. More compactly, the system (4.4) may be rewritten as (4.5) Z=1"AZ , z=[zi] . The general solution to (4.5) is given by4 )(t S (4.6) 2, - 20 (t)ej [1=1,2] 1 j=1 ij Where 3 s 2 is the number of distinct characteristic roots of PA: Qj(t) is a polynomial in t of one degree less than the Quirk and Ruppert [50, pp. 312-13] and Sohmen [59, pp. 518-19]. For more details, see Appendix C. QUirk and Ruppert, p. 313. 52 number of times the jth root is repeated, and A) is the char- acteristic root of PA. The system (4.5) is stable if and only if all the real parts of the characteristic roots of FA are negative. The characteristic equation of the system (4.5) will take the form 2 where D1 and D2 are the sum of all the first and second order principal minors of PA. The necessary and sufficient condition for system (4.5) to be stable 185 (4.8) D1 < 0 and (4-9) D2 > 0 i.e. the trace of matrix A must be negative and its determinant must be positive6. Referring back to matrix A in (4.1) we see that if Ky is smaller than m or Ki’ then condition (4.8) is satisfied, but condition (4.9) will not be satisfied until (4.10) (-h-qm) (L i-quKi) + 2v2q2K K - + - _ y i Ei(Ly 2qm) > (Ly+2qm Ei)qui These conditions are too complex to be able to derive meaningful prOpositions for the analysis. We will look among the eight cases 5 This is Routh-Hurvitz's condition for stability, see Quirk and Saposnik [51, p. 165]. Baumol [5, Proposition Eleven and PrOposition Twelve, p. 365]. 53 for the ones which unambiguously satisfy those conditions. But, before doing this, lets look back to Chapter II and Chapter III and especially at the A matrices in (2.1) and (3.3). They satisfy the necessary and sufficient condition for stability, i.e., both conditions (4.8) and (4.9) are fulfilled unambiguously. Among the eight possible cases in Table 4.2, Cases I and IV should be rejected as their determinants are definitely negative, Cases 11, III, V, and VIII do not satisfy both conditions simultaneously, they must also be rejected. Only Cases VI and VII pass the test of stability. As a consequence, they will be retained for our study. Section 4.3 Analysis of Cases VI and VII In this section the impacts of fiscal and monetary policies on income and interest rate and on the balance of payments will be examined. As usual, the case of increase in government expenditures with constant money supply will be the representative case for fiscal policy. A - Effects on Income and Interest Rate With the sign patterns presented in Table 4.2, the determinants for Cases VI and VII must be positive, more precisely = O G In - - + - o (4.11) A ( h vqm m-I‘quy) (Li 2qLi) (E1+"qK1) (Ly 2qm 2quy) > o For Case VI, the effects of an increase in outside money M, inside money MI, and government expenditures, on income and interest rate are given by 54 -qL - 2qE (4.12) {g— .. i A i > 0 qL + 2q(-h-m) (4.13) SIM—i =- y A 2 0 E, + qu dY 1 i (4.14) dMI A > 0 d i -h -vqm + WK! 2qu - L, (4.16) g— - + A 1 > 0 L +-2vqm - 2qu 2.1. a v 1 (4.17) (16 A >0 . These results are the same as those in case CSI of Chapter II and ROI of Chapter III. i between zero and the neighborhood of infinity. They may only vary Unlike the cases 081 and ROI, Ky and K may not vary between zero and an upper bound determined by the constraints imposed on the elements of matrix A, Case VI. In fact, h +-qm-+ m (4.18) all < 0 a Ky < .51 (4.19) 812< 0031Ki<-v—q L +-2qm (4.20) 821 > 0 a Ky < L——-2vq . Table 4.3 represents the directions of change of different multipliers in response to increasing values and decreasing values of K and Ky. "High K 1 " indicates increasing values of Ki’ 1 "Low Ki" decreasing values of Ki’ mutatis mutandis for Ky. The signs in the columns represents the signs of the multipliers, the 55 TABLE 4.3 CHANGES IN THE SIZES OF INCOME AND INTEREST MULTIPLIERS FOLLOWING CHANGES IN THE VALUES 0F Ki AND Ky Cases VI and VII .4: 513. g: a .d_i_. 9.1. dM dMI dG ggp dMI d IA CASE VI Sign + + + '2 - + Low Ki ? ? ? 9 ? ? High Ki ? ? ? ? ? ? Low Ky l 1 1 ? ? ? High Igl 1 1 1 ‘7 7 7 CASE VII Sign + - +’ ? - - (Low Ki 1 ? ? ? 1 1 High Ki l ? ? ? 1 3 Low KY ? ? ? ? ? ? High KY ? ? ? ? ? ? Source: Section 4.2, this chapter. 56 arrow (t) indicates an increase in the magnitude, the arrow (1) a decrease in the magnitude. The question mark (7) shows an indeterminancy concerning either the sign or the change in magnitude or both. From that table, we can derive the following remarks for Case VI: l-The influences of different values of K1 on the magnitudes of the multipliers cannot be determined. 2-0n the other hand, the lower is Ky, the smaller is the increase in income due to an increase in M, MI, and G, and vice versa. 3-The results in (l) and (2) are the same as those obtained by Takayama's model [63, pp. 344-45] whose main difference with ours is his neglecting of the influence of capital flows on the determina- tion of the aggregate expenditures. The similarity of the results are not surprising, however, since in our model, capital flows enter into the determination of the aggregate expenditures through the increase in the amount of real balances, which is a component of his net wealth (A), and which is itself an argument of his expenditures function [63, pp. 333-34]. We may conclude that the consideration ' of the capital-flow influences on the aggregate expenditures will not basically change his results. 4-Again here, the main difference between changes in M and MI is that an increase in M will have an indeterminate effect on the interest rate, while an increase in MI will definitely depress it. For Case VII, the signs of the multipliers resulting from an increase in G and M are the same as in Case VI, except that 57 (4 21) .91 = Ly + 2qm - 2quy ' dG A < O For an increase in MI, the multipliers are E +-qu dY _ i i (4.22) M - A < o . -h - qm - m +'qu Expression (4.21) states that an increase in G will de- crease the interest rate. The only possibility for this to occur would be for the balance of payments to be in surplus following the increase in G. The confirmation of this proposition will be found below in section B. Expressions (4.22) and (4.23) show that an increase in inside money will reduce both income and the interest rate. In fact, the increase in MI tends to reduce the interest rate which causes capital to outflow. The monetary authorities causes in turn the amount of real balances in the economy to decline, thus, tending to reduce income. This tendency is so strong that it outweighs the increase in income resulted from the fall in the interest rate, and income declines. For Case VII the sign constraint (4.18) remains the same, while (4.19) and (4.20) become 1 (4.24) a12 > O ”’Ki > vq 21—. + (4.25) a12 < O a'Ky > qu m = Ky > m (4.18) and (4.25) yield 58 L (4.26) m+-l—’m then 55') 0 for cases VI and VII (4.29) K.y < m then g%'< 0 for case VII and dR EM—I-< 0 for case VI . 59 In order to analyze the influences of different values of KY and Ki on the balance of payments we can derive the necessary and sufficient condition for its improvement must be under different policies. Therefore, for an increase in M, the condition reads: . - , + > 2 , + - — 2 , (4 30) Ky(-qLi 2qu) Kiqu q(h+m(K1 m( qLi qu) for an increase in ‘MI (4.31) ZVinKy - m'Ei > Ki(h + qu + m - Ei) for an increase in C (4.32) -K L, +KL > -mL. y 1 1 iy From those three inequalities, the influences of K1 and K.y on the positions of the balance of payments can easily be shown. They are presented in Table 4.4 where the meanings of the symbols are the same as in Table 4.3, but more precisely the arrow (1) will indicate a tendency to improvement in the balance of payments and vice versa. From that table, the following main characteristics may be pointed out. l-When Ki increases or decreases, there is no clear indication whether an increase in M and MI will improve the balance of payments. On the other hand, when Ky increases (de- creases) the greater is the chance for an increase in ‘M and M1 to improve (deteriorate) the balance of payments. This is valid for both cases VI and VII. Z-For case VI, the higher K and Ky are, the more i likely is that an increase in G will improve the balance of 60 TABLE 4.4 EFFECTS OF AN INCREASE IN M, MI, AND G ON THE BALANCE-OF-PAYMENTS POSITION WITH DIFFERENT VALUES OF 1LIf AND K i SE 9.13. 21: .Jfli 4M1 4%; Cases VI VII VI VII VI VII Sign ? ? ? ? ? ? Low Ki ? ? ? ? i 1 High Ki ? ? ? 7 T 1 Low KY 1 l l l l 1 High 191 1 1 1 1 1 1 KY >1m ? ? ? - +' + KY < m ? ? - ? ? - Source: Section 4.3, B, Chapter IV. 61 payments and vice versa. 3-For case VII, constraint (4.25) implies that Ky >Im, which makes §%'> O. The size of the surplus in the balance of payment is directly proportionate to the values of Ki and Ky. This surplus increases the money supply. Thus, it explains the possibility of a decrease in the interest rate following an in- crease in G (4.21). Conclusion For the general case (GCI) the following main conclusions can be drawn from the above discussion. l-The results of the General Case I are not fundamentally different from those obtained in case CSI of Chapter II and case ROI of Chapter III. Expansionary monetary policy and fiscal policy will increase income, except in case VII where an increase in MI will decrease it. 24Therefore, due to the possible existence of case VII, an increase in inside money will not be retained as an instrument for increasing income and employment. 3-Finally, with any value of K1 and K.y and in any case - except when K.y < m for case VII - it is preferable to use fiscal policy to increase income, employment and to improve the position of the balance of payments. 4-The correction to Johnson's and Takayama's main limitation: capital flows do not enter into the determination of aggregate expenditures, does not basically change their qualitative results: increases in G and M are effective to raise income and employment. PART 11 TWO - COUNTRY MODEL CHAPTER V FORMULATION OF THE TWO-COUNTRY MODEL In Part I, the small-country assumption has not allowed for repercussions in income and interest rate abroad. The abandon- ment of this assumption and the recognition of the interdependence among countries lead to the introduction to the previous model of a second country representing the rest of the world. Thus, we require some slight modifications and additional assumptions. l-Imports of one country are equal to the exports of the other country. 2-The net capital outflow from one country is equal to the net capital inflow received by the other country. 3-The marginal propensity to spend out of an increase in the amount of real balance is the same for both countries, i.e. = ' = ER ER q. With those adjustments, the two-country model may be written as follows. COUNTRY I A - Commodity Market (I) Y=E+X-IM+G (II) E=E(aY,i,M+BT+vK) [0 o . By virtue of the assumptions made about the signs and the magnitudes of the partial derivatives in the system the determinant must be positive. The policy vector B takes the same form as it did in (5.1). Under these conditions, one may ask what are the effects of fiscal and monetary policies initiated by one country on incomes 66 67 and interest rates of both countries. Section 6.1 Monetary Policy A - Effects on Incomes and Interest Rates If country I increases its money supply, i.e. either in outside or in inside money, what will be the effects on incomes and interest rates both at home and abroad? 1 - Increase in Outside Money For an increase in outside money M, the policy vector B becomes (6.3) BM = L-qu (1 -q)dM O 01' Using Cramer's rule the following results can be obtained: (M) if? g [L;L][cl:Li + <1-q>E,] > (6.5) gm, ___ [(q-l)(h+m>+qu][Li<-h'-m')~E;Lj;]-(q-1>mm'L; 2 o (6.6) 3;. g Iago-«:2, + qLi] > 0 (6.7) 3;. = fillet]? + qLi) > 0 We can see that an increase in the amount of outside money in country I will raise incomes in both countries and the interest rate in country II, while its impact on country I interest rate is indeterminate. In fact, given a constant money supply in country II, the increase in its exports due to the economic expansion in country I cannot help but to result in higher income and interest rate for country II. For country I, the increase in the amount 68 of outside money tends to lower the interest rate and to increase the amount of real balances in the economy. These two tendencies tend to raise expenditures and consequently income, which is in turn additionally stimulated by the economic expansion in country II. While the increase in the amount of outside money tends to drive the interest rate down, the increase in income and consequent expenditures tend to drive it up. These two forces will determine the final direction of change of the interest rate in country I. Therefore, without the knowledge of the magnitudes of different partial derivatives involved in the determination of di/dMg this cannot have a predictable sign. Due to the indeterminacy of di/dM, the comparison with di'ldM cannot be made. We can, however, immediately see that dY/dM is greater than dY'/dM. These results may be compared with Kemp's when he considered the presence of capital immobility [25, pp. 599-601]. Like ours, his model yields rises in the level of income and the interest rate of country II, but unlike ours, the income change in country I is indeterminate while its interest rate decreases. The difference stems from the Specification of his model where the export of each country depends not only on the level of income of the other country (like ours), but also on the other- country interest rate. Therefore, the indeterminacy of the income change in country I may be explained by the relative forces of the internal and external effects produced by the increase in M. The internal effect is the increase in Y due to the decrease in the interest rate. The external effect deals with the change in the 69 level of country I net exports. Since the interest rate decreases, imports of country I tend to rise. In country 11, imports may be income inelastic and interest elastic. Under these circumstances, an increase in Y' and i' will bring about a reduction in its imports which are exports of country I. Thus, the level of country I net exports tend to decrease, hence its level of income. The internal and external effects of the increase in M produce con- tradicting forces, which explains the indeterminacy in the sign of f3- [25, pp. 601-602]. 2 - Increase in Inside Money The structural matrix A remains the same. The policy vector B takes the form (6.8) 13MI = [0 (MI 0 01' . The hmplications of an increase in inside money MI by country I on the levels of income and the rates of interest at home and abroad are: -E _1 I I_ IEI iEhmn‘I Lyi] dY a (6.9) an A > O I I I I I I (6 10) 61 g (mfih)(h Li+LyEi) +'hm Li < 0 ° dMI A HERE dY' g i 1 (6.11) dMI A >0 I E (11' -va i (6.12) dMI = A > 0 . Thus, an increase in inside money by country I will raise incomes both at home and abroad and the interest rate in country 11 70 while it depresses the interest rate in country I. This certainty of the direction of change of the home interest rate is the main difference between the effects of changes of inside and outside money. The income increase in the country initiating the policy action is still greater than that of the other country. As a result of the different effects on the interest rate, we may conclude that if (6.13) E.§L. 1 1. then le_<§X_ d_Y_'1dM , dMI > dMI , and dMI > dM, . ,§_- Effects on the Balance of Payments The fundamental equation for the change in the balance of payments is given by (6.15) dR = (KY - m)dY + (m' - KY)dY' + Ki(di - di') or dR = KY(dY - dY') + m'dY' - de + Ki(di - di') 1 - Increase in Outside Money RE}? The necessary and sufficient condition for —* to be pos it ive is : 1 1 1_ 1 _ 1 I - _ 1 (6.16) qu(L1+2Ei)[(h +m )Li mLi] h (Li+2Ei)qui + Ki(d1 di ) . As one can see the expression is too complex to be easily com- prehensible. The best one can guess is that an increase in the amount of outside money brings about an-indeterminate result on the balance of payments. However: 71 l-If there is no capital movement at all, i.e. Ky = Ki = 0 then an increase in M, worsens the balance of payments. 2-If m s m' the higher Ky is the better is the chance for the balance of payments to improve and vice versa. 3-Since the sign of di/dM is unknown the effect on the balance of payments of increasing values of Ki is also unknown. 2 - Increase in Inside Money The result of an increase in MI on the balance of payments is (6.17) g}; g K1[E1Li(h'-lm')+EiEi-mEi:i]-mEi(h'L;+L}"Ei)+Ki(di-di') Z 0 . In the most general setting the result of an increase in MI on the balance of payments is uncertain, however, l-If there is no capital movement at all, K.y = Ki = O, the balance of payments will deteriorate; 2-If Ki tends to zero, the result is uncertain; 3-If Ki becomes greater and greater, and K.y smaller and smaller, the balance of payments will tend to deteriorate; 4-If KY becomes greater and greater, the balance of payments will tend to improve. As far as the level of foreign reserves is concerned, with a high Ky, an increase in either M or MI will increase it. With a low Ki there is no preference to use either M or MI, but with a low Ky or high Ki a desire to increase reserves means it is preferable to use an increase in M instead of MI since with the latter, although it will increase income like the former, but it will tend to deteriorate the balance of payments 72 with certainty. Section 6.2 Fiscal Policy As in Part I, fiscal policy will be examined with the following alternatives: A-Deficit financing with constant money supply; B-Change in tax; C-Balanced budget; D-Monetization of the debt. A - Deficit Financinngith Constant Money Supply The structural matrix A remains as before, but the policy vector B becomes: (6.18) BG = [-d6 0 o 01' Using Cramer's rule, the following results have been obtained: Li[(h'+m')Li + Big] dY (6.19) dG A > 0 _ I 1 I 1 1 (6 20) d1 = L [(h +m#)Li + EiL11> 0 ° dG A L L' dY' m 1 1 (6.21) *dG A > O ~mL di' __ 1 An increase in government expenditures in country I will increase both incomes and interest rates in country I as well as in country II. These results are to be contrasted with Kemp's conclusions. An increase in G increases both the level of in- come and the interest rate in country I while in country II, the 73 changes in the level of income and the interest rate are in- determinant. The explanation lies in the fact that an increase in G creates contradicting forces: the increase in Y in country I tends to increase imports from country II while the increase in i tends to reduce it [25, p. 601]. Back to our model it is clear that the income increase in the country which initiates the policy action is greater than the increase in income in the other country. Not very much can be said about the relative magnitudes of the interest rate changes, however di/dG is definitely greater than di'ldG if E; is greater than "Li/LY in absolute values. A comparison can be made between the effects of incomes and interest rates of increases in M and G, with the exception of di/dM and di/dG as. di/dM is indeterminate in sign. One can see that a multiplier resulting from an increase in M, e.g., dY/dM is greater (smaller) than its counterpart from an increase in G, e.g., dY/dG according to whether E is greater (smaller) 1 than L1 in absolute values. More formally, if G. H. > dY> (6.23) Ei < Li a dM< é! dG ’ > dY' dY' EIT 0 which is always positive. The policy vector B is rewritten as: (6.25) BT = [edT 0 O 01' Having taken those changes into account the different multipliers may be expressed as: eLi[(-h'-m')Li - E EL'] $1.- 1.1 (6-26) dT — AT < 0 _ _ 1_ 1 I _ I I di eLy[(11 m)Li EiLy] (6.27) dT.: AT < 0 - L L'm dY' e 1 1 (6.28) -— = —— < O dT AT . emL L' (6.29) 5.1.1... = ...Ll < 0 dT AT Incomes and interest rates in both countries vary inversely prOportionate to the change in tax. Therefore, a tax cut in one country will raise incomes and interest rate both at home and abroad. Again the country which initiates the action will have a higher income increase than will the other country. C - Balanced Budget. For this case the determinant is (6.24), but the policy vector B becomes (6.30) BGB = [(e-1)dG O O 03' The expression for different multipliers are: 75 (e-1)Li[(-h'~m')Li - EiLi] (6.31) E = AT > 0 (6.32) $75 = (1-8)Ly[('h;r'm')"1 ' 31131] > o (6.33) % - (l-eifiL; > o (6.34) 61%;: .. (”12:11”); > 0 An equal increase in tex and government expenditures will result in an increase in incomes and interest rates in both countries. Again, the country initiating the action has a higher income in- crease than does the other country. It is to be noted that the multipliers of this case are smaller than those obtained from deficit financing with constant money supply. D - Monetiggtion of thgTDebt The matrix A is the same as in (6.1), but the policy vector B becomes: (6.35) BGM = [-(l+q)dG (l-q)dG 0 01' The results are as follows: [(11 '+m')Li+E 1'1;le (l+q)Li+(l -q)E 1] (6.36) 2%)} = A > 0 (6.37) 33M = [(l-q)(h-I-m)-(l+q)Ly2[(h'im')L£+EiL;]+(q-l)mm'Li < O (6.38) $61.? = “alga-(1m: + (”quill > o (6.39) (H. = mLEm-lmi - (“1013] > O dGM A 76 The monetization of the debt by country I will increase incomes in both countries and the interest in country II, leaving the change in the interest rate in country I indeterminate. The interest rate i will decrease (increase) whenever (l+q)Ly is less (greater) and (l-q)(hhm). Once again the income increase in country I is greater than that in country II. If one compares this case with the case of an increase in outside money M, one will find that the multipliers for Y, Y', and i' are higher with this case than with the pure monetary policy. Economic reasoning will confirm the results established by algebra. In fact, the monetization of the debt increases both G and M, thus the increase in income resulting from this policy should be greater than that resulting from an increase in M alone. Country I should import more, thus the income increase in country 11 should also be greater. As a consequence, given a constant money supply M', the interest rate in country II should experience a greater increase. As for the behavior of the interest rate in country I, one can see that whenever di/dM and di/dGM. are negative then di/dM is greater in absolute value than di/dGM; and whenever they are positive then di/dGM is greater than di/dM. How can this be explained economically? In country I, it has already been seen (pp. 67-68) that, with an increase in M alone, the change in the interest rate depends on the magnitude of the increase in M (which drives the interest rate down); and the subsequent increase in the induced expenditures resulting from the increase in the amount of real balance, the decrease in the interest rate, and the increase 77 in income abroad (which drives the interest rate up). If the former force is stronger, the final result will be a decline in the interest rate. In the case where the debt is monetized, the in- crease in M is accompanied by an equal increase in government expenditures, which are autonomous. It is those autonomous expenditures added to the previous rise in the induced expenditures that drive the interest rate down - the increase in the amount of ‘M - is still dominant, then the interest rate will decrease, but it will not decrease by as much as in the case of an increase in M alone. This confirms that when the interest rate 1 decreases di dG—M holds. Similar reasoning shows the inequality {gfi- > | that when the interest rate rises, the other inequality, i.e. di di 'dGM >|dM holds. Effect of Figgal Policy on the Balance of Payments For the impact of fiscal policy on the balance of payments, we will take the case of an increase in G with constant money supply as the representative case. Then the equation of change in the balance of payments is: I 1 1 1 I 1 _1 1 1_ 1 I gg = KyELiuh +m )Li-i'EiLy)-mLiLi]+KiLy[( h -m )Li EiLy] + dG A (6.40) K.L.mL'-mL.(h'L!‘+E'L') 1 1 j 1 1 iv 20 The impact of an increase in G on the balance of payments is indeterminate. This is also the case for other alternatives of fiscal policy. However, if l-There is no capital movement at all, i.e. K. = KY = 0 1. then the balance of payments certainly deteriorates; 78 Z-Ky tends to zero and K1 to higher and higher values, then nothing can be said about the position of the balance of pay- ments; 3-K.y increases, then the greater is the chance for the balance of payments to improve. Conclusion After examining the above economic policies relating to case CSII, i.e. complete sterilization in both countries, some salient features may be pointed out: l-All economic policies which do not involve a change in outside money M, do provide an unambiguous change in incomes and interest rates at home and abroad; 2-When M changes, and in the case of monetization of the debt, only the sign of the change in the interest rate in the country initiating the policy action is ambiguous; 3-The country which initiates a stimulative policy action experiences an income increase greater than does the other country; 4-The effect of an economic policy on the balance of pay- ments is ambiguous. It may improve or deteriorate. However, the higher KY, the better is the chance for the balance of payments to improve . S-With a low KY and a high Ki’ it is preferable to use either M or G rather than MI to increase income and employ- ment, since with an increase in M1, the balance of payments will tend to deteriorate. CHAPTER VII INTERNAL AND EXTERNALIEQUILIBRIUM Instead of completely sterilizing the balance of payments as we have examined in Chapter VI, the authorities choose not only to pursue the internal goal of raising income and employment but also the external goal of equilibrating the balance of payments. As we have found in Chapter III, except under highly improbable circumstances, fiscal or monetary policy alone is incapable of simultaneously attaining the internal and external goals. In order to achieve those goals there must be at least two policy instruments. Thus, proving in this particular context the validity of Tinbergen's principle of the equality between the number of instruments and the number of targets. Furthermore, we will examine the implications of fiscal and monetary policies on incomes and the interest rates, and the difference, if any, with the C511 case. The external equilibrium requires that (7.1) R = X - IM +'K = 0 or X - IM = -K These equations, with v = v' = 1, while leaving the matrix B in (5.1) unchanged, transforms the structural matrix into 79 80 (7.2) A = Lo 0 Its determinant is: = I I I_ I _ I I I I _ (7.3) A (EiLy'i‘hLi)[(h +Ky)Li+(E1 Ki)Ly] (h Li-FEiL y)(LyKi LiKy) > o which is always positive. Since most of the Operations are similar to those of Chapter VI, in particular for each policy, the vector B remains the same as it was in the case CSII, Chapter VI. Therefore what was said will not be repeated, only those comments of some interest will accompany the results of each policy. Section 7.1 Monetary Policy A - Increase in Outside Money For an increase in.M the following expressions have been obtained: 1Y- [ (h '+Ky) L {+(E i-K1)L;][ (1 -L)E 1L+LL 1] - (1 -L)1 O d_1_ .- h(L-1)[(-h'-Ky)Li-(Ei-K1)L}"]+Ky(1-L) (h 1:15ng) + (7.5) cm - A LLX[(-h'~Ky)Li-L;I(Ei-Ki)] O I I dY' 511(2qu + qLi] + KiLi[(h+Ky)2q - qu] > (7.6) E = A < 0 81 > -KL'2E + L. + L -2 h+K KL' dM A We may ask why the changes in the level of income and the interest rate in country II are indeterminate? Initially, the increase in M in country I raised its income and by importing more it led to the expansion of country II. In terms of the IS - LM (EE - LM in this study) analysis, the BE curve of country II (EE') would shift rightward because of the increase in exports. Y' and i' would rise had the LM' been invariant. But, the LM' did not remain invariant, even though the supply of money in country II had remained constant. In fact, the function of the demand for money of country II reads as (7.7.1) MD' =L'(Y', 1', M') E' + my - m'Y' +'G' and where Y' Y E( Y, i, M) + m'Y' - my +-G then (7.7.1) becomes (7-7-2) MD' = L'(Y',i',M'.y,i,M) - Since Y,i,M changed, LM' had to shift. The final position depended on the effects of Y, i, and M on the demand function. EE' shifted upward, LM' shifted but its shift was not known. This situation explains the indeterminacy of the signs of dY'/dM and di'ldM. B - Increase in Inside‘Money, The effects of an increase in inside money M1 on interest rates and incomes of both countries are: 82 I+ I I_ I _ I I _ I I Ei[h 1 0 I I I _ I I I I I di h[(h +Ky)Li + (E1 Ki)Ly] + 1(th L1 + EiLl‘J (7.9) EMT = A < 0 I (N. L1(+gKi + EiKy) > - . + K (7 11) 9.1"; = Lla‘Kl Eij) 2 0 0 m1 A 0 Income in country I increases, while its interest rate de- clines. The changes in income and interest rate of country II are indeterminate. It is to be noted that income and interest rate in country II move in synchronization. If income increases, then the interest rate also increases, if income decreases, then the interest rate also decreases. The responsiveness of the income change in country I to different values of KY and Ki is in- determinate. On the contrary, for country II, its income change varies inversely proportionate to the value of Ki' The inde- terminacy of the changes in the level of income and the interest rate of country II confirms the analysis made by Cooper [14, pp. 8-9] and Mundell [40, pp. 263-65] who concluded that allowing for inter- national capital mobility an expansion in one country may lead to a recession in the rest of the world. Cooper established this result for an increase either in G or M, Mundell for an increase in G while our study for an increase in. M. and MI. Here again, we find the familiar main difference between inside money and outside money, with an increase in M the interest rate in country I may increase or decrease while with an increase in.MI the interest rate declines unambiguously. 83 Section 7.2 Fiscal Policy Following the same plan as before, we will examine successively: A - Deficit financing with constant money supply; B - Change in tax; C- Balanced Budget; D - Monetization of the Debt A - Deficit Financigg with Conggapt Money Supply Contrary to the monetary policy, the signs of all relevant expressions can be determined unambiguously. They are all positive. -L1[L;(-h ' -Ky) - (E i-Kyn (7-12) 35= A >0 (7 13) Ql.= LY[( h KY)L1 (E1 y)] > 0 ' dG A -L'(LK -KL.) iY..'.___ i 371 yl (7.14) dG A >10 L'(LK -L.K) 111..., v Ii 11 (7.15) dG A > 0 The directions of changes for (7.12) to (7.15) with dif- ferent values of K1 and KY are indeterminate. B - C - Change in Ta; and Balagced Budget The determinant used in these two cases has been derived from A (7.3) by substituting (e-l) for h. More precisely: = .. ' '. '- ' .. (7.16) AT [LyEi+(e 1)Li][(h +Ky)Li 1 Ki)Ly] I I + I I _ . (h Li EiLy)(LyKi LiKy) > 0 The expressions for dY/dT, di/dT, dY'/dT, and di'/dT may be Obtained by multiplying all of the numerators of the 84 multipliers resulting from an increase in G by (~e) while replacing in them A by AT. The multipliers for the balanced budget may be derived in similar fashion, but instead of (-e), we must use (l-e). A decrease in tax and a balanced budget will increase incomes and the interest rate both at home and abroad. D - Monetigation of the Debt The results are: [ (h 'fiy)Li+L1'(Ei-Ki)][ (1 -q)Ei+(l+q)Li]-(1 -q)Ki[h 'Li'LLiE i] (7 .17) 3%},- = A > 0 (7.18) gag = [(-h'-Ky)L£-L;’(Ei-Ki)][ (q;l)h+(1+q)1.l]+(l-q)Ky[h'Li-I-KyLij 2 0 (7.19) 35% g LiKL[(l+q)Li+(l-q)E1:+LiKi[(l-q)h-(l+q)Lyl 2 O (7.20) it = ~131Ky£ (146)130-0131] + L;K1[(1+‘I)Ly - (l-qm 2 O dGM A In terms of sign, the results are exactly the same as those obtained in the case of an increase in M. One can see that it suffices to replace L by (1+q), while (l-q) remains unchanged, in all of the multipliers involving an increase in M in order to obtain the above expressions. Taking these remarks into account, the necessary and sufficient condition for di/dGM to be positive (negative) is: (q-1)Ky(h'Lf + K L' di (7.18.1) (1+q)Ly< (l-q)h + ( -'h "YK )Lj- Ly (E13 -K :) a dGM 20 for dY'/dGM and di'/dGM to be positive (negative) is: K (171011)," (1"!)h dYI diI > (7.18.2) kl: (l+q)L: + (1-q)Ei ” dGM ’ dG’M < 0 1 85 A glance at the multipliers will convince one that the simultaneous goals of increasing income and achieving equilibrium in the balance of payments cannot be reached by using M. or G alone. What has been said earlier (pp. 43-46) still applies here, i.e. essentially at least two instruments (e.g. increase in G and in tariffs or increase in G and decrease in M) are necessary to achieve internal and external balances. If there is no capital movement at all, the impacts of an increase in M and G on the balance of payments are: -m[h'L{ + EiL;][(l-q)Ei + LLi] dR (7.21) (M: A <0 -L.[-hL' - E'L'] (7.22) %§-= 1 1A 11 >0 . The first expression is always negative; the second always positive. Thus, in absence of capital movement an increase in M will de- teriorate the balance of payments, while an increase in G improves it. We find another Obvious fact that if the system is allowed to adjust to market forces, then without some degree of capital mobility the external equilibrium condition is impossible to achieve. Conclusion In this conclusion we will point out the main characteristics of this case ROII and where relevant a comparison with case CSII will be made. l-Both fiscal and monetary policy are effective in raising income and employment. 86 2-All expansionary economic policies which do not involve a change in the money supply, i.e., change in both ‘M and MI, and not in M alone as in the case CSII, do provide an unambiguous increase in incomes and interest rates at home as well as abroad. 3-An increase in the money supply produces in country I exactly the same results in ROII as in CSII, while for country II instead of an increase both in its income and its interest rate, there is an indeterminacy in their changes. They may decrease or increase. 4-Unlike the Case CSII, one cannot conclude that the country initiating the action always experiences an increase in income greater than that of the other country. 5-The influences of K1 and KY on the relative effective- ness of fiscal and monetary policies to increase income are indeterminate. 6-The effects of an increase in the money supply and the monetization of the debt corroborate the analyses made by R. Cooper and R. Mundell who concluded that allowing for international capital mobility, an expansion in one country may lead to a recession in the rest of the world. 7-Unless by chance, the use of either G, M, or MI to raise income under the constraint of the equilibrium in the balance of payments, is not feasible. There must be at least two policy instruments, e.g. G and M to reach those two goals. Thus, this instance corroborates Tinbergen's principle of the necessity of the equality between the number of instruments and goals. CHAPTER VIII GENERAL CASE In the most general case/the system with v, v' and R, R' different from zero is represented by the system (5.1). As we can see the system is so complex that the method we have used in the previous chapters to analyze the influence of fiscal and monetary pelicies on incomes and interest rates would become very burdensomaand unmanageable. In order to obtain a clearer view of the whole process a graphical approach will be used. Section 8.1 Determination of Different Cases The structural matrix A in (5.1) may be more conveniently rewritten as: r- a a 813 a ‘1 11 12 14 a21 822 823 824 (8'1) A a a a a a 31 32 33 34 841 a42 a43 844 L a where all’ 812, a13, a21, a23 belong to country I and a31, a33, 834, 841’ 843 to country II and may be positive, negative, or zero. An exhaustive counting of all possible combinations will involve 310 matrices of type A. Such a number of cases is quite unmanageable, unless some 87 88 assumptions are formulated to reduce it to a feasible number. l-The case of zero value may be ruled out as highly accidental and improbable. Then, 210 cases remain. 2-It is assumed that the two countries have similar economic structure, i.e. the coefficients of dY, dY' should have the same sign whenever they are indeterminate in signs. The same hypothesis is extended to di and di'. This is the symmetry assumption. Only 25 cases are left. 3-Each element aij consists of many terms which may also be present in other elements of the same matrix A. One may find that the signs of some elements are not completely independent of some others, therefore if the sign of one element is determined, the signs of some other elements may be also determined. The above considerations result in the selection of ten cases whose relations Of signs among the elements of matrix A is shown in Table 8.11 and complete sign patterns in Table 8.2. Section 8.2 Determinants and Stability Conditions What has been said about the dynamic adjustment of the tatonnement process in Part I, Chapter IV, Section 4.2 remain valid for this section, except that the vectors A, X, and B are those of this chapter. Then similar to (4.5) this system becomes: By vitue of the symmetry assumption, 8 similar set of relations exists for a13, a23, a33, a34, and a43. 89 TABLE 8.1 SIGN RELATIONS AMONG THE FIRST-TWO-COLUMN ENTRIES OF MATRIX A 9&8. a12 > 0 I -—a21 > 0 . a12 < 0 II a11>0aa31<0~a41>0-— > K! m :112 > 0 III L821 < 0 a12 < 0 IV 'r—— a12 > O V an > 0.. ‘ a12 < 0 VI -—a > O 41 a > 0 VII 12 KY >'m a21 > 0.— all < O —+ a31 > 0—1 ‘ a12 < 0 VIII a12 > 0 IX L__841<0—0821>0 a12 < 0 X l8 o 1 = 1,2,3,4 . Quirk and Ruppert [50, p. 313]. 92 D1 D3 0 (8.5) D1 D3 1 D2 D4 > O . > O ; 1 D2 0 D1 D3 As can be seen this necessary and sufficient condition will yield very complex expressions that are very difficult to interpret in any general sense. However if the system is to be potentially stable the trace of the matrix A must be negativea. It turns out that the system (6.1) for the case C811 and system (7.2) for the case ROII have such a trace. They are, thus, potentially stable. As for the present system (8.1), its trace is of in- determinate sign, the condition for it to be negative can be derived easily: (8.6) (m+m')(1+q) > -(h+h') + (v+v')(Ky - 2Ki)q + Li + L; One can see immediately that the above condition is always satisfied if KY < Ki’ since by assumption the marginal prOpensities to tax, to import, and to spend are smaller than unity. However, the remaining conditions (8.4) and (8.5) will give too complex expressions as to be economically useful and comprehensible. We must simply assume that the conditions for stability are satisfied. Having assumed the stability of the system, the study can be now conducted for the above ten cases. However, using the earlier approach would be very unpractical and burdensome and above all it would not give a clear picture how the system works Quirk [52, pp. 299-300]. 93 under different economic policies. Instead a graphical approach will be used to derive a set of general results for the system as a whole. For this purpose, a graph has been developed in Appendix B where the external condition has been added to the traditional IS - LM framework, and where the stability of the system has been insured for the analysis of the impacts of alternative policies on incomes and interest rates in both countries. In Chapter VII, the case of internal and external balances has been examined. In the following pages, the behavior of the system when R is different from zero will be studied with the graphical tool that we developed in Appendix B. It is to be re- called that the deficit in the balance of payments in one country is the surplus of the other country. For the individual country this may be considered as a quasi-equilibrium situationa, but for the system as a whole it must be an equilibrium one by virtue of our very model and our imposing the stability condition upon it. Starting from a general equilibrium position where the internal and external stiuations are perfectly balanced, a change in policy will entail a change in the balance-of-payments situation: it will remain in equilibrium, or it will experience a deficit or a surplus. The case of equilibrium was studied in Chapter VII. Two cases remain to be scrutinized. It is then perfectly legitimate 4 "A quasi-equilibrium.position is one in which a disequilibrium in (at least) one market is consistently prevented from spreading to other markets and from returning the system (assumed to be stable) to equilibrium". See Swoboda [61, pp. 164-66]. 94 to formulate two hypotheses concerning the impacts of a change in policy on the balance of payments, then from these hypotheses we will attempt to retrace what has been happening to incomes and interest rates when a specific policy had been implemented. Hypothesis I states that there will exist a balance-of- payments deficit in the country initiating the action. Hypothesis II stipulates that a balance-of-payments surplus will emerge in the country initiating the action. As a consequence, the effects of fiscal policy, namely an increase in G, and monetary policy, an increase in M and MI, will successively be examined under those hypotheses. We will choose the case represented by Panel A (Figure 8.3, p. 154) to conduct our analysis. Section 8.3 Fiscal Policy A - Hypothesis I In country I, suppose that there is an increase in G with constant money supply, the EE curve shifts rightward to EE1 (Figure 8.1). Income and the interest rate increase. This will lead to a balance-of-trade deterioration and an increase in the capital inflow due to the increase in income and the interest rate. Their net result on the balance of payments cannot be determined with certainty because it depends crucially on the magnitudes of the parameters in the system which are not known. However after all adjustments, during which the balance of payments may go over a series of successive deficits and surpluses, country I will experience a deficit by Hypothesis I. It is represented by a shift 95 Payments Surplus in Country II FIGURE 8.1 FISCAL EXPANSION UNDER HYPOTHESIS I 96 from BPo to BPZS. This deficit affects the economy by reducing the money supply and the volume of real balance. As a consequence, in addition to the effects of an increase in imports due to the initial rise in income, there are the real balance effects. The BB curve cannot stay at E31, it must shift back to a lower position, say EEZ' In the money market, there is a concomitant decline in the money supply as well as in the demand for money. The final position of the LM curve depends on their relative strengths. Since it has been assumed that any change in the real balance is equally distributed among the three markets, therefore, the absolute value of the decline of the demand for money must be smaller than that of the money supply. Thus the final position must be an upward shift from, LMb to DMZ. The interest rate must rise, while income may rise, remain unchanged, but not decline. In fact, if income in country I fell below its initial level Yo’ the imports from country II would decrease to a level lower than that existing before the increase in G. Country 11 would lose the stimulus that had resulted in the increases in its exports, income, which would have to decline eventually to Ya. But we will see below that, under Hypothesis 1, income in country II must rise. Thus, Y cannot fall below Yo. However, if K was Y huge, Y could have fallen below Yo. In fact, after the possible 5 The subscript 1 is used to indicate a transitory position only, the final position of a curve, after all adjustments, by a sub- script greater than 1. 97 return of Y to Yo due to the deficit in the balance of pay- ments, Y could fall farther, this in turn would cause a further increase in the deficit, thus causing a further fall in Y and so on. The result would be a continuous fall in the level of income of country I and a continuous deficit in its balance of payments. Since the stability of the system was assumed, this unstable situation could not have occurred. Thus, following an increase in G, country II level of income may rise, remain un- changed, but not decline. In country II, there will be a surplus whose absolute value is equal to the deficit in the balance of payments of country I. The previous reasoning may be applied to country II without loss of validity. 3P5, EEé, and EM; are respectively the final positions taken by the balance of payments, the commodity market, and the money market after all adjustments. EB; moves upward to EEi because country II exports more to country I and because of the increase in the amount of real balance due to that increase in exports. However, more income entails more imports, EEi is shifted back to EEé. Income must increase, the interest rate may increase, decrease, or remain con- stant. It is to be noted that if the effects of the increase in imports are greater than those of real balance and the interest rate on income, then the EE' curve may move back to a position lower than the original EEg. Income and interest rate will decline. This possibility implies that there must exist a marginal propensity to import so large as to reduce income to a level lower than that existing before the increase in government 98 expenditures. Such a case is obviously unrealistic, thus it will be ignored subsequently. In the money market, the increase in the balance-of-payments surplus leads to an increase in the demand for money as well as the supply of money. By the previous reasoning, one may conclude that there will be an excess supply of money, therefore, EM; shifts downward to its final equilibrium position LMé. Income must increase, while the direction of change in the interest rate remains indeterminate. The results on incomes and interest rates of both countries of an increase in C have been summarized in Table 8.3, where any cell of the country experiencing a deficit in its balance of pay- ments (e.g. C11 of Country I) may be combined with any cell of the surplus country (e.g. C23 of Country II). B - Hypothesis I; Under Hypothesis II, instead of having a deficit country I has a surplus in its balance of payments. The previous reasoning is still valid, but in order to produce these results, it suffices to change the assignments on Table 8.3. Country II is now the deficit country and country I the surplus country. From that table some salient features may be pointed out: l-The interest rate in the deficit country will always increase and the direction of change in its income level is in- determinate. On the contrary, income in the surplus country will always rise, but the direction of change of its interest rate is indeterminate; 99 TABLE 8.3 CHANGES IN INCOMES AND INTEREST RATES FOR A PAYMENTS-DEFICIT AND A.PAXMENTS-SURPLUS COUNTRY UNDER A FISCAL EXPANSION Deficit Country, Income + cll Interest + Surplus Country Income + c21 Interest + c12 c22 c13 c23 Source: Figure 8.4, and Section 8.4. 100 2-There will never be a decline in the interest rate and income in both countries simultaneously. There must exist at least one country which experiences an increase in interest rate or income; 3-Since the use of fiscal policy may lead either to a deficit or a surplus in the balance of payments, it is clear that both fiscal and monetary policies should be used to achieve internal and external equilibria. This implies once they are reached in one country, they must be reached in the other country too. Although the above analysis was made for only one alternative of fiscal policy, the method of analysis and the conclusions reached thus far are general enough to apply to the cases of a decrease in tax as well as a balanced budget. Section 8.4 Monetary Policy Ag:_lgcre§§e,in Outside Money 1 - Hypothesi§_l Under Hypothesis I, an increase in the amount of outside money M will lead to a deficit in the balance of payments of the country initiating the action, i.e. country I. The first re- actions of the system are the shifts of EB and LM to the right. But their positions, after all adjustments, cannot be determined, unless the relative size of the increase in the money supply and the deficit in the balance of payments are known. Three cases may be distinguished: whether the initial increase in the money supply (dM) is greater, equal to, or smaller than the final deficit in the balance of payments (dR) in absolute value. 101 l-If dM>dR then EEo shifts to EE and LMo to 2 LM2 (Panel A, Figure 8.2). Income must increase, the change in the interest rate is indeterminate. 2-If dM = dR; after all adjustments, the final position LM3 will coincide with LMO, since the total amount of real balance and the money supply in the economy have not changed. Even under those conditions, the EB curve will still shift up to say EEZ’ income and interest rate must rise from (i0, Yo) to say (13, Y3). The explanation of this shift requires the examination of country II's reactions to the increase in M in country 1. Initially, the increase in. M induces a drOp in the interest rate and an increase in income in country I. The former will lead to an outflow of capital due to Ki and the latter an inflow of capital due to KY and an increase in the imports from country II. Country 11 exports more and at the same time improves its balance of payments, which makes its income rise and which in turn, induces more imports from country I. This is the reason why even though ultimately there is no change either in the amount of real balance or the money supply the EB curve is able to shift up to EE2 thus making income and the interest rate to rise in country I. 3-If dM‘< dB then the amount of real balance and the money supply decline. The final position of the LM curve will be LM4 back and over the original position LMO. As for the EB curve, it will shift up to EE4 below EE2 to account for the decline in the amount of real balance in the economy. The in- terest rate must rise, but the change in income is indeterminate. 102 Y Y0 Y3 A - Payments Deficit in Country I O B - Payments Surplus in Country I FIGURE 8.2 MONETARY EXPANSION IN OUTSIDE MONEY M FOR COUNTRY I UNDER HYPOTHESES I AND II 103 Since there must be a surplus in country 11 its income must rise while the interest change remains indeterminate as was seen earlier in the fiscal policy case. 2 -_Hypothgsis_;l Instead of having a deficit, country I now has a surplus in its balance of payments. Since this surplus brings an addi- tional volume of real balances and increases its money supply, the EE and LM curves shift farther than EE and LM to, say 2 2 3 and LM3 respectively (Panel B, Figure 8.2). The income EE increase in country I is greater than that with Hypothesis I, while the change in the interest rate is indeterminate. For country II which experiences a deficit in its balance of pay- ments, the familiar results follow. Its income change is in- determinate but its interest rate must rise. A summary of the results is presented in Table 8.4. It is to be noted that the case of monetization of the debt yields the same results as with the case of an increase in 'M alone. The only obvious difference is that the size of the income multipliers is greater than that with the increase ion case, since in addition to the shift brought about by the increase in M.as was previously, there is the increase in government expenditures that makes the BE curve shift farther upward. B - Increase inglngide Money . In general, an increase in inside money MI will produce the same effects on incomes and interest rates as an increase in outside money M. If inside money were net wealth then there would be no difference between inside and outside money. On the contrary, 104 TABLE 8.4 EFFECTS OF AN INCREASE IN THE MONEY SUPPLY M.AND THE MONETIZAIION OF THE DEBT ON INCOMES AND INTEREST RAEES OF COUNTRY I AND II, UNDER HYPOTHESES I AND II Hypothesis I: Countpy I Income Interest Country,II Income Interest Hypothesis II: Paypents Deficit in Country I, Surplus in Country II Case A: dM>dR Case B: dMFdR Case C: dM dR, dMI = dR, or dMI < dR. The different outcomes for country I are presented in Table 8.5. For country II, there is no change as far as the signs of the multipliers are concerned, they are the same as in the case of outside money. 6 The FSOE are the effects of forces originated in a foreign country and are spilled-over to the home country, the Domestic Spill Over Effects indicate the contrary. 106 //BP2 // BP2 // \ H ”‘4 \ m. = mg //// /, / 1 F303 >’RBE L, son =- RBE FSOE < RBE s Payments Deficit in Country I FIGURE 8.3 MONETARY EXPANSION IN INSIDE MONEY FOR COUNTRY I UNDER HYPOTHESIS I 1 FSOE I Foreign Spillover Effect; RBE - Real Balance Effect 107 TABLE 8.5 EFFECTS OF AN INCREASE IN INSIDE MONEY ON INCOMES AND INTEREST RATES OF COUNTRY I AND II, UNDER HYPOTHESES I AND II Hypothesis I: Countpy I ngpents Deficit in Country I, Surplus in Countrypll dMI > dR DMI = dR dM < dR Foreign Spill Over Effect > Real Balgpge Effect Income Interest Foreign Spill Over Effect Income Interest A B ‘ C + + + + + o - cll ch cl3 cl4 c15 cl6 cl7 + o - + + + 4- Real Balance Effect D E F + O - c18 cl9 c110 - O + Foreign Spill Over Effect < Real Balance Effect G H I Income + 0 - - - - - c111 c112 c113 c114 c115 c116 cll7 Interest - - - - 4- O - Countpy II Income +- + + c21 c22 c23 Interest + O - Hypothesis II: Countpy I Income Interest Country II Income Interest Payments Surplus in Country I, Deficit in Country II + + + cll c12 c13 + 0 - + 0 - c21 c22 c23 + + + Source: Figure 8.6 and Section 8.5, B. 108 Under Hypothesis II, the results are similar to those obtained with an increase in M.under the same hypothesis. Two remarks may be made: l-If one compares Table 8.4 and Table 8.5 for outcomes of an increase inoutside‘money and inside money, one can say that the case of inside money is more general in the sense that all outcomes in Table 8.4 are included in Table 8.5 and not vice versa; 2-In country I, the increase in income, if any, is smaller than that obtained from an equivalent increase in outside money, this is due to the fact that inside money is not considered as net wealth. Conclusion From Tables 8.3, Table 8.4, and Table 8.5 which give dif- ferent results of an increase in G, in M5 and MI on incomes and interest rates of both countries, we can draw the following con- clusions: l-For Hypothesis I, in the deficit country (country I) which is also the country which initiates the change in policy, the use of fiscal policy and monetary policy to increase income and employment may be frustrated and may even lead to an actual decline in income and employment. As long as no corrective action is taken to sterilize changes in the money supply. b) For both fiscal and monetary policies, there will never be a decline in incomes and interest rates in both countries simultaneously. There must exist at least one country which experiences an increase in its income or interest rate. 109 c) For an increase in G and M, in the country initiating those policies there will never be a simultaneous decline in its income and interest rate or a constancy in them. But for an in- crease in.MI, those two events are possible. d) The results in the surplus country (Country II) are the same for fiscal and monetary policies. Income must increase while the interest rate remains indeterminate. 2-For Hypothesis II, both fiscal and monetary policies have the same results on incomes and the interest rates, as far as the signs are concerned for the surplus country as well as the deficit country. b) For the surplus country, which is also the country initiating the policy, income must increase while the interest rate change is indetenminate. c) In Country II, the deficit country, its interest rate must rise, while the change in its income is indeterminate. d) There will never be a simultaneous decline in incomes and interest rates in both countries. There must exist at least one country which experiences an increase in either income or the interest rate. CHAPTER IX SENSITIVITY ANALYSIS FOR THE GENERAL CASE The results obtained in Chapter VIII for the general case (CCII) concerning the effects of an increase in G, M, and MI on incomes, interests, and the balance of payments, are too broad in numbers. We would like to determine first, which one of the ten possible sign patterns of the structural matrix A in Table 8.1 are likely to approximate the reality given certain conditions imposed on the system itself, then how incomes, interest rates and the balance of payments react to changes in policies and in the values of different parameters. To do this, the sensitivity analysis technique will be used. Given the system. AX = B as represented in (5.1) or (8.1) we will attempt to solve for the value of the column vector X for different values of one parameter in A while the other para- . 1 meters remain constant . Section 9.1 Copstraints and Choices of Values for the Parameters The sign pattern of each case from I to X imposes certain constraints on the relationships among the parameters. In addi- tion to this, the prior knowledge about the range within which a 1 Tai Ming Chan [62, p. 4]. 110 111 parameter may take its values, e.g. the marginal prOpensity to import m, to tax t, to spend e, etc. must be greater than zero and less than one, may make our choice less arbitrary. An example of such conditions are given in Table 9.1, where the range of variations of KY, Ly, and Ki are completely determined when the values of m and E1 are known or vice versa. However, the actual values of the parameters are not known (e.g. KY or Ki) or if they are known they are characterized by "disagreement and dispute"2. It may nevertheless be useful by utilizing the values approximating those for the United States as found in some previous studied made by G. Ackley [1, p. 222], R. Cooper [14, pp. 12-13], D. Laidler [30, pp. 89-109], and by D. Ott and A. Ott [44, pp. 319-25], to have an idea about the effects of fiscal and monetary policies on incomes, interest rates and the balance of payments. This numerical analysis is only a casual empiricism. It does not pretend to reflect the reality faithfully. In Table 9.2, different values for the partial derivatives of the variables with respect to i and Y are presented. They indicate the change in billions of dollars resulting from one percentage point change in the interest rate i and from one billion of dollars change in income Y respectively. Four dif- ferent values have been assigned to each parameters of country I, such that each value is higher than the preceding one by ten per- cent, except for m, t, and e where each value is generated from Ott and Ott [44, p. 319]. 112 TABLE 9.1 RELATIONS AMONG Kl, Ly, m, E1, AND K FOR CASES IX AND x 1 Case IX CaseX §O LY<0 Ki > 3|Ei| Ki < 3‘s“ Source: Table 8.1. 113 TABLE 9.2 VALUES USED FOR THE SENSITIVITY ANALYSIS CASES IX AND X A - Values Common to Both Cases Country I m 0.05 0.10 0.15 t 0.15 0.20 0.25 e 0.65 0.70 0.75 KY 0.036 0.04 0.044 LY 0.15 0.165 0.182 B - Vglues Specific to Case IX Bi -1.0 -1 .16 -1.21 Ki 4.0 4.40 4.84 Li -1.15 -1.035 -O.93 C - Values Specific to Case X E1 -600 -606 -7026 K1 4.0 4.4 4.84 L -5.1 -5.67 -6.3 v = v' = l 0.20 0.30 0.80 0.048 0.20 -l.33 5.33 -0.83 -8.0 5.33 -7 .00 Country II 0.12 0.22 0.73 0.17 -l.21 -0.9 Source: See Section 9.1. 114 its preceding one by adding to it five percent. For country 11, the value of each parameter (e.g. ‘m') has been chosen such that two values of the corresponding parameter in country I (e.g. m) are lower and the other two higher. In order to see the sensitivity of different multipliers relative to each parameter when fiscal and monetary policy are implemented, calculations have been made for four different values for each parameter. Given the existence of eight (8) parameters and four (4) different values for each one of them, thirty two (32) inversions were needed to solve the system AX = B for each of the ten cases. It is to be noted that for country II, only one value has been assigned to each parameter and for each case. This is suf- ficient, since by the symmetry assumption of the countries in- volved, the qualitative results concerning the direction changes of different multipliers obtained for a particular parameter of country I are also valid for the corresponding parameter in country II. §gction 9.2. Elimination of the Improbably Cases We can immediately eliminate case I through IV. Because all their diagonal entries are not negative, they are not potentially stab1e3. For the remaining cases the sensitivity analysis results in a constant pattern of the signs of different multipliers when the values of the parameters are allowed to change. Then’which of Quirk [52, pp. 299-300]. 115 the remaining cases, from'V to X, may be accepted as plausible realistically? The answer to that question is based on two criteria: l-The plausible case must have the necessary condition for stability, i.e., the determinant must have a positive signa. On this ground cases VII and VIII were eliminated; 2-The second criterion requires that the plausible cases should yield multipliers having signs similar to those figuring in Tables 8.3, 8.4, and 8.5. Thus, for the remaining cases V, VI, IX, and X, calculations were made to see the effects of an in- crease in G, M, and ‘MI on incomes, interest rates, and the balance of payments of both countries. For a given country, the sign of each multiplier (e.g. dY/dG or di/dG) was then compared to Table 8.3 (increase in G), Table 84. (increase in M), and Table 8.5 (increase in MI) which encompass all possible outcomes. If a case yields a multiplier sign which does not agree with those in the tables, that case is then eliminated. Only cases IX and X remain as plausible. The multiplier values are presented in Appendix D for case IX and Appendix E for case X. Those Appendices also record the sensitivity of different multipliers to different in- creasing values of different parameters. Section 9.3 Analysis of the Results Although there are some variations in details, the results of an increase in G, in M, and MI yield certain regular patterns 4 Quirk and Ruppert [50, p. 313]. 116 on incomes, interest rates and the balance of payments which warrant some interesting conclusions. _A_-_-__Increasg in the Money Supply 1) With different values assigned to the parameters as given in Table 9.2, we can see that there is no difference between an increase in outside money GM) and inside money (MI) as far as the signs of the multipliers on incomes, interest rates, and the balance of payments are concerned. An increase in the money supply will increase incomes and decrease the interest rates both at home and abroad. It worsens the balance-of-payments position. 2) For the country which initiates the change in policy (country I) the income increase is greater with M than with MI. However, the decrease in the interest rate i is greater with MI than with M. The explanation is to be found in the difference between M and MI. The former is net wealth, while the latter is not. Thus, an increase in M generates two forces to stimulate the increase in expenditures: the decrease in the interest rate and the increase in the amount of real balance, whereas an increase in MI generates only first force. Therefore, the effects of an increase in‘M are stronger than those of an increase in MI. Thus, income increases more and the interest rate decreases less with an increase in out- side money M.than with inside money MI. 3) Since income increases more and the interest rate de- creases less in country I with an increase in,M than with MI, the balance-of-payments deficit must be greater with MI than with M. 117 4) Since for country II, the surplus in its balance of payments is greater with MI than with M, therefore, its income increase and its interest decrease is greater with MI than with M. B - Increase in Government Expenditures and Cogparison with the Increase in the Money Supply 1) While an increase in the money supply increases in- comes and lowers the interest rates both at home and abroad, an increase in G increases incomes and the interest rate both at home and abroad, but with a possible decline in income abroad with case IX. 2) From the point of view of internal equilibrium an in- crease in G expenditures generates a higher income expansion than an increase in the money supply. 3) The country which initiates the change in expansionary policy will always have greater multipliers in income and the interest rate than the other country, except for the increase in MI and for the case IX. 4) From the viewpoint of external equilibrium, an in- crease in the money supply will always lead to a deterioration in the balance of payments, whereas an increase in government expenditures will generally lead to its improvement. 5) From the viewpoint of the policy maker, the two prob- lems of unemployment and payments deficit can be simultaneously resolved by applying a mix of contractionary monetary policy and expansionary fiscal policys. Wrightsman [70, pp. 206-207]. Such a mix is in accordance with Mundell's principle of matching policy instrument with policy objective on the basis of comparative advantages, Mundell [40, pp. 233-39]. 118 Section 9.4 Sensitivity of the System to Changes in Parappters Appendix D and Appendix E give a detailed response of in- comes, interest rates, and the balance of payments to increasing values in different parameters. Needless to say, the results would be exactly the reverse were the parameters made to decrease instead of increasing. Examining for each parameter its influences on incomes, interests, and the balance of payments would be very tedious. It suffices to refer to the above Appendices. However, we can divide the parameters into two groups: the ones whose increases in value worsen the balance of payments, and the others whose in- creases in value improve it. For instance, with an increase in outside money M, K and m worsen the balance of payments, the i rest of the parameters improve it. For an increase in government expenditures, m, E1, Li worsen the balance of payments, while t, e, LY’ Ky, and K1 improve it. Attempting to retrace the effects of changes of each parameter on the economic system would be very tedious, therefore doing the analysis for one or two parameters is largely sufficient, since the same type of reasoning may easily be extended to other parameters as well. Since the sensitivity of capital flows to changes in the level of income and the interest rate concern us most, we will analyze the influences of these two parameters. Take case IX for instance. We will study the effects on incomes, interest rates, and the balance of payments of an increase in government expenditures G and an increase in outside money M. 119 When G is increased, the effects of Ki’ KY are identical as far as the signs of the multipliers are concerned. The greater their values are, the larger are the increases in Y and i', the greater the decrease in Y' and the smaller the increase in i, and finally the greater the improvement in the balance of payments. With an increase in the money supply M, the greater Ky, the greater the increase in Y and the decrease in i, the smaller the increase in Y' and the decrease in i', and the smaller the deficit in the balance of payments, this equivalent to the effects of K.y on the balance of payments when there is an increase in G. On the contrary, with increasing values of K the behavior of the multipliers 1: and the balance of payments is exactly the reverse of that obtained with increasing value of Ky. In sum, with different economic policies, KY and K1 have different impacts on incomes, interest rates, and the balance of payments. With an increase in G, the balance-of-payments surplus is directly prOportionate to the values of K and KY, but with an 1 increase in the money supply M. while KY still has the same impact as above, the impact of K1 is different: the deficit in the balance of payments is inversely prOportionate to the values of Ki' Can we explain this? In the case of an increase in G, we know that the income and interest rate multipliers of country I (country initiating the change in policy) are higher than those of country II. The income and interest rate differentials just produced will cause an inflow of capital into country I. The balance of payments tends to improve. The question is that whether that payments surplus 120 tends to increase or decrease with increasing values of K1 and KY? Appendix D shows that when R1 or KY increase the in- come increase in country I and the income decrease in country II become larger and larger. This produces a widening of the income differential to the advantages of country I. On the contrary, the interest rate increase in country I becomes smaller and smaller and that of country II becomes larger and larger, this produces a widening of the interest rate differential to the advantages of country II. The widening of the income differential will produce a marginal inflow of capital to country I, when Ki or KY in- creases, while the widening of the interest differential generates a marginal capital outflow from country I. Within the range of the values assigned to KY and Ki’ if the marginal capital in- flow due to income changes dominates the marginal outflow due to the interest changes, which is the case here, the surplus in the balance of payments becomes larger and larger with increasing values of K1 and KY. For an increase in the money supply M, increasing values of K.y produce smaller and smaller deficits (or larger and larger improvements) while increasing values of K greater and greater 1’ deficits. Given the multiplier signs of this case (Appendix D), an increase in KY makes the marginal capital inflows due to in- come changes to dominate the marginal capital outflows due to the interest changes, the balance of payments must improve or the size of the deficits must become smaller and smaller. On the contrary, an increase in X1 will make the marginal outflows due to income changes dominate the marginal capital inflows due to the interest 121 changes, the balance of payments must deteriorate or the deficit becomes larger and larger. The same analysis was conducted with the case X, and we were able to reach the conclusion that the effects of income changes, on international capital flows tend to dominate the effects of the interest changes. At this point, we need not go no further into the analysis of the effects of the other parameter increasing values on the system since the same method of reasoning will be repeated and since the goals of this chapter have been reached, i.e., which cases are most likely to exist in reality? and how does the system respond to the changes in the values of the parameters? In conclusion, within the limits of our study only cases IX and X are likely to be realistic. From the numerical analysis, we know that the higher KY is, the greater is the effectiveness for an expansionary fiscal policy and monetary policy (M) to in- crease income and improve the balance of payments. But the greater K the greater the effectiveness for an expansionary i fiscal policy and the less the effectiveness for an expansionary monetary policy to increase income and improve the balance of pay- ments . CHAPTER X SUMMARY AND CONCLUSIONS This study took the three-market economy of Patinkin and opened it to the international dimension where not only goods and services, but also capital flows were exchanged. The latter were made to be dependent on the interest rate differential as well as on the income differential between the home country and the rest of the world. Moreover, those capital flows explicitly entered into the determination of the aggregate demand by changing the quantity of real balances in the economy. With those main characteristics in the model, we proposed to investigate the impacts of fiscal and monetary policy (con- sisting of outside money M and inside money MI) on income, interest rate, and the balance of payments under the small-country assumption and then the large-country assumption. In Part I, the analysis was conducted with the small-country assumption, in Part II that assumption was relaxed, permitting the feedback mechanism on foreign economic variables to operate. In each Part, three different cases were considered. A-The authorities of the country or countries desire that the internal goals of increasing income and employment should not be disturbed by the international conditions. They may realize this by completely sterilizing their balance of payments. This is 122 123 the case of complete sterilization (or CS). B-The authorities are not only concerned with the above internal goals but also with maintaining equilibrium in the balance of payments. This is the case of internal and external equilibrium (or R0). C-While they can continue to use fiscal and monetary policy to pursue the internal goals they may not either actively seek the equilibrium in the balance of payments or completely sterilize it. This was called the General Case (GC). Throughout the study, it had been assumed that the economy was functioning at less than full employment level, the price level was constant, and the exchange rate was fixed between countries. In Part I, for the case of Complete Sterilization (CSI), the following conclusions were reached: l-The income and interest multipliers depend only on the marginal propensity to import m and not on the income and interest sensitivity of international capital flows (KY and Ki); 2-Both fiscal and monetary policies are effective to in- crease income and employment; 3-Any fiscal policy which tends to raise income and employ- ment with a constant money supply M.will result in an increase in income and interest rate; 4-Any policy which tends to stimulate the economy and which is accompanied by a change in the amount of outside money will result in a rise in income, but its effect on the interest rate is in- determinate; 124 5-With a high K.y it is easier for a fiscal expansion and a monetary expansion to improve the balance of payments than with a low Ky; 6-With a high K it is easier for a fiscal expansion to i improve the balance of payments whose change, however, is inde— terminate with an increase in M. 7-With an increase in.outside money (M), the effects on the interest rate is indeterminate, but with an increase in inside money (M1), the interest rate decreases unambiguously. Further- more, if KY is smaller than m, the effect of an increase in M on the balance of payments is uncertain, while an increase in MI deteriorated it. 8-The qualitative impacts of an increase in inside money and government expenditures on thelevel of income, the interest rate, and the balance of payments are similar to those obtained by Johnson, where instead of an increase in inside money there is simply an increase in the money supply. For the case of internal and external balances (ROI) certain conclusions are the same as before, certain others are not. l-Both fiscal and monetary policies are effective in raising income and employment. 2-Any policy which tends to raise income with a constant money supply M will result in an increase in income and the interest rate . 3-Any policy which tends to stimulate the economy and which is accompanied by an increase in the amount of outside money M will result in an increase in income, but its effect on the interest 125 rate is indeterminate. 4-A high K militates against the use of the fiscal 1 expansion - except the case of the monetization of the debt - and in favor of the use of the monetary expansion to achieve the internal balance. A low K1 favors use of fiscal and monetary expansion to achieve the internal balance. 5-With either a high or low K the effectiveness of i fiscal and monetary policies to achieve the equilibrium in the balance of payments cannot be clearly determined. 6-In the absence of capital movements, i.e. Ky and K1 tending to zero, both fiscal and monetary expansion are equally efficient in increasing income and employment. 7-When there is perfect capital mobility, i.e. K and Y K tending to infinity, monetary expansion is very effective and i fiscal expansion is completely ineffective in increasing income and employment. These results are at variance with those obtained by Mundell, Sohmen: monetary expansion is ineffective while fiscal expansion is effective to raise income and employment. 8-Unless by chance, the use of either G, M, or M1 to in- crease income under the constraint of the equilibrium in the balance of payments, is not feasible. There must be at least, two policy instruments, e.g. G and M, to reach those two goals. Thus, this instance corroborates Tinbergen's principle of the necessity of the equality between the number of instruments and goals. 9-If K.y is smaller than m, to achieve internal and external balances, the use of G and MI is preferred to that 126 of G and M. In the General Case (GCI), the sign of determinant of the structural matrix A as presented in (4.1) could not be determined since some of its entries were indeterminate in sign, we were thus forced to examine all its possible sign patterns (cf. Table 4.2), eight in number, from which Case VI and VII had unambiguously satisfied the necessary and sufficient condition for stability and consequently were retained for study. The results of this Case (GCI) were not fundamentally different from those obtained in Case CSI and Case ROI. Expansionary fiscal and monetary policy increase income, except in Case VII where an increase in MI decreases it. Finally, with any value of K1 and Ky and in any case - except when KY < m for Case VII - it is preferable to use the fiscal expansion to increase income and to improve the position of the balance of payments. In Part II, the recognition of the interdependence among countries and the repercussions in income and interest abroad made it necessary to introduce a second country - Country II - into the model to represent the rest of the world. Thus, some additional assumptions were needed: (1) Imports of country I are equal to exports of country II, and vice versa; (2) the net capital inflow received by country I is equal to the net capital outflow from country II, and vice versa;.(3) the marginal prOpensity to Spend out of an increase in the amount of real balance is the same for both countries. The Case of Complete Sterilization in both countries, (CSII) yielded the following characteristics: 127 As far as the income and interest rate multipliers of country I are concerned, the results are similar to those of the CSI case. Both fiscal and monetary expansions are effective to increase income, but whenever there is an increase in the amount of outside money (M), the interest change is indeterminate, while an increase in inside money (MI) decreases it. For country II, its interest rate and its income increase with fiscal and monetary expansions initiated by country I. How- ever, the increase in income in country II is always smaller than the increase in income in country I. The effect of an economic policy on the balance of payments is ambiguous. It may improve or deteriorate. However, the higher KY the better is the chance for the balance of payments to improve. With a low KY and a high Ki’ it is then preferable to use either M or G rather than M1 to increase income and employment, since with an increase in.MI, the balance of payments tends to deteriorate. For the case of Internal and External balances, (ROII), the main conclusions were pointed out and where relevant a comparison with case CSII was made. l-Both fiscal and monetary policy are effective in raising income and employment. 2-A11 expansionary economic policies which do not involve a change in the money supply, i.e., change in both M and MI and not in M alone as in the Case CSII, do provide an unambiguous increase in incomes and interest rates at home as well as abroad. 3-An increase in the money supply produces in country I exactly the same results in ROII as in CSII while for country II 128 instead of an increase both in its income and its interest rate, there is an indeterminacy in their changes. They may decrease or increase. 4-Unlike the Case CSII, one cannot conclude that the country initiating the action always experiences an increase in income greater than that of the other country. S-The influences of K1 and KY on the relative effective- ness of fiscal and monetary policies to increase income are in- determinate. 6-The effects of an increase in the money supply and the monetization of the debt corroborates the analyses made by R. Cooper and R. Mundell who concluded that allowing for international capital mobility, an expansion in one country may lead to a re- cession in the rest of the world. 7-Finally, unless by chance, the use of either G, M, and MI to raise income under the constraint Of the equilibrium in the balance of payments, is not feasible. There must be at least two policy instruments, e.g. G and M to reach those two goals. Thus, this instance corroborates Tinbergen's principle of the necessity Of the equality between the number of instruments and goals. For the General Case (GCII), the same difficulties en- countered in GCI Case occurred again: some entries of the structural matrix A as represented in (8.1) were indeterminate in signs. In addition to this, the dimension of matrix A had increased from 2 x 2 to 4 X 4. The number of possible sign patterns for matrix A'became unmanageably large unless some 129 assumptions were made to reduce it. By assuming that the structure of the two countries are symmetrically similar and by investigating the sign relations among the indeterminate entries, we were able to reduce to ten (10) the number of possible sign patterns for matrix A (cf. Table 8.1). The earlier method could not be used to calculate different multipliers, due both to the large size of the matrix A and to the indeterminancy of the sign of the determinant. A graphical approach was used instead by superimposing on the traditional IS - LM - we called EE-LM - graph, the curve BP representing the equilibrium in the balance of payments. It was then shown that the stability of the system depended on the relative positions of the EE, LM, and BP curves as well as on the signs of their sIOpes. For the study of the impacts of fiscal and monetary policy on the interest rates and the level of incomes at home and abroad, a stable case was adapted, where the BE and LM curves assumed their traditional slopes and the BP curve a positive lepe corresponding to the case when KY is smaller than the marginal prOpensity to import (m). Since the case of the equilibrium in the balance of payments had been examined earlier in Chapter VII, there remained two cases to analyze. The first case corresponded to the Hypothesis that there would exist a deficit in the balance of payments of the country initiating the eXpansionary policy (country I), thus a surplus in country II. This was Hypothesis I. Hypothesis II stipulated that a surplus would occur in country I and a deficit in country II. 130 From those two hypotheses, an attempt was made to retrace what had been happening when expansionary fiscal and monetary policy had been initiated by country I. A-l-For Hypothesis I, in the deficit country (country I), the use of fiscal and monetary policy to increase income and employment may be frustrated and may even lead to an actual decline in its income and employment. 2-For both fiscal and monetary policies, there will never be a decline in incomes and interest rates in both countries simultaneously, there must exist at least, one country which experiences an increase in its income or interest rate. 3-For an increase in G and M in country I, there will never be a simultaneous decline in its income and interest rate or a constancy of them. But, for an increase in MI, those two events are possible. 4-The results in the surplus country (country II) are the same for both fiscal and monetary policies. Income must rise while the interest rate is indeterminate. B-l-For Hypothesis II, both fiscal and monetary policies produce the same results on incomes and interest rates as far as the signs are concerned for the surplus country as well as the deficit country. 2-In fact, for the surplus country, which is also the country initiating the action, income mst increase while the interest change is indeterminate. 3-In country II, the deficit country, its interest rate must rise, while the change in its income is indeterminate. 131 4-There will never be a.simultaneous decline in income and the interest rate in both countries. There must exist, at least, one country which experiences an increase in income or the interest rate. A The results obtained for the General Case (GCII) concerning the effects of fiscal expansion and monetary expansion on incomes, interest rates, and the balance of payments were too broad in number. we wished to know which of the ten possible sign patterns of the matrix A (Table 8.2) were likely to approximate the reality, and how do incomes, interest rates, the balance of payments react to changes in policies and in the values of different parameters. To answer this, the sensitivity analysis was used in Chapter IX. The numerical values of the parameters were chosen as to approximate those obtained for the United States in previous studies. The plausible case had to satisfy the necessary condition for stability, i.e. its determinant had to be positive, and it had to yield results that are present in Tables 8.3, 8.4, and 8.5, corresponding to an increase in government expenditures G, in the amount of outside money M, and inside money MI. This process re- sulted in the choice of Cases IX and X as plausible realistically. The main results were: l-While an increase in the money supply increases incomes and lowers the interest rates both at home and abroad, an increase in G increases incomes and the interest rates both at home and abroad; 2-From the viewpoint of internal equilibrium an increase in G expenditures generates a higher income expansion than an increase in the money supply; 132 3-The country which initiates the change in expansionary policy will always have a greater multiplier in income and the interest rate than the other country, except when there is an in- crease in MI for case IX; 4-From the view point of external equilibrium, an increase in the money supply will always lead to a deterioration in the balance of payments, whereas an increase in government expenditures will generally lead to its improvement; S-From the viewpoint of the policy maker, the two problems of unemployment and payments deficit can be simultaneously resolved by applying a mix of contractionary policy and expansionary fiscal policy. 6-The higher KY’ the greater is the effectiveness of a fiscal expansion and monetary expansion (M) to increase income and improve the balance of payments. But, the greater K1 the greater the effectiveness of a fiscal expansion and the less the effectiveness of a monetary expansion to increase income and improve the balance of payments. As a conclusion to this study, we would like to point out its main limitations whose corrections may constitute the starting points for further research. First, our study was conducted under the assumption of constant price and fixed-exchange rate. This might be relaxed by adopting the alternative assumption of a flexible-exchange-rate system. If it was the case, then the balance of payments would always be equal to zero, the CS and GC cases would vanish. Only the RO cases would remain; however some changes should be made in 133 the behavioral equations. One possible change, for instance would be to make the import function dependent on income and on the rate of exchange as well. Second, we might explicitly introduce into the model the supply side with a two-factor production function similar to that presented in Section 1.2. Finally, we might examine the problems arisen in our study within the framework of the optimal control theory. In fact, our study was mainly concerned with the effective- ness of fiscal and monetary policy on the endogeneous variables Y and R, when capital flows were allowed to influence the level of aggregate demand. If that problem is important in itself, it is equally or even more important to know how much income can in- crease and how much the balance of payments can improve given an increase in the instrument (control) variables G and M. Suppose the authorities wished to attain the targets Y* and R* within N periods by changing the control variables G and M. At the first try in period t, they cannot, unless by chance, immediately hit the targets, since they do not have complete in- formation on the structure of the economy. Thus, some deviations are expected to occur between the desired Y and the actual Y, the desired R and the actual R. At period (t+l), they must make some adjustments in G and M to correct those deviations. The authorities may decide to make the sizes of those adjustments de- pend on the difference between the desired values and the actual values of Y and R and the sizes of AG and AM in the pre- vious periods. If, again, the targets are not hit, then the 134 authorities, with the same decision rule, have to make other ad- justments until the actual values of the endogeneous variables equal the targets at the terminal time t = N. The problem is to determine the Optimal decision sequence for changing G and M and the corresponding Optimal time path (trajectory) for the endogenous variables Y and R. As a matter of fact, our model which is static in nature cannot solve such a problem, we must then reformulate our model within the framework of the optimal control theory. Before getting into more details, a formal statement of the Optimal control prOblem will help to clarify how our model should be reformulated. Statement of the Optimal Control Proplgp Let Z(t) be the vector of the endogenous variables des- cribing the state of a discrete dynamic system at time t. The dynamic behavior of Z(t) (equations of motion) is given by (10.1) z(t+l) = ft[Z(t), u(t)] where u(t) is the vector of control variables. At the initial state t = 0 (10.2) Z(O) = 20, Z0 6 Z * and at a specified terminal time t N the vector Z(N) E ZN set of the terminal targets. Then the problem is to determine the Optimal control sequence 135 (10.3) {0(t); t = 0,1,...,N-1} and the corresponding time path (10.4) {2(c); t = 0,1,2,...,N} such that 2(c+1) = £t[i(t), 0(t)] , c = 1, .,N-l 2(0) = 20 (10.5) 0(t) eu t=l,...,N-l * Z(N) e 2N and among all sequences {u(t)} and {Z(t)} satisfying the above conditions, the cost functional N (10.6) J = Z ct[Z(t), u(t-l)] t=0 attains its minimum value at {u(t)} = {fi(t)} and {Z(t)} = {2m}- To illustrate the Optimal control problem, we will take the case of one country with fixed price. The system will be described by the following equations. I. Planninngorgzon (10.7) OStSN. At time t = 0, the vector of the endogeneous variables Z(O) = 20’ and the control variables 06(0), AM(0) = 0. 136 II . State Variables l -Commod ity Market (10.8) Yt = Et + Xt - IMt + Gt (10.9) Et .-. alYt-l - azitm1 + 83Mt-1 + a4BTt-l + a4VKt-l (10.10) Xt = Xo (10.11) IM = myt_1 (10.12) Gt = Gt_1 + AG 2 -Mone)p Marke t M +b (10.13) MD a b Y - b2it_1 + b3 t_1 4 c 1 c-1 ”Tc 4. vb Kt- -1 5 l (10.14) MSt Mt + BTt + vxt (10.15) MDt = M8: 3-Balance of Pamts (10.16) Rt = BTt + Kt (10.17) BT = X - th (10.18) Kt = clYt + c2it III. Eguat 10% of Motion The dynamic behavior of the system is given by the following equations. l-Commodity Market (10.19) AYt = AEt - AIMt + AGt (10.20) wt :1 alAYt-l - 82A1t_1 + 83AMt_l + aath‘d' + a4vAKt-l 137 (10.21) AXt = 0 (10.22) AIMt = mAYt-l 24Money Market (10.23) AMI)t = bIAYt-1 - b2A1t_1 + bngt_1 +'b443Tt-1 + bSVAKt-l (10.24) OMSt = AMt + ABTt +~vA1 (3'1) (EB) 31? ___ E. + vLK. < 0 1. 1 (B 2) (1M) d_i= -1.Y + 2q(v1§1 - m) > 0 ‘ dY Li - 2vL1 m, EE and LM can be either positive or negative while BP is definitely negative. The economic meaning of EE and LM curves and the different regions they partition are familiar so they need not be examined further. Instead a greater attention will be paid to the BP curve. 1 - The BF Curve Why must the sIOpe of B? be positive when KY < m? If there was an income increase in domestic there would be a deficit in the balance of payments, since the capital inflow due to the change in income (KY) is smaller than the increase in imports. Therefore, if the equilibrium is to be reestablished, the interest rate must rise to attract more capital inflow. This establishes the upward sloping shape of the curve BP. On the contrary, when KY > m, an increase in income would generate an inflow of capital greater than the increase in imports. To reestablish the equilibrium in the balance of payments, the interest must fall. This is the reason why the sIOpe of BP must be negative when KY >1m. It is to be recalled that by the assumptions of the model, i.e. (1) the deficit in the balance of payments of one country is equal to the surplus of the other; (2) and the symmetry assumption about the economic structure of the countries, the slopes of BP curves of both countries must have the same signs. 148 Surplus and Deficit Regions Consider the case when KY < m, i.e. when BP is positive. In Figure B.l, any point on BP represents an equilibrium position where R = 0. Taking point A for instance, at that point with income level Yo, the interest rate should be io to insure that neither surplus nor deficit exists in the balance of payments. But, if instead the interest rate is at i1 this will create an inflow of capital, which will result in a net surplus in the balance of payments. Therefore, any point located above BP re- presents a surplus position, and any point below BP a deficit position. 2 - Relative Position of BF, EE, and LM Curves It has been seen that the signs of EB and LM slopes change according to the relative magnitudes of KY and m. To study all combinations of EE, LM, and BP curves is a possible task, but it would be very unpractical and improductive. Therefore, without loss of generality we will take the traditional case where EE is negatively sloped and LM positively sloped. To establish the relative position of the BP with reSpect to the BE and LM curves, we will follow the method of reasoning suggested by Wrightsman [70, pp. 203-208]. a - KY < m Consider Panel A of Figure 3.2. Suppose that the economy was in equilibrium initially at (io, Yo); a recession was to strike. Income and interest would fall because EE shifts to EEl. But in a financially mobile country like the United States, money demanders would be expected to adjust their case balances rapidly 149 BP Deficit Region ‘1 - a -.na ’o-flo—O—-—o—- FIGURE B.l THE BP CURVE, SURPLUS AND DEFICIT REGIONS 150 i 1 K < 111 Y 'P EE BP I o r---- --—- ------ (I I l i, : I l I I l u : 5 1 J EE' I f Y Y1 Y0 Y A B Income Effect Dominant Interest Effect Dominant 1 1 BP Ky > m 18, > m ' //ILM EE EE / LM BP 1 ..-..- --- 1 I\I 1 -——- --1--- o I I i l . l ' I l I I l v I l, i i Y Y1 Y0 Y C D Income Effect Dominant Interest Effect Dominant FIGURE B.2 RELATIVE POSITIONS OF BP, EE, AND LM CURVES 151 so that the lower (i,Y) combination would still be on the LM curve but only lower down. The money market would soon return to equilibrium, say at (i1, Y1). This recession could be expected to disrupt the external equilibrium and create either a surplus or a deficit in the balance of payments. The precise outcome depends on the relative force of the income effect and the interest effect of the recession. The income effect consists of a net decrease in the capital inflow and an increase in the net exports of goods and services, both due to the decrease in income. Since KY‘< m the income effect tends to improve the balance of payments. The interest effect consists of an outflow of capital due to the decrease in the interest rate, which tends to deteriorate the balance of payments. Consequently, when the income effect is dominant, the BP' curve lies below the LM curve to the left of their intersection point I, and it lies above the LM curve to the right of I. In Panel B, the interest effect is dominant, the BP curve lies above the LM curve to the left of their point of intersection and below it to the right of their point of intersection. b - KY >1m Now consider Panel C, and assume that the economy was in equilibrium initially and suddenly there was an increase in the demand for cash LM shifts to LMl. This would drive the interest rate up, which would cause a reduction in expenditures, thus in income. The external equilibrium would be disturbed. Would there be a deficit or a surplus in the balance of payments? 152 If the income effect is dominant, a fall in income would generate a deficit in the balance of payments. The capital inflow due to the increase in the interest rate could not offset the deterioration in the balance of payments due to the decrease in income (since the increase in net exports when KY > m is smaller than the outflow of capital due to the reduction in incom). The BF curve would lie above the BE curve to the left of I and below EE to the right of I. The same reasoning leads to the establish- ment of the relative positions of BP and EE in Panel D when the interest effect is dominant. B - Stabilitypof the System We have seen that the relative values of KY and m de- termine the signs of the slopes of BP, EE, and LM curves. Since we are interested only in stable cases, the relative positions of the curves will determine the existence of the absence of stability in the system, we are consequently led to look for the positions of the curves which make the system stable. To achieve this we will use the graphical description of the tatonnement process used by Patinkin [46, pp. 233-36]. The reasoning will be conducted for country I, but it will be also valid for country II. The next few pages do not pretend to exhaustively study all the possible combinations of the curves, but prOpose simply to show that the stability of the system depends on the relative positions of different curves and the signs of their slopes. Then, a stable combination will be chosen for analyzing the impacts of alternative policies on levels of incomes and rates of interest. 153 Consider Figure B.3. The three curves EE, LM, and BP divide the i-Y plane into six regions. Only at point I where three curves intersect does general equilibrium exist. Any point other than point I represents appartial equilibrium if it is on one of the curves, and if it is in one of the six regions and not on any curve it represents a total disequilibrium. At any point of disequilibrium, income and interest tend to adjust to bring the market back to equilibrium, each point in the plane i - Y is subject to such forces coming from the commodity market, money market, and the balance of payments. Consider Panel A in Figure B.3 for instance. In the deficit regions of the balance of payments (I, II, and VI) income tends to decline due to the real balance effect, and the interest rate tends to rise. The contrary happens to the surplus regions. In the excess-supply regions of the commodity market (I, II, III) income and the interest rate tend to decline, the contrary occurs to the excess-demand regions. In the excess-supply regions of the money market (11, III, IV) income tends to rise, the interest rate to decline. The reverse holds for the excess-demand regions. .If each point in the plane i-Y is subject to the above forces of all three markets, it is impossible a priori and without the knowledge of their relative magnitudes, to tell whether their resultant will force the system back to the general equilibrium point I after the tatonnement process. One is led to make a few assumptions: l-The income effect of the commodity market is dominant over the income effects of the other two markets; 154 FIGURE B.3 RELATIVE POSITIONS OF EE, LM, AND BP CURVES AND STABILITY OF THE SYSTEM 155 2-The interest effect of the money market and the balance of payments are dominant; 3-Since M and R are all real balances, their interest effects are equal. With these considerations in mind, the adjustments for some cases have been worked out in Figure B.3. Consider any point P in region I of Panel A. The arrows attached to it indicate the directions of dynamic forces operating on income and interest when the market is at a position corresponding to that point. These arrows show that should the economy be at any point in region I, automatic market forces are generated such that the interest rate is driven upward and income leftward. Similarly, the directions of dynamic market forces Operating in other sectors are indicated by the arrows whose resultants converge toward the equilibrium point I. The positions of different curves in Panel A insure the stability of the system. The cases represented in Panels B, C, and D are alSo stable. However, the same set of assumptions does not guarantee the stability of the cases represented in Panels E and F. Since the resultants of the forces in regions I and IV move the system away from point I, a characteristic which does not exist in the other panels, there is no guarantee that the dynamic market forces Operating in other regions will be able to make the system to converge toward point I. Having shown that the stability of the system depends on the relative positions of the curves and the signs of their slopes, we will choose the case in Panel A to conduct our analysis of the impacts of fiscal and monetary policies on the level of incomes and interest rates both at home and abroad. APPENDIX C STABILITY CONDITION General Considergtion Assume a dynamic system of the form dt — f1(x1’ x2) (C.l) dt f2(x1’ *2) where f1 and f are assumed to be differentiable functions. 2 Let x10 and x20 denote an equilibrium point, i.e. f = 0; f2(x 1(x10’ x20) 10’ “20) g 0’ The equilibrium point (x10,x20)is said to be locally Stable if given any initial point (x30, x20) in a sufficiently small neighborhood of (x10, x20), the system (C.l) generates time paths for x1(t), x2(t) such that 11m x1(t) = x10 and 11m.x2(t) = x t—ooo t—ooo 20 If these limits exist for any initial point (XIO’ x30) then (x10, x20) IS said to be globallyystable. Local Stability Necessary and sufficient conditions for local stability are given by the Routh-Hurwitz theorem [45] 156 157 + d (C.2) £11 £22 < 0 an (C.3) f11f22 - f12f21 > 0 afl sz afl 3f where f 1 = ; f22= ; f = --'; f = -——' and where 1 5x1 3x2 12 nxz 21 3x1 all partial derivatives are evaluated at (x x). Global Stability Sufficient conditions for global stability were derived by Olech [42]. Assume f1, f2 have continuous derivatives every- where, then (xlo, x20) is globally stable, if (C.4) f + f 2 < 0, V x CV = for all values of ...) 11 2 I’xz f f > 0 V x ,x (0.5) f11f22 ' 12 21 ’ 1 2 (C.6) either £11 £22 # 0, V x1,x2 or f12f21 # 0, V x1,x 2 . Sufficient conditions for global stability are not known for systems of more than two simultaneous differential equations. In this study, we are concerned with the local stability pply. Stability Conditions in our Model The dynamic adjustment of the tatonnement process of our economy is described by the following dynamic equations dY _ (0.7) dt-y1[(E+X-IM+G) -Y] (C.8) §—:'=v2[L(Y,i,M+BT+vK) - (M+BT+vK+Mi)] where Yl’ V2 are positive constants representing the speed of adjustment. 158 From Appendix A, we know that the total differentiation of the above equations gives (C.9) (-h - qm - m - quY)dY +(Ei + qui)di = -dG - qu (0.10) (LY + 2qm - 2vq1q)dy + (Li - 2qui)di = dMI + (l-q)dM . In a small neighborhood of the equilibrium point (i0, Yo) the adjustment process may be approximated by the linear term of a Taylor series expansion of expressions (C.7) and (C.8) iY-= <-h -- )(YY>+ (E + K (' °> ' dt Y1 'qm m quY 0 Y1 1 vq i) 1 ' 1o (C.12) 04'0- rr H. : y2(LY + 2qm - quKY)(Y4Yo) + Y2(Li ' 2VqK1)(i ' 10) ° In matrix form, it is z r A z "111 ' l P 7 ‘ dt Y1 0 -h-qm-m+vq1% Ei-WqKi [Y - Yo (0.13) = 3% 0 yz LY+2qm-2quY Li-quKi 1 - 10 L a L a L "J L J More compactly, the system may be rewritten as , Y1811 Y1812 (C.14) Z = PAZ where Z = [21], F A = . Y2321 Y2822 The solution of (C.13) is given by [45, pp. 312-313]. More specifically, if all the characteristic roots xj of FA are distinct, then (C .15) _ . . = 1 22 — l - 1o Q21 e i'Q (C.15) may be represented as 2 (0.16) z = )3 Q , ej 1 = (1,2) If a root is repeated, then the solution becomes Alt (C.17) 21 = Y - Yo =Q11 te Alt 22 = 1 10 "Q21 te (C.17) may be represented as 1 1t zi=20 tej i=(1,2)andj=1. We may combine (0.16) and (C.17) to give the general solution to a system of n equations Lt (0.18) z = (c) e 3 J' IIMU’ 1Qij where i = (1,...,n) and s s n, the number of distinct characteristic roots of the system, Qij(t) is a polynomial in t of one degree less than the number of times the jth root is repeated and is the jth characteristic root of the systema Q depends on the matrix 1.1 A, the speed of adjustment. If the system is to be stable, when t a m, t must tend to zero. This is possible if the real parts of all the characteristic roots are negative. 160 The characteristic equation of FA takes the form Y1‘11 ' A Y1812 (0.19) \I‘A - 111 - = o . Y2‘21 Y2°22 ' A The eXpanded form of this equation is 2 (C-ZO) A ' (Y1311 ""1232?k +Y112(811822 ' “21812) or 0 21 2 - D +'D = 0 ( - ) A 1* 2 ° The solution to (C.21) is (c 22) 11. 1, = The necessary and sufficient conditions for (C.14) to be stable is [51, p. 165] (0.23) 01 < o (0.24) D2 > 0 i.e. the trace of the matrix A must be negative and its determinant positive [Baumol, p. 336]. The trace is equal to = + = + (C°25) D1 11 12 Y1811 Y2‘22 < 0 ° If all Since the y's are all positive. This is the case with the CS and a22 are negative the above relation is satisfied, and R0 cases. 161 The determinant is equal to (C.26) D2 = y1y2(811822 - 812821) > 0 . Since yl, V2 are pOSItive thus (alla22 - 812821) > 0 which is the determinant of A, and if Y1 and Y2 are equal to one what has been said for matrix PA is valid for matrix A. 162 HQo.u noo.u «#0.: Now.- coo.u N¢~.u o¢~.u omN.u nam.u mam.u Ham. mam. omm. amm. 0mm. ao¢.u m~¢.n HN¢.1 mHO.n w~¢.u mom. Hon. man. can. «mm. 0mm.n mmm.u mam.n mmm.u HOm.n NNH.- wNH.u Oma.u omu.u NmH.u own. awn. «on. man. now. NHN.1 HNN.1 omN.u NNN.I oNN.1 mm.H m~.H HH.H can. «an. Ham. ama. HRH. mom. ama. mad. moH. wmo. noa. HOH. ~¢H.1 oma.a NHH.1 o¢H.u ou.Hn NwH. cog. omH. new. mma. mn.~ ma.~ am.H m¢.a um.H mHo.n Om~.u Ham. HN¢.1 cum. mam.n mnH.u Own. Hm~.u Hum. omH. omo. HOH.1 mqa. so.H Noo.u wmu.u ao.a w~¢.n one. sue.- oOH.u ham. HON.- mob. moo. who. now. «ma. HN.H Omo.s omm.u mo.H n~¢.n Ham. 50¢.u dqa.n ans. mmu.n com. moo. nmo. cod. mMH. um.H one.: man.- ooo.H ou¢.u Nwm. mmm.n NdH.I Nwo. wm~.u Ham. mHH. Omo. «ma. mma. om.H nao.n mm~.u mmm. mNO.u moo. oom.u mma.u mam. nm~.u mmo.H EH. Hmo. mod. mma. m~.H Hzo\mo H2o\.wo Hzo\.wp Hzo\«o Hzo\wo ze\Mp ze\.ap zp\.»p ee\ap ze\»p Uo\mo Qv\.wo Uo\.ub Uo\fio uo\wo Am=a<> unseemm UZHQEQZH mBHZ mmmHAAHHBADZ Bmflmaa 92¢ mMZOUzH ZH manage-mu Q NHQZflhQQ 163 mmo.u Nwo.n man.u 5mm.1 «00.1 oHo.u mmm.1 090.1 «Ho.u oo~.- th.n NmH.u H¢~.u m¢~.u o¢~.n ¢¢~.1 ndm.n on~.u Nmo. mo.H 0H.H mma. «Om. mam. mmm. mmm. dam. mm¢.u moO.u Nm¢.n 50¢.u ma¢.u ma¢.n HH¢.1 oH¢.u H~¢.u awe. «mm. mom. son. mam. ans. Nae. one. nmo. Hum.u omm.u ma¢.n oOn.: mmm.u mmm.n nmm.u mmm.u mam.n ~¢~.u NmH.u ooH.u Hma.u mmH.u oMH.u mNH.n oma.n «MH.1 m3. «no. m8. 8m. am. can. Hmm. won. «mm. «ON.1 HoN.u «5N.u oNN.u om~.u mmN.u mH~.n MNN.1 om~.u mo.~ no.H mo.H 0H.H NH.H no.H oo.H Ho.H No.H mod. mwa. omH. ans. «ma. was. new. mma. owu. moo. moo. OOH. mmo. wwo. mmo. NHH. noH. umo. wHH.u H¢H.n mmH.u doayn ooa.u ROH.1 HmH.1 NoH.u «ma.u «OH. «ma. HoH. mma. mma. NNH. ona. moa. and. mn.a on.H mm.~ Hm.a m~.~ om.H mn.a mn.H mm.~ HA gm VA .oqucoo 1 Q Nanumm< 164 .m nouamoo mom "mousom mmo.n oNo.u dao.u omo.a mNo.u mHo.u ow~.u mnu.u moN.u ommN.n HmoN.n Hmom.n aHo.H Noo.H owm. mama. oama. mmmm. oH¢.u o~o.u n~¢.n Homo.u mmN¢.n mmma.u ooo. moo. «so. Hmoo. Nmoo. mmoo. mom.c mom.n mom.u mnm.n mom.u wom.n oma.n oma.n naa.u nma.u mma.u wnH.u omo. nuo. oHo. 5mm. woo. wmm. om~.n nm~.u onN.u nm~.u nnN.n umu.n wNo.H omo.~ o¢O.H ooo.~ mmo.H mmo.a wmu. NMN. mum. mos. wow. moH. mmo. moo. omo. mmo. Nmo. Hmo. wNH.u mNH.u wHH.u oHH.n NHH.| OHH.I nma. me. ooH. an. wma. on”. N¢N.H mw~.H own.a omm.H Hm5.H omn.H gm WM .o.ucoo I D NHszmm< 165 pa~.- AHN.- N-.- maw.- 8H~.- Hmw.- mon.- pmN.- HpN.- oo~.- Hze\Mp omao.- meao.- pqao.- mHo.- nHo.- Hmoa.- peso.- AHo.- pHo.- nHo.- Hze\.ap oee. ems. mms. mos. Hes. «Ne. one. use. «mm. me. Hzp\.»p Hmo.- mmo.- mmo.- «mo.- ewo.- eao.- Amo.- Amo.- Aao.- Amo.- H2p\ap Ne.H Hm.H HN.H Hem. hem. no.9 one. mum. was. HH.H H2p\wp ANH.- ANH.- oma.- HMNH.- amNH.- omH.- wN~.- o~.- AH.- mH.- ze\ap Aeoo.- okoo.- meoo.- mnoo.- Naoo.- noo.- oHo.- moo.- woo.- moo.- ze\ap «on. men. man. now. mAN. AwN. awn. man. was. on. ze\.wp Hmo.- «mo.- mmo.- Hmo.p Hmo.- mmo.- aemo.- pemo.- «no.- emo.- ze\ap pe.a oq.a mm.e aw.a NH.A ou.H New. Haw. mH.H on.H ze\~p nee. pee. Ase. so. “no. «no.- so.- so.- No.- eHo.- Op\Mp naoo. mkoo. Shoo. powoo. Hwoo. omoo. «co. «co. poo. moo. op\.ap «no. mno. «mo.. Aoo.- Hoo. AHo. Hos. eon. owe. no. up\.9p oawo. omNo. one. mmo. smo. mmo. one. one. Hmo.. «no. op\ap om.a an.a No.4 «m.a ms.H an.H HH.H p~.H ss.~ po.e up\»p Am 0 e Ayah—94> EAOmQ-v x 99-0 .Hz 92¢ .2 .0 29 99-92029 2m 09. Mme/993.992 .mmagm 929. 90 mm59<> 0295-9905“ 29.93 mmdemHHHaa HmflmPHzH 92¢- 920029 29 mmozéo .9 2992993 166 m9~.n w9~.u o9~.u o9N.u m9~.n MNN.1 ¢¢9o.u ~¢9o.u n9o.u wm9o.u od9o.u od9o.u 99¢. m9o. owo. ooo. one. moo. Noo.: «oo.u moo.u 9oo.: moo.s ooo.n oo.9 no.9 noo.9 No.9 9m.9 o9.9 o~9.u mm9.n 5N9.n mm9.n 5N9.u mN9.u ooo.u oooo.n «noo.u onoo.n ooo.1 soo.u «mm. now. now. won. mom. «on. woo.u no.1 «no.1 woo.u coo.u «no.1 «N9. mu.9 5N.9 oo.9 no.9 om.9 woo. woo. moo. oo. woo. woo. moo. mooo. 9ooo. moo. ooo. woo. mooo. ~9o. «No. ooo. 9oo. nmo. omo. mmo. mmo. omo. omo. ”no. no.9 oo.9 no.9 99.N oo.9 55.9 >9 O o¢~.u om~.1 ooN.n mo9o.n m59o.u mo9o.u m9o. woo. omm. oo9.u «99.: 9N9.n o9.9 oN.9 oo.9 od9.n om9.u No9.u «woo.n mooo.| omoo.s o9m. 5mm. mom. ono.: Noo.n noo.u oo.9 oo.9 oo.9 moo. moo. moo. 9woo. mooo. owoo. ouo. «900. 9oo. mmo. nmo. wmo. no.9 oo.9 no.9 99 .o.ucoo I m NH92999< 167 .m nouoooo wow "meadow m5~.u om~.u oom.u ~N~.u n-.u m-.u m9o.u 59o.u o9o.u o¢9o.u mo9o.u 9m9o.u «on. ooo. omo. oNo. mNo. «no. omo.n moo.u omo.u o5mo.u 55mo.n m5oo.u Noo.9 9oo.9 woo.9 N~9.9 o~9.9 599.9 9o9.s 9n9.u om9.n omu9.u 9NM9.: mNM9.u 5moo.u oooo.u ooo.- oooo. 95oo. ¢5oo. 9am. 5am. m9m. mom. oom. mom. Nmo.u moo.u «no.1 mono.n ommo.n «no.1 oo~.9 55~.9 5o~.9 oom.9 Nom.9 ma~.9 5oo. 5oo. moo. oom.9 mom.9. mm~.9 oooo. mooo. 9ooo. wooo. aooo. oooo. m9o. 9N0. ouo. o9o. «No. omo. ammo. Nomo. mono. ammo. Nomo. oomo. ¢5o.9 moo.9 99oo.9 M5o.9 5oo.9 moo.9 9M rm .o.ucoo I 9 2992999< ”71111111111111!flflfllflffl'l'ljflflflflfllfflflflm“