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FW: Monetary and Fiscal Strategies in the World Economy_7

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FW: Monetary and Fiscal Strategies in the World Economy_7

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  1. 218 Monetary and Fiscal Cooperation between Europe and America unemployment functions, and the structural deficit functions. Taking account of equations (1) to (6), the loss function under policy cooperation can be written as follows: L = (B1 + M1 − 0.5M 2 + G1 + 0.5G 2 )2 (8) + (B2 + M 2 − 0.5M1 + G 2 + 0.5G1 ) 2 + (A1 − M1 + 0.5M 2 − G1 − 0.5G 2 ) 2 + (A 2 − M 2 + 0.5M1 − G 2 − 0.5G1 ) 2 + (G1 − T1 ) 2 + (G 2 − T2 ) 2 Then the first-order conditions for a minimum loss are: 5M1 = 2A1 − A 2 − 2B1 + B2 − 3G1 + 4M 2 (9) 5M 2 = 2A 2 − A1 − 2B2 + B1 − 3G 2 + 4M1 (10) 7G1 = 2A1 + A 2 − 2B1 − B2 + 2T1 − 3M1 − 4G 2 (11) 7G 2 = 2A 2 + A1 − 2B2 − B1 + 2T2 − 3M 2 − 4G1 (12) Equation (9) shows the first-order condition with respect to European money supply. Equation (10) shows the first-order condition with respect to American money supply. Equation (11) shows the first-order condition with respect to European government purchases. And equation (12) shows the first-order condition with respect to American government purchases. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. We assume T = T1 = T2 . The solution to this problem is as follows: 3M1 = 2A1 + A 2 − 2B1 − B2 − 9T (13) 3M 2 = 2A 2 + A1 − 2B2 − B1 − 9T (14) G1 = T (15) G2 = T (16)
  2. 1. The Model 219 Equations (13) to (16) show the cooperative equilibrium of European money supply, American money supply, European government purchases, and American government purchases. As a result there is a unique cooperative equilibrium. An increase in A1 causes an increase in European money supply, an increase in American money supply, no change in European government purchases, and no change in American government purchases. A unit increase in A1 causes an increase in European money supply of 0.67 units and an increase in American money supply of 0.33 units. As a result, monetary and fiscal cooperation can reduce the loss caused by inflation, unemployment, and the structural deficit. Monetary and fiscal cooperation is different from monetary and fiscal interaction. This applies to cases A, B and C of monetary and fiscal interaction, see Part Seven. On the other hand, monetary and fiscal cooperation is equivalent to pure monetary cooperation of type B. And what is more, monetary and fiscal cooperation is equivalent to pure monetary interaction of type B, see Part Three.
  3. 220 Monetary and Fiscal Cooperation between Europe and America 2. Some Numerical Examples It proves useful to study eight distinct cases: - a demand shock in Europe - a supply shock in Europe - a mixed shock in Europe - another mixed shock in Europe - a common demand shock - a common supply shock - a common mixed shock - another common mixed shock. 1) A demand shock in Europe. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to a decline in the demand for European goods. In terms of the model there is an increase in A1 of 3 units and a decline in B1 of equally 3 units. Step two refers to the outside lag. Unemployment in Europe goes from zero to 3 percent. Unemployment in America stays at zero percent. Inflation in Europe goes from zero to – 3 percent. Inflation in America stays at zero percent. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. Step three refers to the policy response. What is needed, according to the model, is an increase in European money supply of 4 units, an increase in American money supply of 2 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Unemployment in Europe goes from 3 to zero percent. Unemployment in America stays at zero percent. Inflation in Europe goes from – 3 to zero percent. Inflation in America stays at zero percent. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. For a synopsis see Table 7.19. As a result, given a demand shock in Europe, monetary and fiscal cooperation produces zero inflation, zero unemployment, and a zero structural deficit in each of the regions. The loss function under policy cooperation is:
  4. 2. Some Numerical Examples 221 2 2 2 2 2 2 L = π1 + π2 + u1 + u 2 + s1 + s 2 (1) The initial loss is zero. The demand shock in Europe causes a loss of 18 units. Then policy cooperation brings the loss down to zero again. Table 7.19 Monetary and Fiscal Cooperation between Europe and America A Demand Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 3 Shock in A1 −3 Shock in B1 Unemployment 3 Unemployment 0 −3 Inflation Inflation 0 Change in Money Supply 4 Change in Money Supply 2 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 2) A supply shock in Europe. In each of the regions let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the supply shock in Europe. In terms of the model there is an increase in B1 of 3 units and an increase in A1 of equally 3 units. Step two refers to the outside lag. Inflation in Europe goes from zero to 3 percent. Inflation in America stays at zero percent. Unemployment in Europe goes from zero to 3 percent. And unemployment in America stays at zero percent.
  5. 222 Monetary and Fiscal Cooperation between Europe and America Step three refers to the policy response. What is needed, according to the model, is no change in European money supply, no change in American money supply, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Inflation in Europe stays at 3 percent. Inflation in America stays at zero percent. Unemployment in Europe stays at 3 percent. Unemployment in America stays at zero percent. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. For an overview see Table 7.20. As a result, given a supply shock in Europe, monetary and fiscal cooperation is ineffective. The initial loss is zero. The supply shock in Europe causes a loss of 18 units. Then policy cooperation keeps the loss at 18 units. Table 7.20 Monetary and Fiscal Cooperation between Europe and America A Supply Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 3 Shock in A1 3 Shock in B1 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Change in Money Supply 0 Change in Money Supply 0 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Structural Deficit 0 Structural Deficit 0
  6. 2. Some Numerical Examples 223 3) A mixed shock in Europe. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the mixed shock in Europe. In terms of the model there is an increase in B1 of 6 units. Step two refers to the outside lag. Inflation in Europe goes from zero to 6 percent. Inflation in America stays at zero percent. Unemployment in Europe stays at zero percent, as does unemployment in America. Step three refers to the policy response. What is needed, according to the model, is a reduction in European money supply of 4 units, a reduction in American money supply of 2 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Inflation in Europe goes from 6 to 3 percent. Inflation in America stays at zero percent. Unemployment in Europe goes from zero to 3 percent. Unemployment in America stays at zero percent. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. Table 7.21 presents a synopsis. First consider the effects on Europe. As a result, given a mixed shock in Europe, monetary and fiscal cooperation lowers inflation in Europe. On the other hand, it raises unemployment there. And what is more, it produces a zero structural deficit. Second consider the effects on America. As a result, monetary and fiscal cooperation produces zero inflation, zero unemployment, and a zero structural deficit in America. The initial loss is zero. The mixed shock in Europe causes a loss of 36 units. Then policy cooperation brings the loss down to 18 units.
  7. 224 Monetary and Fiscal Cooperation between Europe and America Table 7.21 Monetary and Fiscal Cooperation between Europe and America A Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 0 Shock in A1 6 Shock in B1 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 −4 −2 Change in Money Supply Change in Money Supply Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Structural Deficit 0 Structural Deficit 0 4) Another mixed shock in Europe. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the mixed shock in Europe. In terms of the model there is an increase in A1 of 6 units. Step two refers to the outside lag. Unemployment in Europe goes from zero to 6 percent. Unemployment in America stays at zero percent. Inflation in Europe stays at zero percent, as does inflation in America. Step three refers to the policy response. What is needed, according to the model, is an increase in European money supply of 4 units, an increase in American money supply of 2 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Unemployment in Europe goes from 6 to 3 percent.
  8. 2. Some Numerical Examples 225 Unemployment in America stays at zero percent. Inflation in Europe goes from zero to 3 percent. Inflation in America stays at zero percent. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. Table 7.22 gives an overview. First consider the effects on Europe. As a result, given another mixed shock in Europe, monetary and fiscal cooperation lowers unemployment in Europe. On the other hand, it raises inflation there. And what is more, it produces a zero structural deficit. Second consider the effects on America. As a result, monetary and fiscal cooperation produces zero inflation, zero unemployment, and a zero structural deficit in America. The initial loss is zero. The mixed shock in Europe causes a loss of 36 units. Then policy cooperation brings the loss down to 18 units. Table 7.22 Monetary and Fiscal Cooperation between Europe and America Another Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 6 Shock in A1 0 Shock in B1 Unemployment 6 Unemployment 0 Inflation 0 Inflation 0 Change in Money Supply 4 Change in Money Supply 2 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Structural Deficit 0 Structural Deficit 0
  9. 226 Monetary and Fiscal Cooperation between Europe and America 5) A common demand shock. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to a decline in the demand for European and American goods. In terms of the model there is an increase in A1 of 3 units, a decline in B1 of 3 units, an increase in A 2 of 3 units, and a decline in B 2 of 3 units. Step two refers to the outside lag. Unemployment in Europe goes from zero to 3 percent, as does unemployment in America. Inflation in Europe goes from zero to – 3 percent, as does inflation in America. Step three refers to the policy response. What is needed, according to the model, is an increase in European money supply of 6 units, an increase in American money supply of 6 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Unemployment in Europe goes from 3 to zero percent, as does unemployment in America. Inflation in Europe goes from – 3 to zero percent, as does inflation in America. And the structural deficit in Europe stays at zero percent, as does the structural deficit in America. For a synopsis see Table 7.23. As a result, given a common demand shock, monetary and fiscal cooperation achieves zero inflation, zero unemployment, and a zero structural deficit in each of the regions. The initial loss is zero. The common demand shock causes a loss of 36 units. Then policy cooperation brings the loss down to zero again.
  10. 2. Some Numerical Examples 227 Table 7.23 Monetary and Fiscal Cooperation between Europe and America A Common Demand Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 3 3 Shock in A1 Shock in A2 −3 −3 Shock in B1 Shock in B2 Unemployment 3 Unemployment 3 −3 −3 Inflation Inflation Change in Money Supply 6 Change in Money Supply 6 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 6) A common supply shock. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the common supply shock. In terms of the model there is an increase in B1 of 3 units, as there is in A1 . And there is an increase in B 2 of 3 units, as there is in A 2 . Step two refers to the outside lag. Inflation in Europe goes from zero to 3 percent, as does inflation in America. Unemployment in Europe goes from zero to 3 percent, as does unemployment in America. Step three refers to the policy response. What is needed, according to the model, is no change in European money supply, no change in American money supply, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Inflation in Europe stays at 3 percent, as does inflation in America. Unemployment in
  11. 228 Monetary and Fiscal Cooperation between Europe and America Europe stays at 3 percent, as does unemployment in America. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. For an overview see Table 7.24. As a result, given a common supply shock, monetary and fiscal cooperation is ineffective. The initial loss is zero. The common supply shock causes a loss of 36 units. Then policy cooperation keeps the loss at 36 units. Table 7.24 Monetary and Fiscal Cooperation between Europe and America A Common Supply Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 3 3 Shock in A1 Shock in A2 3 3 Shock in B1 Shock in B2 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Change in Money Supply 0 Change in Money Supply 0 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Structural Deficit 0 Structural Deficit 0 7) A common mixed shock. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the common mixed shock. In terms of the model there is an increase in B1 of 6 units and an increase in B2 of equally 6 units. Step two
  12. 2. Some Numerical Examples 229 refers to the outside lag. Inflation in Europe goes from zero to 6 percent, as does inflation in America. Unemployment in Europe stays at zero percent, as does unemployment in America. Step three refers to the policy response. What is needed, according to the model, is a reduction in European money supply of 6 units, a reduction in American money supply of 6 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Inflation in Europe goes from 6 to 3 percent, as does inflation in America. Unemployment in Europe goes from zero to 3 percent, as does unemployment in America. The structural deficit in Europe stays at zero percent, as does the structural deficit in America. Table 7.25 presents a synopsis. Table 7.25 Monetary and Fiscal Cooperation between Europe and America A Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 0 0 Shock in A1 Shock in A2 6 6 Shock in B1 Shock in B2 Unemployment 0 Unemployment 0 Inflation 6 Inflation 6 −6 −6 Change in Money Supply Change in Money Supply Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Structural Deficit 0 Structural Deficit 0
  13. 230 Monetary and Fiscal Cooperation between Europe and America As a result, given a common mixed shock, monetary and fiscal cooperation lowers inflation. On the other hand, it raises unemployment. And what is more, it produces zero structural deficits. The initial loss is zero. The common mixed shock causes a loss of 72 units. Then policy cooperation brings the loss down to 36 units. 8) Another common mixed shock. In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well. Step one refers to the common mixed shock. In terms of the model there is an increase in A1 of 6 units and an increase in A 2 of equally 6 units. Step two refers to the outside lag. Unemployment in Europe goes from zero to 6 percent, as does unemployment in America. Inflation in Europe stays at zero percent, as does inflation in America. Step three refers to the policy response. What is needed, according to the model, is an increase in European money supply of 6 units, an increase in American money supply of 6 units, no change in European government purchases, and no change in American government purchases. Step four refers to the outside lag. Unemployment in Europe goes from 6 to 3 percent, as does unemployment in America. Inflation in Europe goes from zero to 3 percent, as does inflation in America. And the structural deficit in Europe stays at zero percent, as does the structural deficit in America. Table 7.26 gives an overview. As a result, given another common mixed shock, monetary and fiscal cooperation lowers unemployment. On the other hand, it raises inflation. And what is more, it produces zero structural deficits. The initial loss is zero. The common mixed shock causes a loss of 72 units. Then policy cooperation brings the loss down to 36 units.
  14. 2. Some Numerical Examples 231 Table 7.26 Monetary and Fiscal Cooperation between Europe and America Another Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 6 6 Shock in A1 Shock in A2 0 0 Shock in B1 Shock in B2 Unemployment 6 Unemployment 6 Inflation 0 Inflation 0 Change in Money Supply 6 Change in Money Supply 6 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Structural Deficit 0 Structural Deficit 0 9) Summary. Given a demand shock in Europe, policy cooperation achieves zero inflation, zero unemployment, and a zero structural deficit in each of the regions. Given a supply shock in Europe, policy cooperation is ineffective. Given a mixed shock in Europe, policy cooperation lowers inflation in Europe. On the other hand, it raises unemployment there. And what is more, it produces a zero structural deficit. Given another type of mixed shock in Europe, policy cooperation lowers unemployment in Europe. On the other hand, it raises inflation there. And what is more, it produces a zero structural deficit. 10) Comparing policy cooperation with other regimes. First, monetary and fiscal cooperation is equivalent to pure monetary cooperation of type B, see Part Three. Second, monetary and fiscal cooperation is equivalent to pure monetary
  15. 232 Monetary and Fiscal Cooperation between Europe and America interaction of type B, see Part Three. Third, monetary and fiscal cooperation is superior to monetary and fiscal interaction of type B, see Part Seven.
  16. 233 Chapter 5 Cooperation within Regions, Interaction between Regions 1) Introduction. The framework of analysis is as follows. There is policy cooperation between the European central bank and the European government. Similarly, there is policy cooperation between the American central bank and the American government. On the other hand, there is policy interaction between Europe and America. The targets of policy cooperation within Europe are zero inflation, zero unemployment, and a zero structural deficit in Europe. The targets of policy cooperation within America are zero inflation, zero unemployment, and a zero structural deficit in America. The model of unemployment, inflation, and the structural deficit can be represented by a system of six equations: u1 = A1 − M1 + 0.5M 2 − G1 − 0.5G 2 (1) u 2 = A 2 − M 2 + 0.5M1 − G 2 − 0.5G1 (2) π1 = B1 + M1 − 0.5M 2 + G1 + 0.5G 2 (3) π2 = B2 + M 2 − 0.5M1 + G 2 + 0.5G1 (4) s1 = G1 − T1 (5) s 2 = G 2 − T2 (6) 2) Policy cooperation within Europe. The policy makers are the European central bank and the European government. The targets of policy cooperation within Europe are zero inflation, zero unemployment, and a zero structural deficit in Europe. The instruments of policy cooperation within Europe are European money supply and European government purchases. There are three targets but only two instruments, so what is needed is a loss function. We assume that the European central bank and the European government agree on a common loss function: M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 233 DOI 10.1007/978-3-642-10476-3_25, © Springer-Verlag Berlin Heidelberg 2010
  17. 234 Cooperation within Regions, Interaction between Regions 2 2 2 L1 = π1 + u1 + s1 (7) L1 is the loss caused by inflation, unemployment, and the structural deficit in Europe. We assume equal weights in the loss function. The specific target of policy cooperation within Europe is to minimize the loss, given the inflation function, the unemployment function, and the structural deficit function. Taking account of equations (1), (3) and (5), the loss function under policy cooperation within Europe can be written as follows: L1 = (B1 + M 1 − 0.5M 2 + G 1 + 0.5G 2 ) 2 + (A 1 − M 1 + 0.5M 2 − G 1 − 0.5G 2 ) 2 + (G 1 − T1 ) 2 (8) Then the first-order conditions for a minimum loss are: 2M1 = A1 − B1 − 2G1 − G 2 + M 2 (9) 3G1 = A1 − B1 + T1 − 2M1 + M 2 − G 2 (10) Equation (9) shows the first-order condition with respect to European money supply. And equation (10) shows the first-order condition with respect to European government purchases. The cooperative equilibrium in Europe is determined by the first-order conditions for a minimum loss. The solution to this problem is as follows: 2M1 = A1 − B1 − 2T1 − G 2 + M 2 (11) G1 = T1 (12) Equations (11) and (12) show the cooperative equilibrium of European money supply and European government purchases. Equation (11) is the reaction function of the European central bank. And equation (12) is the reaction function of the European government. 3) Policy cooperation within America. The policy makers are the American central bank and the American government. The targets of policy cooperation
  18. Cooperation within Regions, Interaction between Regions 235 within America are zero inflation, zero unemployment, and a zero structural deficit in America. The instruments of policy cooperation within America are American money supply and American government purchases. There are three targets but only two instruments, so what is needed is a loss function. We assume that the American central bank and the American government agree on a common loss function: L 2 = π2 + u 2 + s 2 2 2 (13) 2 L 2 is the loss caused by inflation, unemployment, and the structural deficit in America. We assume equal weights in the loss function. The specific target of policy cooperation within America is to minimize the loss, given the inflation function, the unemployment function, and the structural deficit function. Taking account of equations (2), (4) and (6), the loss function under policy cooperation within America can be written as follows: L 2 = (B 2 + M 2 − 0.5M 1 + G 2 + 0.5G 1 ) 2 + (A 2 − M 2 + 0.5M 1 − G 2 − 0.5G 1 ) 2 + (G 2 − T2 ) 2 (14) Then the first-order conditions for a minimum loss are: 2M 2 = A 2 − B2 − 2G 2 − G1 + M1 (15) 3G 2 = A 2 − B2 + T2 − 2M 2 + M 1 − G1 (16) Equation (15) shows the first-order condition with respect to American money supply. And equation (16) shows the first-order condition with respect to American government purchases. The cooperative equilibrium in America is determined by the first-order conditions for a minimum loss. The solution to this problem is as follows: 2M 2 = A 2 − B2 − 2T2 − G1 + M1 (17) G 2 = T2 (18)
  19. 236 Cooperation within Regions, Interaction between Regions Equations (17) and (18) show the cooperative equilibrium of American money supply and American government purchases. Equation (17) is the reaction function of the American central bank. And equation (18) is the reaction function of the American government. 4) Policy interaction between Europe and America. The Nash equilibrium is determined by the reaction functions of the European central bank, the American central bank, the European government, and the American government. We assume T = T1 = T2 . The solution to this problem is as follows: 3M1 = 2A1 + A 2 − 2B1 − B2 − 9T (19) 3M 2 = 2A 2 + A1 − 2B2 − B1 − 9T (20) G1 = T (21) G2 = T (22) Equations (19) to (22) show the Nash equilibrium of European money supply, American money supply, European government purchases, and American government purchases. As a result there is a unique Nash equilibrium. An increase in A1 causes an increase in European money supply, an increase in American money supply, no change in European government purchases, and no change in American government purchases. 5) Comparing the system of cooperation and interaction with other types of systems. First, the system of cooperation and interaction is equivalent to the system of monetary and fiscal cooperation, see Part Seven. Second, the system of cooperation and interaction is equivalent to the system of monetary cooperation B, see Part Three. Third, the system of cooperation and interaction is equivalent to the system of monetary interaction B, see Part Three.
  20. 238 Synopsis Table 8.1 Monetary Policies in Europe and America Monetary Interaction Unique between Europe and America Nash Equilibrium Monetary Cooperation Unique between Europe and America Solution Cooperative Solution Is Identical to Nash Equilibrium Table 8.2 Fiscal Policies in Europe and America Presence of a Deficit Target Fiscal Interaction Unique between Europe and America Nash Equilibrium Fiscal Cooperation Unique between Europe and America Solution Generally, Cooperative Solution Is Different from Nash Equilibrium 238
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