Monetary policy strategies in the world economy carlberg_3 potx

57 central bank is zero inflation in America. In case B the targets of the European central bank are zero inflation and zero unemployment in Europe. And the targets of the American central bank are zero inflation and zero unemployment in America. In case C the European central bank has a single target, that is zero inflation in Europe. By contrast, the American central bank has two conflicting targets, that is zero inflation and zero unemployment in America. This chapter deals with case A, and the next chapters deal with cases B and C. The target of the European central bank is zero inflation in Europe. The instrument of the European central bank is European money supply. By equation (3), the reaction function of the European central bank is: 112 2M 2B M=− + (5) Suppose the American central bank lowers American money supply. Then, as a response, the European central bank lowers European money supply. The target of the American central bank is zero inflation in America. The instrument of the American central bank is American money supply. By equation (4), the reaction function of the American central bank is: 221 2M 2B M=− + (6) Suppose the European central bank lowers European money supply. Then, as a response, the American central bank lowers American money supply. The Nash equilibrium is determined by the reaction functions of the European central bank and the American central bank. The solution to this problem is as follows: 112 3M 4B 2B=− − (7) 221 3M 4B 2B=− − (8) Equations (7) and (8) show the Nash equilibrium of European money supply and American money supply. As a result there is a unique Nash equilibrium. According to equations (7) and (8), an increase in 1 B causes a decline in both 1. The Model 58 European money supply and American money supply. A unit increase in 1 B causes a decline in European money supply of 1.33 units and a decline in American money supply of 0.67 units. From equations (1), (7) and (8) follows the equilibrium rate of unemployment in Europe: 111 uAB=+ (9) From equations (2), (7) and (8) follows the equilibrium rate of unemployment in America: 222 uAB=+ (10) From equations (3), (7) and (8) follows the equilibrium rate of inflation in Europe: 1 0π= (11) And from equations (4), (7) and (8) follows the equilibrium rate of inflation in America: 2 0π= (12) As a result, given a shock, monetary interaction produces zero inflation in Europe and America. Monetary Interaction between Europe and America: Case A 59 2. Some Numerical Examples For easy reference, the basic model is summarized here: 111 2 uAM0.5M=− + (1) 222 1 uAM0.5M=− + (2) 11 1 2 B M 0.5Mπ= + − (3) 22 2 1 BM0.5Mπ= + − (4) And the Nash equilibrium can be described by two equations: 112 3M 4B 2B=− − (5) 221 3M 4B 2B=− − (6) It proves useful to study six 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. 1) A demand 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 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. And inflation in America stays at zero percent. Step three refers to the policy response. According to the Nash equilibrium there is an increase in European money supply of 4 units and an increase in 2. Some Numerical Examples 60 American money supply of 2 units. 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. And inflation in America stays at zero percent. Table 3.1 presents a synopsis. Table 3.1 Monetary Interaction between Europe and America A Demand Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 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 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 As a result, given a demand shock in Europe, monetary interaction produces zero inflation and zero unemployment in each of the regions. The loss functions of the European central bank and the American central bank are respectively: 2 11 L =π (7) 2 22 L =π (8) The initial loss of the European central bank is zero, as is the initial loss of the American central bank. The demand shock in Europe causes a loss to the European central bank of 9 units and a loss to the American central bank of zero Monetary Interaction between Europe and America: Case A 61 units. Then monetary interaction reduces the loss of the European central bank from 9 to zero units. And what is more, monetary interaction keeps the loss of the American central bank at zero units. 2) A supply 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 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. 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 zero percent. Unemployment in Europe goes from 3 to 6 percent. And unemployment in America stays at zero percent. Table 3.2 gives an overview. First consider the effects on Europe. As a result, given a supply shock in Europe, 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 produces zero inflation and zero unemployment in America. The initial loss of each central bank is zero. The supply shock in Europe causes a loss to the European central bank of 9 units and a loss to the American central bank of zero units. Then monetary interaction reduces the loss of the European central bank from 9 to zero units. And what is more, it keeps the loss of the American central bank at zero units. 2. Some Numerical Examples 62 Table 3.2 Monetary Interaction between Europe and America A Supply Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 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 Unemployment 6 Unemployment 0 Inflation 0 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 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. According to the Nash equilibrium there is a reduction in European money supply of 8 units and a reduction in American money supply of 4 units. Step four refers to the outside lag. Inflation in Europe goes from 6 to zero percent. Inflation in America stays at zero percent. Unemployment in Europe goes from zero to 6 percent. And unemployment in America stays at zero percent. For a synopsis see Table 3.3. First consider the effects on Europe. As a result, given a mixed shock in Europe, 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 A 63 America. As a result, monetary interaction produces zero inflation and zero unemployment in America. The initial loss of each central bank is zero. The mixed shock in Europe causes a loss to the European central bank of 36 units and a loss to the American central bank of zero units. Then monetary interaction reduces the loss of the European central bank from 36 to zero units. And what is more, it keeps the loss of the American central bank at zero units. Table 3.3 Monetary Interaction between Europe and America A Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Shock in A 1 0 Shock in B 1 6 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 Change in Money Supply − 8 Change in Money Supply − 4 Unemployment 6 Unemployment 0 Inflation 0 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 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. According to the Nash equilibrium there is no change in European money supply, nor is there in American money 2. Some Numerical Examples 64 supply. Step four refers to the outside lag. Unemployment in Europe stays at 6 percent. Unemployment in America stays at zero percent. Inflation in Europe stays at zero percent, as does inflation in America. For an overview see Table 3.4. First consider the effects on Europe. As a result, given another mixed shock in Europe, 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 produces zero inflation and zero unemployment in America. The mixed shock in Europe causes no loss to the European central bank or American central bank. Table 3.4 Monetary Interaction between Europe and America Another Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Shock in A 1 6 Shock in B 1 0 Unemployment 6 Unemployment 0 Inflation 0 Inflation 0 Change in Money Supply 0 Change in Money Supply 0 Unemployment 6 Unemployment 0 Inflation 0 Inflation 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 1 A of 3 units, a decline in 1 B of 3 units, an increase in 2 A of 3 units, Monetary Interaction between Europe and America: Case A 65 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. According to the Nash equilibrium there is an increase in European money supply and American money supply of 6 units each. 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. Table 3.5 presents a synopsis. Table 3.5 Monetary Interaction between Europe and America A Common Demand 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 6 Change in Money Supply 6 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 As a result, given a common demand shock, monetary interaction produces zero inflation and zero unemployment in each of the regions. The initial loss of each central bank is zero. The common demand shock causes a loss to the European central bank of 9 units and a loss to the American central bank of equally 9 units. Then monetary interaction reduces the loss of the European 2. Some Numerical Examples 66 central bank from 9 to zero units. Correspondingly, it reduces the loss of the American central bank from 9 to zero units. 6) 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 and American money supply of 6 units each. Step four refers to the outside lag. Inflation in Europe goes from 3 to zero percent, as does inflation in America. Unemployment in Europe goes from 3 to 6 percent, as does unemployment in America. Table 3.6 gives an overview. As a result, given a common supply shock, monetary interaction produces zero inflation in Europe and America. However, as a side effect, it raises unemployment there. 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 equally 9 units. Then monetary interaction reduces the loss of the European central bank from 9 to zero units. Correspondingly, it reduces the loss of the American central bank from 9 to zero units. 7) Summary. Given a demand shock in Europe, monetary interaction produces zero inflation and zero unemployment in each of the regions. Given a supply shock in Europe, monetary interaction produces zero inflation in Europe. However, as a side effect, it raises unemployment there. Given a mixed shock in Europe, monetary interaction produces zero inflation in Europe. However, as a side effect, it causes unemployment there. 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 America. However, as a side effect, it raises unemployment there. Monetary Interaction between Europe and America: Case A [...]... unemployment On the other hand, it raises inflation 10) Comparing monetary interaction case A and monetary interaction case B In case A the target of the European central bank is zero inflation in Europe And the target of the American central bank is zero inflation in America In case B the targets of the European central bank are zero inflation and zero unemployment in Europe And the targets of the American... Europe, monetary interaction produces zero inflation and zero unemployment in each of the regions Given a supply shock in Europe, monetary interaction is ineffective Given a mixed shock in Europe, monetary interaction lowers inflation in Europe On the other hand, it raises unemployment there Given another mixed shock in Europe, monetary 82 Monetary Interaction between Europe and America: Case B interaction... zero inflation and zero unemployment in America First consider a demand shock in Europe In case A monetary interaction produces zero inflation and zero unemployment in each of the regions In case B we have the same effects Second consider a supply shock in Europe In case A monetary interaction produces zero inflation in Europe In case B monetary interaction is ineffective Third consider a mixed shock in. .. unemployment in Europe On the other hand, it raises inflation there 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 is ineffective Given a common mixed shock, monetary interaction lowers inflation On the other hand, it raises unemployment Given another common mixed shock, monetary interaction... 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 According to the Nash equilibrium there is an increase in European... in A1 And there is an increase in B2 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 no change in European money supply, nor is there in. .. shock in Europe In case A monetary interaction produces zero inflation in Europe In case B monetary interaction lowers inflation in Europe On the other hand, it raises unemployment there 83 Chapter 3 Monetary Interaction between Europe and America: Case C 1 The Model This chapter deals with case C The European central bank has a single target, that is zero inflation in Europe By contrast, the American... 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... 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 According to the Nash equilibrium there is a reduction in European... 0 Change in Money Supply −4 Change in Money Supply −2 Unemployment 3 Unemployment 0 Inflation 3 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 A1 of 6 units Step two refers to the outside lag Unemployment in Europe . 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 − 6 Change in. 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. 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