Consider the following information in the market where British pounds are exchanged for U.S. dollars: Supply of British pounds (supplied by Brits): Sf = Xg + Xa where: Xg= 100 - 100 (Pus/PB) + 3 YB + 500 e Xa=60,000 (rus - 1B) - 400 Demand for British pounds (demanded by Americans): De = IMg + IM where: Mg=900 + 100 (Pus/PB) +.15 Yu.s. - 300 e IMa = - 80,000 (rus - 1B) +1,000 Meaning of Symbols: Xg=U.S. exports of goods and services to Britain, in billions of British Pounds per year. Xa = British purchases of U.S. assets in billions of British Pounds per year. IMg = U.S. imports of goods and services from Britain, in billions of British Pounds per year. IM = U.S. purchases of British assets, in billions of British Pounds per year. Pus. = price index measuring the average price of good and services in the U.S. PB = price index measuring the average price of goods and services in Britain Yu.s. = real GDP in the U.S. (in billions of pounds per year) YB= real GDP in Britain (in billions of pounds per year) tu.s.= interest rate in the U.S. (in decimal form, e.g. "1%" would be 0.01) 1B = interest rate in Britain. in decimal form, e.g. 1%" would be 0.01) e=the exchange rate $ (dollars per pound, or the price of the pound in dollars). Note that, because we're looking at the supply and demand for pounds in this market, the horizontal axis in your graphs will be "pounds per period. For this reason, the values of Xg, Xa, IMg, and IMa, as well as all other monetary variables like GDP in each country, are all measured in British pounds, rather than U.S. dollars. Also note that we have not included all of the variables from our classroom model in these equations, to keep it simpler. But the variables that do appear have the same "sign as in our classroom model. For example, a rise in rus - 1B causes a decrease in the demand for pounds, and an increase in the supply of pounds, just as we discussed in class. Check through the signs on the other variables to see that they correspond to what we discussed in class. Assume the following initial values for the following variables: Price level in U.S. = 1.0 Price level in Britain = 1.0 Interest rate in U.S. - 6% (so use .06 in the equations) Interest rate in Britain = 5% (so use .05 in the equations) real GDP in Britain is 1,000 (i.e., 1,000 billion pounds per year, so use 1,000 for this variable in the equation) real GDP in the U.S. is 6,000 (1.e., 6,000 billion pounds per year, so use 6,000 for this variable in the equation). Assume throughout this problem set that the exchange rate floats. 1. Solve for the equilibrium exchange rate, "e" (the dollar price of the pound). 2. Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year). 3. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year). 4. What is the value of the U.S. trade balance with Britain? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. have a trade deficit, trade surplus, or neither? 5. Solve for Xa and I Ma and calculate the U.S. net financial inflow measured in pounds. Is your answer consistent with your answer in 4. above? Explain briefly. 6. Sketch a rough diagram (Graph #1) with the following four curves: IMg, D, Xg and S. Note: Don't worry about drawing to scale; just make the curves slope in the proper direction and have the proper relationships to each other. But graph #1 should take up just half the page; save room for Graph #2 later. On your diagram, add numbers (in the appropriate locations) that you've found above for each of the following variables when the dollar-pound market is in equilibrium: e (the exchange rate) IMg (put the number on the horizontal axis) Xg (put the number on the horizontal axis) IMa (label a distance with the number) Xa (label a distance with the number) the total demand for pounds (put the number on the horizontal axis) the total supply of pounds (put the number on the horizontal axis) a distance representing the trade deficit or surplus (if any), or a point illustrating zero trade balance . . 7. Go back to the original initial values in this problem set. Now, suppose that Britain imposes a quota on some (but not all) U.S. goods, which causes the value of U.S. exports to Britain to decrease by 400 billion pounds at each exchange rate. (Think: Which equation at the top of this problem set will change? And how will it change?) Assume there are no other exogenous changes. [Note: This is an example of a change in other in one of the equations] a. What is the equilibrium exchange rate now? b. Compared to the initial situation, has the pound appreciated or depreciated? Has the dollar appreciated or depreciated? c. Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year) d. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year) e. What is the value of the U.S. trade balance with Britain now (in pounds per year)? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. now have a trade deficit, trade surplus, or neither? f. Explain briefly why your answer in e. above makes sense, given the British quota. . 8. [Note: This graph should be on the SAME PAGE as Graph #1, so you can upload both later as a single PDF.] For the values you found above, draw a new graph (Graph #2), showing the following four curves only: IMg, Df, Xg and S. Label the original exchange rate (the one you found in Graph #1) on your diagram, but don't carry over any of the other numbers or curves from Graph #1 or it will get overcrowded! On this graph, include the new numbers you found above (after the quota is imposed) for each of the following variables: e (the exchange rate) IMg Xg . . IMa Xa the total demand for pounds the total supply of pounds a distance representing the trade deficit or surplus (if any), or a point illustrating zero trade balance c. 9. Go back to the original initial values of this problem set. Now suppose the interest rate in the U.S. rises from 6% to 6.1%, with no other exogenous change. [There's no graph for this one - just calculations, but sketching a graph for yourself is a good idea] a. What is the equilibrium exchange rate now? b. Compared to the initial situation, has the pound appreciated or depreciated? Has the dollar appreciated or depreciated? Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year) d. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year). What is the value of the U.S. trade balance with Britain now? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. now have a trade deficit, trade surplus, or neither? f. Solve for Xa and IMa and calculate the U.S. net financial inflow. Is this consistent with your answer above? Explain briefly. g. Explain briefly why the change (or lack of change) in the U.S. trade balance makes sense, given the change in the U.S. interest rate. h. For yourself, sketch a graph for the new equilibrium after the interest rate change, labeled with appropriate numbers. You won't turn in this graph, but you should check it against the graph in the answer sheet that will be posted later. e. 10. [Note: These are qualitative, not quantitative, questions.] For each of the following changes, all else remaining constant, state (1) whether the pound would appreciate, depreciate, or remain unchanged; and (2) whether the U.S. trade deficit would get larger, smaller, or remain unchanged. (For example, starting with a trade deficit of zero, a change that would cause a trade deficit to appear would make the deficit larger.) You should not do any math or turn in any graphs for this part - just give the direction of change. a. A rise in U.S. GDP b. A rise in the U.S. price level. c. A new fear that the British government might default on its debts. [Hint: Greater fear of default was not identified explicitly as a variable in our model. It would be part of "other" in one or more of the functions. But ask yourself: Which curve or curves would shift? And in which direction?] [Continued on next page] 11. Fill in the following blanks with one of the phrases that follow the blanks. [Use our classroom model of exchange rate determination, and that we measure the U.S. trade balance in foreign currency units (here, pounds).] In our classroom model, when exchange rates float, any shift in the supply or demand curve for foreign currency that works through the IMgor Xg functions (e.g. changes in relative price levels, changes in real GDP in either country, or changes in protectionist policies) (can/ cannot) change the U.S. trade balance. Any shift in the supply or demand curve for foreign currency that works through the IMa or Xa functions (e.g. changes in relative interest rates, changes in the expected rate of appreciation or depreciation of either currency, or other things such as changes in the likelihood of default by either country). (can/cannot) change the U.S. trade balance. Consider the following information in the market where British pounds are exchanged for U.S. dollars: Supply of British pounds (supplied by Brits): Sf = Xg + Xa where: Xg= 100 - 100 (Pus/PB) + 3 YB + 500 e Xa=60,000 (rus - 1B) - 400 Demand for British pounds (demanded by Americans): De = IMg + IM where: Mg=900 + 100 (Pus/PB) +.15 Yu.s. - 300 e IMa = - 80,000 (rus - 1B) +1,000 Meaning of Symbols: Xg=U.S. exports of goods and services to Britain, in billions of British Pounds per year. Xa = British purchases of U.S. assets in billions of British Pounds per year. IMg = U.S. imports of goods and services from Britain, in billions of British Pounds per year. IM = U.S. purchases of British assets, in billions of British Pounds per year. Pus. = price index measuring the average price of good and services in the U.S. PB = price index measuring the average price of goods and services in Britain Yu.s. = real GDP in the U.S. (in billions of pounds per year) YB= real GDP in Britain (in billions of pounds per year) tu.s.= interest rate in the U.S. (in decimal form, e.g. "1%" would be 0.01) 1B = interest rate in Britain. in decimal form, e.g. 1%" would be 0.01) e=the exchange rate $ (dollars per pound, or the price of the pound in dollars). Note that, because we're looking at the supply and demand for pounds in this market, the horizontal axis in your graphs will be "pounds per period. For this reason, the values of Xg, Xa, IMg, and IMa, as well as all other monetary variables like GDP in each country, are all measured in British pounds, rather than U.S. dollars. Also note that we have not included all of the variables from our classroom model in these equations, to keep it simpler. But the variables that do appear have the same "sign as in our classroom model. For example, a rise in rus - 1B causes a decrease in the demand for pounds, and an increase in the supply of pounds, just as we discussed in class. Check through the signs on the other variables to see that they correspond to what we discussed in class. Assume the following initial values for the following variables: Price level in U.S. = 1.0 Price level in Britain = 1.0 Interest rate in U.S. - 6% (so use .06 in the equations) Interest rate in Britain = 5% (so use .05 in the equations) real GDP in Britain is 1,000 (i.e., 1,000 billion pounds per year, so use 1,000 for this variable in the equation) real GDP in the U.S. is 6,000 (1.e., 6,000 billion pounds per year, so use 6,000 for this variable in the equation). Assume throughout this problem set that the exchange rate floats. 1. Solve for the equilibrium exchange rate, "e" (the dollar price of the pound). 2. Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year). 3. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year). 4. What is the value of the U.S. trade balance with Britain? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. have a trade deficit, trade surplus, or neither? 5. Solve for Xa and I Ma and calculate the U.S. net financial inflow measured in pounds. Is your answer consistent with your answer in 4. above? Explain briefly. 6. Sketch a rough diagram (Graph #1) with the following four curves: IMg, D, Xg and S. Note: Don't worry about drawing to scale; just make the curves slope in the proper direction and have the proper relationships to each other. But graph #1 should take up just half the page; save room for Graph #2 later. On your diagram, add numbers (in the appropriate locations) that you've found above for each of the following variables when the dollar-pound market is in equilibrium: e (the exchange rate) IMg (put the number on the horizontal axis) Xg (put the number on the horizontal axis) IMa (label a distance with the number) Xa (label a distance with the number) the total demand for pounds (put the number on the horizontal axis) the total supply of pounds (put the number on the horizontal axis) a distance representing the trade deficit or surplus (if any), or a point illustrating zero trade balance . . 7. Go back to the original initial values in this problem set. Now, suppose that Britain imposes a quota on some (but not all) U.S. goods, which causes the value of U.S. exports to Britain to decrease by 400 billion pounds at each exchange rate. (Think: Which equation at the top of this problem set will change? And how will it change?) Assume there are no other exogenous changes. [Note: This is an example of a change in other in one of the equations] a. What is the equilibrium exchange rate now? b. Compared to the initial situation, has the pound appreciated or depreciated? Has the dollar appreciated or depreciated? c. Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year) d. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year) e. What is the value of the U.S. trade balance with Britain now (in pounds per year)? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. now have a trade deficit, trade surplus, or neither? f. Explain briefly why your answer in e. above makes sense, given the British quota. . 8. [Note: This graph should be on the SAME PAGE as Graph #1, so you can upload both later as a single PDF.] For the values you found above, draw a new graph (Graph #2), showing the following four curves only: IMg, Df, Xg and S. Label the original exchange rate (the one you found in Graph #1) on your diagram, but don't carry over any of the other numbers or curves from Graph #1 or it will get overcrowded! On this graph, include the new numbers you found above (after the quota is imposed) for each of the following variables: e (the exchange rate) IMg Xg . . IMa Xa the total demand for pounds the total supply of pounds a distance representing the trade deficit or surplus (if any), or a point illustrating zero trade balance c. 9. Go back to the original initial values of this problem set. Now suppose the interest rate in the U.S. rises from 6% to 6.1%, with no other exogenous change. [There's no graph for this one - just calculations, but sketching a graph for yourself is a good idea] a. What is the equilibrium exchange rate now? b. Compared to the initial situation, has the pound appreciated or depreciated? Has the dollar appreciated or depreciated? Solve for the value of U.S. imports of goods and services (your answer will be in billions of pounds per year) d. Solve for the value of U.S. exports of goods and services (your answer will be in billions of pounds per year). What is the value of the U.S. trade balance with Britain now? (Calculate this directly by comparing exports of goods and services and imports of goods and services.) Does the U.S. now have a trade deficit, trade surplus, or neither? f. Solve for Xa and IMa and calculate the U.S. net financial inflow. Is this consistent with your answer above? Explain briefly. g. Explain briefly why the change (or lack of change) in the U.S. trade balance makes sense, given the change in the U.S. interest rate. h. For yourself, sketch a graph for the new equilibrium after the interest rate change, labeled with appropriate numbers. You won't turn in this graph, but you should check it against the graph in the answer sheet that will be posted later. e. 10. [Note: These are qualitative, not quantitative, questions.] For each of the following changes, all else remaining constant, state (1) whether the pound would appreciate, depreciate, or remain unchanged; and (2) whether the U.S. trade deficit would get larger, smaller, or remain unchanged. (For example, starting with a trade deficit of zero, a change that would cause a trade deficit to appear would make the deficit larger.) You should not do any math or turn in any graphs for this part - just give the direction of change. a. A rise in U.S. GDP b. A rise in the U.S. price level. c. A new fear that the British government might default on its debts. [Hint: Greater fear of default was not identified explicitly as a variable in our model. It would be part of "other" in one or more of the functions. But ask yourself: Which curve or curves would shift? And in which direction?] [Continued on next page] 11. Fill in the following blanks with one of the phrases that follow the blanks. [Use our classroom model of exchange rate determination, and that we measure the U.S. trade balance in foreign currency units (here, pounds).] In our classroom model, when exchange rates float, any shift in the supply or demand curve for foreign currency that works through the IMgor Xg functions (e.g. changes in relative price levels, changes in real GDP in either country, or changes in protectionist policies) (can/ cannot) change the U.S. trade balance. Any shift in the supply or demand curve for foreign currency that works through the IMa or Xa functions (e.g. changes in relative interest rates, changes in the expected rate of appreciation or depreciation of either currency, or other things such as changes in the likelihood of default by either country). (can/cannot) change the U.S. trade balance