218 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: 2 11 21 2 2 22 12 1 2 11 21 2 2 22 12 1 22 11 2 2 L(B M 0.5M G 0.5G) (B M 0.5M G 0.5G ) (A M 0.5M G 0.5G ) (A M 0.5M G 0.5G ) (G T ) (G T ) =+− ++ ++− ++ +−+ −− +−+ −− +− + − (8) Then the first-order conditions for a minimum loss are: 112121 2 5M 2A A 2B B 3G 4M=−−+−+ (9) 2212121 5M 2A A 2B B 3G 4M=−−+−+ (10) 11212112 7G 2A A 2B B 2T 3M 4G=+−−+−− (11) 22121221 7G 2A A 2B B 2T 3M 4G=+−−+−− (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 12 TT T = = . The solution to this problem is as follows: 11212 3M 2A A 2B B 9T=+−−− (13) 22121 3M 2A A 2B B 9T=+−−− (14) 1 GT= (15) 2 GT= (16) Monetary and Fiscal Cooperation between Europe and America 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 1 A 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 1 A 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. 1. The Model 220 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 1 A of 3 units and a decline in 1 B 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: Monetary and Fiscal Cooperation between Europe and America 221 222222 121212 Luuss=π+π++++ (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 Shock in A 1 3 Shock in B 1 − 3 Unemployment 3 Unemployment 0 Inflation − 3 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 1 B of 3 units and an increase in 1 A 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. 2. Some Numerical Examples 222 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 Shock in A 1 3 Shock in B 1 3 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 Monetary and Fiscal Cooperation between Europe and America 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 1 B 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. 2. Some Numerical Examples 224 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 Shock in A 1 0 Shock in B 1 6 Unemployment 0 Unemployment 0 Inflation 6 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 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 1 A 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. Monetary and Fiscal Cooperation between Europe and America 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 Shock in A 1 6 Shock in B 1 0 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 2. Some Numerical Examples 226 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 1 A of 3 units, a decline in 1 B of 3 units, an increase in 2 A of 3 units, and a decline in 2 B 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. Monetary and Fiscal Cooperation between Europe and America 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 Shock in A 1 3 Shock in A 2 3 Shock in B 1 − 3 Shock in B 2 − 3 Unemployment 3 Unemployment 3 Inflation − 3 Inflation − 3 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 1 B of 3 units, as there is in 1 A . And there is an increase in 2 B of 3 units, as there is in 2 A . 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 2. Some Numerical Examples [...]... shock, monetary interaction produces zero inflation in Europe and America 2) A demand shock in Europe Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent Step one refers to the policy response According to the Nash equilibrium there is an increase in. .. Carlberg, Monetary and Fiscal Strategies in the World Economy, DOI 10.1007/978-3-642-10476-3_25, © Springer-Verlag Berlin Heidelberg 2010 233 234 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... 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. .. America 2) A demand shock in Europe Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent Step one refers to the policy response According to the Nash equilibrium there is an increase in European government purchases of 4 units and a reduction in American... model The world economy consists of two monetary regions, say Europe and America The monetary regions are the same size and have the same behavioural functions An increase in European money supply lowers European unemployment On the other hand, it raises European inflation Correspondingly, an increase in American money supply lowers American unemployment On the other hand, it raises American inflation An... percentage point On the other hand, it raises European inflation by 1 percentage point And what is more, a unit increase in European money supply raises American unemployment by 0.5 percentage points and lowers American inflation by 0.5 percentage points For instance, let European unemployment be 2 percent, and let European inflation be 2 percent as well Further, let American unemployment be 2 percent, and. .. 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... zero inflation and zero unemployment in each of the regions 3) A supply shock in Europe Let initial inflation in Europe be 3 percent, and let initial inflation in America be zero percent Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Step one refers to the policy response According to the Nash equilibrium there is a reduction in European money... yields the equilibrium levels of European money supply and American money supply As a rule, inflation in Europe and America is not zero And unemployment in Europe and America is not zero either 2) A demand shock in Europe We assume equal weights in each of the loss functions Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Let initial inflation in. .. Inflation 0 Change in Money Supply 4 Change in Money Supply 2 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 3) A supply shock in Europe Let initial inflation in Europe be 3 percent, and let initial inflation in America be zero percent Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Step one refers to the policy response According to the . M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 233 central bank and the European government. The targets of policy cooperation DOI 10.10 07/ 978 -3-642-10 476 -3_25, © Springer-Verlag. 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 the demand for European and American goods. In terms of the model there is an increase in 1 A of 3 units, a decline in 1 B of 3 units, an increase in 2 A of 3 units, and a decline in 2 B