- Email: [email protected]
What is the optimal size of a monetary union?
WHAT IS THE OPTIMAL SIZE OF A MONETARY UNION?
CYNTHIA
ROYAL TORI
ABSTRACT The literature on monetary
unions primarily
focuses on how a monetary
union effects inflation rates for
member countries and what factors influence a country’s decision to join a monetary union. The literature, however, does not address the question of what is the optimal size of a monetary union? This paper finds that the optimal monetary union size depends upon the marginal benefit of fewer exchange rates and trade, and the marginal cost of influencing
monetary policy. Also, if countries independently
not to join a monetary union, it leads to a sub-optimal
membership
do not consider the spillover benefits that fewer exchange
decide whether or
size. This is because member countries
rates have on other countries.
The literature on monetary unions primarily focuses on how a monetary union effects inflation rates for member countries and what factors influence a country’s decision to join a monetary union. Some of the factors found to influence the inflation rate and a country’s decision to join a monetary union include trade (Canzoneri & Rogers, 1990), a country’s relative size (Casella, 1992), relative collection costs of fiscal tax instruments (Vegh & Guidotti, 1990; Kimbrough, 1991), and seigniorage sharing (Sibert, 1994). The literature, however, does not address the question of what is the optimal size of a monetary union? An example of why this is important is the European monetary union. The European Community is moving toward an economic and monetary union. According to the Maastricht Accord, monetary unification will take place no later than January 1, Direct all correspondence to:
Cynthia Royal Tori, Department of Economics, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 282234001; E-mail: [email protected]. Copyright 0 I997 by JAI Press Inc. International Review of Economics and Finance, 6(l): 57-66 All rights of reproduction in any form reserved. ISSN: 1059-0560
57
58
CYNTHIA
ROYAL TORI
1999. The European Community currently has twelve members, with additional countries requesting admission to the union.’ Inflation rates, growth rates, size, debt level and trade vary greatly among the countries. Given the diversity among the countries, what is the optimal size of the monetary union? Should all countries join the monetary union or should the union consist of a subset of potential members? Defining a monetary union as a club helps to answer these questions (Buchanan, 1965; Ng, 1973). There are three factors that distinguish a club good from a public or private good. First, a club good has some type of mechanism for exclusion. For a monetary union, union membership is the exclusion mechanism. Second, a club is partially rivalrous in consumption. As other countries enter the union, the influence a particular country has over monetary policy diminishes. Third, union membership is voluntary. Countries are not forced to participate in the monetary union. This paper finds that the optimal monetary union size depends upon the marginal benefit of fewer exchange rates and the amount of trade, and the marginal cost of influencing monetary policy. Also, if countries independently decide whether or not to join a monetary union, it leads to a sub-optimal membership size. This is because countries do not consider the spillover benefits that fewer exchange rates have on other countries.
1. THE WORLD The world consists of N countries that may potentially form a monetary union. Each country has its own central government that makes fiscal policy decisions and a separate central bank that makes monetary policy decisions. If countries form a monetary union, the member central banks are consolidated into one central bank for the union. Each central bank prints its own currency. Each zero growth country produces a non-durable consumption good (C’). The technology used to produce the consumption good is assumed to exhibit constant returns to scale, n, = y, where n is labor at time t and y is the number of goods produced during time period t. The representative consumer from each country gains utility from leisure (h) and consuming consumption goods. The consumer may consume consumption goods produced by all countries. The utility function for country i’s (u’) infinitely lived representative consumer is:
where .$ is the exchange rate for country i at time t with respect to country j, j = 1 to N including i, and r is the discount rate and the exogenously given real interest rate for the one-period bond.2 Consumers hold two assets: money and bonds. Consumers hold money to reduce transaction costs or “shopping” time(s). Shopping time is a function of two things.
Optimal Size of a Monetary Union?
59
First, it is a function of the number of exchange rates the consumer must know. A consumer may hold several currencies and must know the exchange rates, or the value of each currency relative to each of the other currencies. The number of exchange rates a N-N*
consumer
must know is equal to
union member countries, ber of countries
c X, w h ere X is the number of non-monetary x=0 N is the number of countries in the world and N* is the num-
that form a monetary
= N*), then the number
of exchange
union.3 If all countries rates is zero. If countries
form a monetary
union (N
do not form a monetary
N-I
union (N* = l), then the number
of exchange
rates is
C X. Second, shopping time is x=0 a function of the amount of trade (7’~.~ The amount of trade depends upon the relative price of consumer goods. Each country’s representative consumer is endowed with one unit of time that is divided between labor, leisure and shopping time. Consumers divide their after-tax real income among the consumption goods, real bond holdings (B), and real money holdings (m). Letting labor be the numeraire, the periodic budget constraint for the representative consumer is:
-[Bj,-(l+r)Bj,_,]-s’
where pit is country i’s income tax rate at time t. The lifetime real budget constraint the representative consumer is:
t= 1
(1+
facing
r-y
where Rj,is the nominal interest rate and satisfies Rjt= (1 + r)qt + I/Pjt - I.'The nominal interest rate at time t is a function of the expected price level at time t+l relative to the price level at time t, or is a function of the expected inflation rate at time t + 1. The representative consumer maximizes the lifetime utility function (1) by choosing the consumption goods and real money balances, subject to the real budget constraint (2). The
CYNTHIA
60 optimal time path of the consumption from the first order condition. It is:
ROYAL TORI
goods and the real money balances is derived directly
for j = 1 to N including i. Each country’s government raises revenue from taxing its consumers’ incomes, net of collection costs (5) and from its seigniorage. The income tax rate (p) is chosen by each government independently and is assumed exogenous in this model. Real seigniorage for a country is equal to the change in its real money demand over time ($/Pit). Each government uses its revenue to provide an exogenously given level of government expenditure (G:) and to influence monetary policy [t(N)]. If a country is not a member of a monetary union, the cost of influencing monetary policy is zero. The central bank determines its monetary policy unilaterally. If however, a country joins a monetary union, the country does not have total control over its monetary policy. The country may need to lobby for a monetary policy that is advantageous to its country. As the size of the monetary union increases, the amount of influence the country has decreases and the cost of lobbying increases. A country’s expenditure must equal its revenue, therefore: Sf Gj + If(N) = Y;pj( 1 - 5’) + F
rt where 5’ is constant over time and may be different among countries. The central bank’s problem is to maximize the utility of its representative consumer (1) subject to its representative consumer’s budget constraint (2) and its government’s revenue constraint (3). The maximization problem for country i is:
(4)
-[Bf-(I
II.
+r)BJ_,]-s’
OPTIMAL MONETARY UNION SIZE
Each country individually decides whether or not to join a monetary union by choosing the N* that maximizes its maximization problem (4). The first order condition indicates that
Optimal
Size of a Monetary
61
Union?
the marginal benefit of adding an additional member to the monetary union (left-hand side) must equal the marginal loss of influence over monetary policy (right-hand side),
a,+
q(N) aN
=
-XT
1
(-_) 1-C’.
The marginal benefit of adding an additional member is the reduction in the number of exchange rates. The fewer the number of exchange rates, the lower the consumer’s shopping time. How beneficial membership is to a consumer also depends upon the amount of trade. If the consumer does not trade with any other countries, the benefit of joining the monetary union is zero. As the number of trade partners increases, the benefit of joining the monetary union increases. It is expected that the marginal benefit of forming a monetary union initially increases, then decreases. There are two reasons for this assumption. First, countries will initially form a monetary union with its major trade partners. As more countries join, the importance of trade between the countries decreases. Second, as countries join the monetary union, the number of exchange rates decreases at an decreasing rate.6 The marginal cost of adding an additional member is a country’s loss of influence over its monetary policy. How great this loss is depends upon the diversity of policy decisions. Researchers find three factors that may effect a country’s monetary policy. First, the cost of collecting fiscal taxes affect the inflation rate choice. As the cost of collecting fiscal taxes increases, governments rely more on money production to fund government expenditures (Aizenman, 1983; Canzoneri & Rogers, 1990; Vegh, 1989; Tori, 1997). Second, the level of trade affects the inflation rate choice (Kimbrough, 1991; Aizenman, 1992). When a foreign consumer purchases domestic goods, the foreign consumer must first obtain the domestic currency. Therefore the government is able to pass on some of the inflation costs to foreign consumers. Finally, central bank independence affects the inflation rate choice (Alesina & Summers, 1993). The more independent the central bank, the lower the inflation rate. Other factors that may influence a country’s monetary policy are its relative size of government expenditure to its RGDP and its relative level of debt to RGDP.7 If consumers are identical and governments face the same constraints, then the equilibrium membership size is N* = N (Figure 1). All countries should join the monetary union. In this case, the marginal cost of influencing monetary policy is zero. This is because all countries are identical, and the monetary policy decisions are the same. The more diversified the countries, the smaller the equilibrium membership size, N*
62
CYNTHIA
ROYAL TORI
Size Figure I.
All Consumers
and Governments
are Identical
MB, MC
0 Figure 2.
N Countries Independently
Union Size
Decide the Union Size
Allowing countries to independently decide the membership size leads to a sub-optimal monetary union size. This is because the countries do not consider the spillover benefits their joining has on non-member countries. As more countries join the monetary union, it decreases the number of exchange rates for member and non-member countries. The maximization problem for the world is:
Optimal
Size of a Monetary Union?
63
-sk
for all j = 1 . N, all member countries d = 1 to N* and all non-member countries k = N*+ 1 to (N - N*). When the world decides the optimal monetary union size, the first order condition indicates that the marginal benefit of adding an additional member to the monetary union for member and non-member countries (left-hand side) must equal the marginal loss of influence over monetary policy for member countries (right-hand side),
The marginal benefit of adding an additional member is the reduction of the number of exchange rates for all consumers. When a country decides to join a monetary union, the country reduces the number of exchange rates not only for its consumers, but also for all other consumers. When spillover benefits are considered, the equilibrium membership size increases (Figure 3).”
III.
CONCLUSION
As countries begin forming monetary unions, they will face the question, what is the optimal monetary union size? The optimal size of a monetary union depends upon the similarities and differences among the potential members and the costs of not forming a monetary union. The cost of influencing monetary policy for a member country may be a function of
CYNTHIA
64
ROYAL TORI
Size Figure 3.
The Community
Decides the Union Size
a country’s relative size of government expenditure to RGDP, a country’s relative level of debt to RGDP, the difference in monetary policy between the countries, and the differences of collection costs. The benefits of joining is a function of the number of exchange rates and the amount of trade with other countries. Allowing countries to independently decide to join the monetary union leads to a suboptimal membership size. This is because countries do not consider the spillover benefits of fewer exchange rates for consumers in other countries. When the spillover benefits are considered, the optimal membership size increases.
ACKNOWLEDGMENT I would like to thank the anonymous
referee for the helpful comments.
NOTES 1. The members of the European Union include Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain and the United Kingdom. Austria, Finland and Sweden are expected to join on January 1, 1996. Other countries seeking membership include Poland, the Czech Republic, Slovakia, Romania, Bulgaria, Hungary, the three Baltic republics and Slovenia. Members of the European Union are potential members of the monetary union. 2. The utility function is twice-continuously differentiable, with positive and diminishing marginal utility.
Optimal Size of a Monetary Union?
65
3. For example, if there are five countries (N = 5) and two countries form a monetary union (N* = 2), then there are three non-monetary union member countries (X = 3). The four central banks and currencies, A B C and D, require the consumer to know six exchange rates (CD), (BC BD), and (AB AC AD). 4. I assume all countries trade with all other countries. The amount of trade between countries may vary. 5. I assume the real interest rates are the same for all countries. The nominal interest rates may be different among countries, if the expected inflation rates are different. 6. As countries join the monetary union, the number of exchange rates decreases at an decreasing rate. For example, if there are six countries that are potential monetary union members (N = 6), and one country joins the union (N* = l), then the number of exchange rates is fifteen (E = 15). If N* = 2, E = 10. If N* = 3, E = 6. If N* = 4, E = 3. If N = 5, E = 1. The benefit of fewer exchange rates increases at a decreasing rate. 7. The Maastricht Accord specifies criteria regarding a country’s deficit and debt as a percent of GDP. See note 9 for further details. 8. The differences may include consumer utility functions, fiscal policy, collection costs, central bank independence, level of government expenditure as a percent of RGDP, a country’s deficit as a percent of RGDP and debt as a percent of RGDP. 9. The Maastricht Accord specifies four criteria for countries to meet before they may join the European monetary union. In short, the criteria are (1) a country’s inflation rate may not exceed the lowest three European Community countries’ inflation rates by more than 1.5 percentage points, (2) a country’s interest rate on its long-term government bond must not exceed by more than 2 percentage points the interest rate on long-term govemment bonds of the countries with the three lowest inflation rates, (3) a country’s total government deficit must not exceed three percent of its gross domestic product, and (4) a country’s outstanding debt may not exceed 60 percent of its gross domestic product [Fratianni, Hagen and Waller, (I 992) p.8-91. 10. The actual increase in membership size may be less than NT because of the potential redistribution of trade between member and non-member countries. Joining a monetary union eliminates the cost of knowing exchange rates for member countries’ goods. This lowers the relative price of member goods and may encourage substitution away from nonmember goods to member goods. The impact substitution has on non-member countries depends upon how sensitive consumers are to a change in the relative price of goods. An interesting extension of this paper would be to examine the effect a monetary union has on trade and how demand elasticity may effect monetary union size.
REFERENCES Aizenman, J. (1983). Government size, optimal inflation tax and tax collection costs. Eastern Economic Journal, 9(2), 103-105. . (1992). Competitive externalities and the optimal seigniorage. Journal ofMoney Credit and Banking, 24(l), 6 l-7 1 Alesina, A., & Summers, L. (1993). Central bank independence and macroeconomic performance: Some comparative evidence. Journal of Money, Credit and Banking, 25(2), 151-160.
66
CYNTHIA
ROYAL TORI
Buchanan, J. (1965). An economic theory of clubs. Economica, 1-14. Canzoneri, M., & Rogers, C.A. (1990). Is the European community an optimal currency area? Optimal taxation versus the cost of multiple currencies. The American Economic Review, 80(3), 419-433. Casella, A. (1992). Participation in a currency union. The American Economic Review 82(4), 847-863. Fratianni, M. von Hagen, J., Waller. C. (1992). The Maastricht way to EMU. Essays in internationalfinance. Princeton: Princeton University Press. Kimbrough, K. (1991). Optimal taxation and inflation in an open economy. JoumaZ of Economic Dynamics and Control, 15, 179-196. Ng, Y.-K. (1973). The economic theory of clubs: Pareto optimality conditions. Economica, 291-298. Sibert, A. (1994). The allocation of seigniorage in a common currency area. Journal of International Economics, 37, 111-122. Tori, C.R. (1997). Monetary unions and the effects of seigniorage sharing. Journal of Macroeconomics, 19( 1). Vegh, C.A. (1989). Government spending and inflationary finance. IMF Staff Papers, 36(3), 657-677. Vegh, C.A., & P.E. Guidotti. (1990). Optimal taxation policies in the EMS: A two-country model of public finance. IMF Staff Papers, 37, 3 1 l-337.
CYNTHIA
ROYAL TORI
ABSTRACT The literature on monetary
unions primarily
focuses on how a monetary
union effects inflation rates for
member countries and what factors influence a country’s decision to join a monetary union. The literature, however, does not address the question of what is the optimal size of a monetary union? This paper finds that the optimal monetary union size depends upon the marginal benefit of fewer exchange rates and trade, and the marginal cost of influencing
monetary policy. Also, if countries independently
not to join a monetary union, it leads to a sub-optimal
membership
do not consider the spillover benefits that fewer exchange
decide whether or
size. This is because member countries
rates have on other countries.
The literature on monetary unions primarily focuses on how a monetary union effects inflation rates for member countries and what factors influence a country’s decision to join a monetary union. Some of the factors found to influence the inflation rate and a country’s decision to join a monetary union include trade (Canzoneri & Rogers, 1990), a country’s relative size (Casella, 1992), relative collection costs of fiscal tax instruments (Vegh & Guidotti, 1990; Kimbrough, 1991), and seigniorage sharing (Sibert, 1994). The literature, however, does not address the question of what is the optimal size of a monetary union? An example of why this is important is the European monetary union. The European Community is moving toward an economic and monetary union. According to the Maastricht Accord, monetary unification will take place no later than January 1, Direct all correspondence to:
Cynthia Royal Tori, Department of Economics, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 282234001; E-mail: [email protected]. Copyright 0 I997 by JAI Press Inc. International Review of Economics and Finance, 6(l): 57-66 All rights of reproduction in any form reserved. ISSN: 1059-0560
57
58
CYNTHIA
ROYAL TORI
1999. The European Community currently has twelve members, with additional countries requesting admission to the union.’ Inflation rates, growth rates, size, debt level and trade vary greatly among the countries. Given the diversity among the countries, what is the optimal size of the monetary union? Should all countries join the monetary union or should the union consist of a subset of potential members? Defining a monetary union as a club helps to answer these questions (Buchanan, 1965; Ng, 1973). There are three factors that distinguish a club good from a public or private good. First, a club good has some type of mechanism for exclusion. For a monetary union, union membership is the exclusion mechanism. Second, a club is partially rivalrous in consumption. As other countries enter the union, the influence a particular country has over monetary policy diminishes. Third, union membership is voluntary. Countries are not forced to participate in the monetary union. This paper finds that the optimal monetary union size depends upon the marginal benefit of fewer exchange rates and the amount of trade, and the marginal cost of influencing monetary policy. Also, if countries independently decide whether or not to join a monetary union, it leads to a sub-optimal membership size. This is because countries do not consider the spillover benefits that fewer exchange rates have on other countries.
1. THE WORLD The world consists of N countries that may potentially form a monetary union. Each country has its own central government that makes fiscal policy decisions and a separate central bank that makes monetary policy decisions. If countries form a monetary union, the member central banks are consolidated into one central bank for the union. Each central bank prints its own currency. Each zero growth country produces a non-durable consumption good (C’). The technology used to produce the consumption good is assumed to exhibit constant returns to scale, n, = y, where n is labor at time t and y is the number of goods produced during time period t. The representative consumer from each country gains utility from leisure (h) and consuming consumption goods. The consumer may consume consumption goods produced by all countries. The utility function for country i’s (u’) infinitely lived representative consumer is:
where .$ is the exchange rate for country i at time t with respect to country j, j = 1 to N including i, and r is the discount rate and the exogenously given real interest rate for the one-period bond.2 Consumers hold two assets: money and bonds. Consumers hold money to reduce transaction costs or “shopping” time(s). Shopping time is a function of two things.
Optimal Size of a Monetary Union?
59
First, it is a function of the number of exchange rates the consumer must know. A consumer may hold several currencies and must know the exchange rates, or the value of each currency relative to each of the other currencies. The number of exchange rates a N-N*
consumer
must know is equal to
union member countries, ber of countries
c X, w h ere X is the number of non-monetary x=0 N is the number of countries in the world and N* is the num-
that form a monetary
= N*), then the number
of exchange
union.3 If all countries rates is zero. If countries
form a monetary
union (N
do not form a monetary
N-I
union (N* = l), then the number
of exchange
rates is
C X. Second, shopping time is x=0 a function of the amount of trade (7’~.~ The amount of trade depends upon the relative price of consumer goods. Each country’s representative consumer is endowed with one unit of time that is divided between labor, leisure and shopping time. Consumers divide their after-tax real income among the consumption goods, real bond holdings (B), and real money holdings (m). Letting labor be the numeraire, the periodic budget constraint for the representative consumer is:
-[Bj,-(l+r)Bj,_,]-s’
where pit is country i’s income tax rate at time t. The lifetime real budget constraint the representative consumer is:
t= 1
(1+
facing
r-y
where Rj,is the nominal interest rate and satisfies Rjt= (1 + r)qt + I/Pjt - I.'The nominal interest rate at time t is a function of the expected price level at time t+l relative to the price level at time t, or is a function of the expected inflation rate at time t + 1. The representative consumer maximizes the lifetime utility function (1) by choosing the consumption goods and real money balances, subject to the real budget constraint (2). The
CYNTHIA
60 optimal time path of the consumption from the first order condition. It is:
ROYAL TORI
goods and the real money balances is derived directly
for j = 1 to N including i. Each country’s government raises revenue from taxing its consumers’ incomes, net of collection costs (5) and from its seigniorage. The income tax rate (p) is chosen by each government independently and is assumed exogenous in this model. Real seigniorage for a country is equal to the change in its real money demand over time ($/Pit). Each government uses its revenue to provide an exogenously given level of government expenditure (G:) and to influence monetary policy [t(N)]. If a country is not a member of a monetary union, the cost of influencing monetary policy is zero. The central bank determines its monetary policy unilaterally. If however, a country joins a monetary union, the country does not have total control over its monetary policy. The country may need to lobby for a monetary policy that is advantageous to its country. As the size of the monetary union increases, the amount of influence the country has decreases and the cost of lobbying increases. A country’s expenditure must equal its revenue, therefore: Sf Gj + If(N) = Y;pj( 1 - 5’) + F
rt where 5’ is constant over time and may be different among countries. The central bank’s problem is to maximize the utility of its representative consumer (1) subject to its representative consumer’s budget constraint (2) and its government’s revenue constraint (3). The maximization problem for country i is:
(4)
-[Bf-(I
II.
+r)BJ_,]-s’
OPTIMAL MONETARY UNION SIZE
Each country individually decides whether or not to join a monetary union by choosing the N* that maximizes its maximization problem (4). The first order condition indicates that
Optimal
Size of a Monetary
61
Union?
the marginal benefit of adding an additional member to the monetary union (left-hand side) must equal the marginal loss of influence over monetary policy (right-hand side),
a,+
q(N) aN
=
-XT
1
(-_) 1-C’.
The marginal benefit of adding an additional member is the reduction in the number of exchange rates. The fewer the number of exchange rates, the lower the consumer’s shopping time. How beneficial membership is to a consumer also depends upon the amount of trade. If the consumer does not trade with any other countries, the benefit of joining the monetary union is zero. As the number of trade partners increases, the benefit of joining the monetary union increases. It is expected that the marginal benefit of forming a monetary union initially increases, then decreases. There are two reasons for this assumption. First, countries will initially form a monetary union with its major trade partners. As more countries join, the importance of trade between the countries decreases. Second, as countries join the monetary union, the number of exchange rates decreases at an decreasing rate.6 The marginal cost of adding an additional member is a country’s loss of influence over its monetary policy. How great this loss is depends upon the diversity of policy decisions. Researchers find three factors that may effect a country’s monetary policy. First, the cost of collecting fiscal taxes affect the inflation rate choice. As the cost of collecting fiscal taxes increases, governments rely more on money production to fund government expenditures (Aizenman, 1983; Canzoneri & Rogers, 1990; Vegh, 1989; Tori, 1997). Second, the level of trade affects the inflation rate choice (Kimbrough, 1991; Aizenman, 1992). When a foreign consumer purchases domestic goods, the foreign consumer must first obtain the domestic currency. Therefore the government is able to pass on some of the inflation costs to foreign consumers. Finally, central bank independence affects the inflation rate choice (Alesina & Summers, 1993). The more independent the central bank, the lower the inflation rate. Other factors that may influence a country’s monetary policy are its relative size of government expenditure to its RGDP and its relative level of debt to RGDP.7 If consumers are identical and governments face the same constraints, then the equilibrium membership size is N* = N (Figure 1). All countries should join the monetary union. In this case, the marginal cost of influencing monetary policy is zero. This is because all countries are identical, and the monetary policy decisions are the same. The more diversified the countries, the smaller the equilibrium membership size, N*
62
CYNTHIA
ROYAL TORI
Size Figure I.
All Consumers
and Governments
are Identical
MB, MC
0 Figure 2.
N Countries Independently
Union Size
Decide the Union Size
Allowing countries to independently decide the membership size leads to a sub-optimal monetary union size. This is because the countries do not consider the spillover benefits their joining has on non-member countries. As more countries join the monetary union, it decreases the number of exchange rates for member and non-member countries. The maximization problem for the world is:
Optimal
Size of a Monetary Union?
63
-sk
for all j = 1 . N, all member countries d = 1 to N* and all non-member countries k = N*+ 1 to (N - N*). When the world decides the optimal monetary union size, the first order condition indicates that the marginal benefit of adding an additional member to the monetary union for member and non-member countries (left-hand side) must equal the marginal loss of influence over monetary policy for member countries (right-hand side),
The marginal benefit of adding an additional member is the reduction of the number of exchange rates for all consumers. When a country decides to join a monetary union, the country reduces the number of exchange rates not only for its consumers, but also for all other consumers. When spillover benefits are considered, the equilibrium membership size increases (Figure 3).”
III.
CONCLUSION
As countries begin forming monetary unions, they will face the question, what is the optimal monetary union size? The optimal size of a monetary union depends upon the similarities and differences among the potential members and the costs of not forming a monetary union. The cost of influencing monetary policy for a member country may be a function of
CYNTHIA
64
ROYAL TORI
Size Figure 3.
The Community
Decides the Union Size
a country’s relative size of government expenditure to RGDP, a country’s relative level of debt to RGDP, the difference in monetary policy between the countries, and the differences of collection costs. The benefits of joining is a function of the number of exchange rates and the amount of trade with other countries. Allowing countries to independently decide to join the monetary union leads to a suboptimal membership size. This is because countries do not consider the spillover benefits of fewer exchange rates for consumers in other countries. When the spillover benefits are considered, the optimal membership size increases.
ACKNOWLEDGMENT I would like to thank the anonymous
referee for the helpful comments.
NOTES 1. The members of the European Union include Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain and the United Kingdom. Austria, Finland and Sweden are expected to join on January 1, 1996. Other countries seeking membership include Poland, the Czech Republic, Slovakia, Romania, Bulgaria, Hungary, the three Baltic republics and Slovenia. Members of the European Union are potential members of the monetary union. 2. The utility function is twice-continuously differentiable, with positive and diminishing marginal utility.
Optimal Size of a Monetary Union?
65
3. For example, if there are five countries (N = 5) and two countries form a monetary union (N* = 2), then there are three non-monetary union member countries (X = 3). The four central banks and currencies, A B C and D, require the consumer to know six exchange rates (CD), (BC BD), and (AB AC AD). 4. I assume all countries trade with all other countries. The amount of trade between countries may vary. 5. I assume the real interest rates are the same for all countries. The nominal interest rates may be different among countries, if the expected inflation rates are different. 6. As countries join the monetary union, the number of exchange rates decreases at an decreasing rate. For example, if there are six countries that are potential monetary union members (N = 6), and one country joins the union (N* = l), then the number of exchange rates is fifteen (E = 15). If N* = 2, E = 10. If N* = 3, E = 6. If N* = 4, E = 3. If N = 5, E = 1. The benefit of fewer exchange rates increases at a decreasing rate. 7. The Maastricht Accord specifies criteria regarding a country’s deficit and debt as a percent of GDP. See note 9 for further details. 8. The differences may include consumer utility functions, fiscal policy, collection costs, central bank independence, level of government expenditure as a percent of RGDP, a country’s deficit as a percent of RGDP and debt as a percent of RGDP. 9. The Maastricht Accord specifies four criteria for countries to meet before they may join the European monetary union. In short, the criteria are (1) a country’s inflation rate may not exceed the lowest three European Community countries’ inflation rates by more than 1.5 percentage points, (2) a country’s interest rate on its long-term government bond must not exceed by more than 2 percentage points the interest rate on long-term govemment bonds of the countries with the three lowest inflation rates, (3) a country’s total government deficit must not exceed three percent of its gross domestic product, and (4) a country’s outstanding debt may not exceed 60 percent of its gross domestic product [Fratianni, Hagen and Waller, (I 992) p.8-91. 10. The actual increase in membership size may be less than NT because of the potential redistribution of trade between member and non-member countries. Joining a monetary union eliminates the cost of knowing exchange rates for member countries’ goods. This lowers the relative price of member goods and may encourage substitution away from nonmember goods to member goods. The impact substitution has on non-member countries depends upon how sensitive consumers are to a change in the relative price of goods. An interesting extension of this paper would be to examine the effect a monetary union has on trade and how demand elasticity may effect monetary union size.
REFERENCES Aizenman, J. (1983). Government size, optimal inflation tax and tax collection costs. Eastern Economic Journal, 9(2), 103-105. . (1992). Competitive externalities and the optimal seigniorage. Journal ofMoney Credit and Banking, 24(l), 6 l-7 1 Alesina, A., & Summers, L. (1993). Central bank independence and macroeconomic performance: Some comparative evidence. Journal of Money, Credit and Banking, 25(2), 151-160.
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