88 2) A common supply shock. In each of the regions, let initial unemployment be zero, and let initial inflation 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. According to the Nash equilibrium there is a reduction in European money supply of 4 units and a reduction in American money supply of 2 units. Step four refers to the outside lag. Inflation in Europe goes from 3 to zero percent. Inflation in America stays at 3 percent. Unemployment in Europe goes from 3 to 6 percent. And unemployment in America stays at 3 percent. Table 3.16 gives an overview. Table 3.16 Monetary Interaction between Europe and America A Common Supply Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 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 − 4 Change in Money Supply − 2 Unemployment 6 Unemployment 3 Inflation 0 Inflation 3 Monetary Interaction between Europe and America: Case C 89 First consider the effects on Europe. As a result, given a common supply shock, monetary interaction produces zero inflation in Europe. However, as a side effect, it raises unemployment there. Second consider the effects on America. As a result, monetary interaction has no effect on inflation and unemployment in America. The initial loss of each central bank is zero. The common supply shock causes a loss to the European central bank of 9 units and a loss to the American central bank of 18 units. Then monetary interaction reduces the loss of the European central bank from 9 to zero units. On the other hand, it keeps the loss of the American central bank at 18 units. 3) A common mixed shock. In each of the regions, let initial unemployment be zero, and let initial inflation be zero as well. Step one refers to the common mixed shock. In terms of the model there is an increase in 1 B of 6 units and an increase in 2 B of equally 6 units. Step two 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. According to the Nash equilibrium there is a reduction in European money supply of 10 units and a reduction in American money supply of 8 units. Step four refers to the outside lag. Inflation in Europe goes from 6 to zero percent. Inflation in America goes from 6 to 3 percent. Unemployment in Europe goes from zero to 6 percent. And unemployment in America goes from zero to 3 percent. For a synopsis see Table 3.17. First consider the effects on Europe. As a result, given a common mixed shock, monetary interaction produces zero inflation in Europe. However, as a side effect, it produces unemployment there. Second consider the effects on America. As a result, monetary interaction lowers inflation in America. On the other hand, it raises unemployment there. The initial loss of each central bank is zero. The common mixed shock causes a loss to the European central bank of 36 units and a loss to the American central bank of equally 36 units. Then monetary interaction reduces the loss of the European central bank from 36 to zero units. Similarly, it reduces the loss of the American central bank from 36 to 18 units. 2. Some Numerical Examples 90 Table 3.17 Monetary Interaction between Europe and America A Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Shock in A 1 0 Shock in A 2 0 Shock in B 1 6 Shock in B 2 6 Unemployment 0 Unemployment 0 Inflation 6 Inflation 6 Change in Money Supply − 10 Change in Money Supply − 8 Unemployment 6 Unemployment 3 Inflation 0 Inflation 3 4) Another common mixed shock. In each of the regions, let initial unemployment be zero, and let initial inflation be zero as well. Step one refers to the common mixed shock. In terms of the model there is an increase in 1 A of 6 units and an increase in 2 A 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. According to the Nash equilibrium there is an increase in European money supply of 2 units and an increase in American money supply of 4 units. Step four refers to the outside lag. Unemployment in Europe stays at 6 percent. Unemployment in America goes from 6 to 3 percent. Inflation in Europe stays at zero percent. And inflation in America goes from zero to 3 percent. For an overview see Table 3.18. First consider the effects on Europe. As a result, given another common mixed shock, monetary interaction produces zero inflation in Europe. However, as a side effect, it produces unemployment there. Second consider the effects on Monetary Interaction between Europe and America: Case C 91 America. As a result, monetary interaction lowers unemployment in America. On the other hand, it raises inflation there. The initial loss of each central bank is zero. The common mixed shock causes a loss to the European central bank of zero units and a loss to the American central bank of 36 units. Then monetary interaction keeps the loss of the European central bank at zero units. And what is more, it reduces the loss of the American central bank from 36 to 18 units. Table 3.18 Monetary Interaction between Europe and America Another Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Shock in A 1 6 Shock in A 2 6 Shock in B 1 0 Shock in B 2 0 Unemployment 6 Unemployment 6 Inflation 0 Inflation 0 Change in Money Supply 2 Change in Money Supply 4 Unemployment 6 Unemployment 3 Inflation 0 Inflation 3 5) Summary. Given a common demand shock, monetary interaction produces zero inflation and zero unemployment in each of the regions. Given a common supply shock, monetary interaction produces zero inflation in Europe. And what is more, monetary interaction has no effect on inflation and unemployment in America. Given a common mixed shock, monetary interaction produces zero inflation in Europe. And what is more, monetary interaction lowers inflation in America. On the other hand, it raises unemployment there. 2. Some Numerical Examples 92 Chapter 4 Monetary Cooperation between Europe and America: Case A The model of unemployment and inflation can be characterized by a system of four equations: 111 2 uAM0.5M=− + (1) 222 1 uAM0.5M=− + (2) 11 1 2 B M 0.5Mπ= + − (3) 22 2 1 BM0.5Mπ= + − (4) As to policy targets there are three distinct cases. In case A the targets of monetary cooperation are zero inflation in Europe and America. In case B the targets of monetary cooperation are zero inflation and zero unemployment in each of the regions. In case C the targets of monetary cooperation are zero inflation in Europe, zero inflation in America, and zero unemployment in America. This chapter deals with case A, and the next chapters deal with cases B and C. The policy makers are the European central bank and the American central bank. The targets of monetary cooperation are zero inflation in Europe and America. The instruments of monetary cooperation are European money supply and American money supply. There are two targets and two instruments. We assume that the European central bank and the American central bank agree on a common loss function: 22 12 L =π +π (5) L is the loss caused by inflation in Europe and America. We assume equal weights in the loss function. The specific target of monetary cooperation is to minimize the loss, given the inflation functions in Europe and America. Taking M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 92 DOI 10.1007/978-3-642-10476-3_12, © Springer-Verlag Berlin Heidelberg 2010 93 account of equations (3) and (4), the loss function under monetary cooperation can be written as follows: 22 11 2 2 2 1 L (B M 0.5M ) (B M 0.5M )=+− ++− (6) Then the first-order conditions for a minimum loss are: 121 2 5M 2B 4B 4M=−+ (7) 212 1 5M 2B 4B 4M=−+ (8) Equation (7) shows the first-order condition with respect to European money supply. And equation (8) shows the first-order condition with respect to American money supply. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. The solution to this problem is as follows: 112 3M 4B 2B=− − (9) 221 3M 4B 2B=− − (10) Equations (9) and (10) show the cooperative equilibrium of European money supply and American money supply. As a result there is a unique cooperative equilibrium. An increase in 1 B causes a reduction in both European and American money supply. Obviously, the cooperative equilibrium is identical to the corresponding Nash equilibrium. That is to say, monetary cooperation case A is equivalent to monetary interaction case A. For some numerical examples see Chapter 1. Monetary Cooperation between Europe and America: Case A 94 Chapter 5 Monetary Cooperation between Europe and America: Case B The model of unemployment and inflation can be represented by a system of four equations: 111 2 uAM0.5M=− + (1) 222 1 uAM0.5M=− + (2) 11 1 2 B M 0.5Mπ= + − (3) 22 2 1 BM0.5Mπ= + − (4) The policy makers are the European central bank and the American central bank. The targets of monetary cooperation are zero inflation and zero unemployment in each of the regions. The instruments of monetary cooperation are European money supply and American money supply. There are four targets but only two instruments, so what is needed is a loss function. We assume that the European central bank and the American central bank agree on a common loss function: 2222 1212 Luu=π +π + + (5) L is the loss caused by inflation and unemployment in each of the regions. We assume equal weights in the loss function. The specific target of monetary cooperation is to minimize the loss, given the inflation functions and the unemployment functions. Taking account of equations (1), (2), (3) and (4), the loss function under monetary cooperation can be written as follows: 22 11 2 2 2 1 L (B M 0.5M ) (B M 0.5M )=+− ++− 22 11 2 22 1 (A M 0.5M ) (A M 0.5M )+−+ + −+ (6) M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 94 DOI 10.1007/978-3-642-10476-3_13, © Springer-Verlag Berlin Heidelberg 2010 95 Then the first-order conditions for a minimum loss are: 11212 2 5M 2A A 2B B 4M=−−++ (7) 221211 5M 2A A 2B B 4M=−−++ (8) Equation (7) shows the first-order condition with respect to European money supply. And equation (8) shows the first-order condition with respect to American money supply. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. The solution to this problem is as follows: 11212 3M 2A A 2B B=+−− (9) 22121 3M 2A A 2B B=+−− (10) Equations (9) and (10) show the cooperative equilibrium of European money supply and American money supply. As a result there is a unique cooperative equilibrium. An increase in 1 A causes an increase in both European and American money supply. Obviously, the cooperative equilibrium is identical to the corresponding Nash equilibrium. That is to say, monetary cooperation case B is equivalent to monetary interaction case B. For some numerical examples see Chapter 2. Monetary Cooperation between Europe and America: Case B 96 Chapter 6 Monetary Cooperation between Europe and America: Case C The model of unemployment and inflation can be characterized by a system of four equations: 111 2 uAM0.5M=− + (1) 222 1 uAM0.5M=− + (2) 11 1 2 B M 0.5Mπ= + − (3) 22 2 1 BM0.5Mπ= + − (4) The policy makers are the European central bank and the American central bank. The targets of monetary cooperation are zero inflation in Europe, zero inflation in America, and zero unemployment in America. The instruments of monetary cooperation are European money supply and American money supply. 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 American central bank agree on a common loss function: 222 122 L0.50.5u=π + π + (5) L is the loss caused by inflation in Europe, inflation in America, and unemployment in America. We assume equal weights in the loss function. The specific target of monetary cooperation is to minimize the loss, given the inflation functions and the unemployment function. Taking account of equations (2), (3) and (4), the loss function under monetary cooperation can be written as follows: M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 96 DOI 10.1007/978-3-642-10476-3_14, © Springer-Verlag Berlin Heidelberg 2010 97 2 11 2 L(B M 0.5M)=+− 2 22 1 0.5(B M 0.5M )++− 2 22 1 0.5(A M 0.5M )+−+ (6) Then the first-order conditions for a minimum loss are: 12122 5M A 4B B 4M=− − + + (7) 22121 5M 2A 2B 2B 4M=+−+ (8) Equation (7) shows the first-order condition with respect to European money supply. And equation (8) shows the first-order condition with respect to American money supply. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. The solution to this problem is as follows: 12 12 3M A 4B B=− − (9) 2212 3M 2A 2B 2B=−− (10) Equations (9) and (10) show the cooperative equilibrium of European money supply and American money supply. As a result there is a unique cooperative equilibrium. Obviously, the cooperative equilibrium is identical to the corresponding Nash equilibrium. That is to say, monetary cooperation case C is equivalent to monetary interaction case C. For some numerical examples see Chapter 3. Monetary Cooperation between Europe and America: Case C [...]... unemployment in America, B1 is some other factors bearing on the rate of inflation in Europe, and B2 is some other factors bearing on the rate of inflation in America The endogenous variables are the rate of unemployment in Europe, the rate of unemployment in America, the rate of inflation in Europe, the rate of inflation in America, the structural deficit ratio in Europe, and the structural deficit ratio in. .. 0 5) A common demand shock In each of the regions, let initial unemployment be zero, and let initial inflation 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, 110 Fiscal Interaction between Europe and America and a decline in B 2 of 3 units... is some other factors bearing on the rate of unemployment in Europe, A 2 is some other factors bearing on the rate of unemployment in America, B1 is some other factors bearing on the rate of inflation in Europe, and B2 is some other factors bearing on the rate of inflation M Carlberg, Monetary and Fiscal Strategies in the World Economy, DOI 10.1007/978-3-642-10476-3_15, © Springer-Verlag Berlin Heidelberg... denotes the rate of unemployment in Europe, u 2 is the rate of unemployment in America, π1 is the rate of inflation in Europe, π2 is the rate of inflation in America, s1 is the structural deficit ratio in Europe, s 2 is the M Carlberg, Monetary and Fiscal Strategies in the World Economy, DOI 10.1007/978-3-642-10476-3_17, © Springer-Verlag Berlin Heidelberg 2010 117 118 Fiscal Interaction between Europe and. .. 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 According to the Nash equilibrium there is an increase... Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 4) Another mixed shock in Europe In each of the regions, let initial unemployment be zero, and let initial inflation 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... Inflation 0 Inflation 0 As a result, given a demand shock in Europe, fiscal interaction produces zero unemployment and zero inflation in each of the regions The loss functions of the European government and the American government are respectively: 106 Fiscal Interaction between Europe and America 2 L1 = u1 (7) u2 2 (8) L2 = The initial loss of the European government is zero, as is the initial loss of the. .. government The demand shock in Europe causes a loss to the European government of 9 units and a loss to the American government of zero units Then fiscal interaction reduces the loss of the European government from 9 to zero units And what is more, fiscal interaction keeps the loss of the American government at zero units 2) A supply shock in Europe In each of the regions let initial unemployment be zero, and. .. Shock in A1 3 Shock in B1 3 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Change in Govt Purchases 4 Change in Govt Purchases − 2 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 3) A mixed shock in Europe In each of the regions, let initial unemployment be zero, and let initial inflation be zero as well Step one refers to the mixed shock in Europe In terms of the model there is an increase... Part Five Fiscal Policies in Europe and America Presence of a Deficit Target 117 Chapter 1 Fiscal Interaction between Europe and America 1 The 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 government purchases lowers European unemployment On the other hand, it raises . Carlberg, Monetary and Fiscal Strategies in the World Economy, 92 DOI 10.1007/978 -3- 642-10476 -3_ 12, © Springer-Verlag Berlin Heidelberg 2010 93 account of equations (3) and (4), the loss function. Carlberg, Monetary and Fiscal Strategies in the World Economy, 94 DOI 10.1007/978 -3- 642-10476 -3_ 13, © Springer-Verlag Berlin Heidelberg 2010 95 Then the first-order conditions for a minimum loss. Carlberg, Monetary and Fiscal Strategies in the World Economy, 101 DOI 10.1007/978 -3- 642-10476 -3_ 15, © Springer-Verlag Berlin Heidelberg 2010 102 in America. The endogenous variables are the rate