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Would you be willing to pay more in order to reduce the probability of dying within the next hour from one sixth to zero or from four sixths to three sixths'? Unfornmately, this is not a hypothetical question: you accidentally entered the ofce of a mad scientist and have been overpowered and tied to a chair. The mad scientist has put six glasses in front of you, numbered 1 to 6, and tells you that one of them contains a deadly poison and the other ve contain a hamess liquid. He says that he is going to roll a die and make you drink from the glass whose number matches the number that shows from the rolling of the die. You beg to be exempted and he asks you \"what is the largest amount of money that you would be willing to pay to replace the glass containing the poison with one containing a harmless liquidT'. Interpret this question as \"what sum of money .1: makes you indifferent between (1} leaving the poison in whichever glass contains it and rolling the die, and (2} reducing your wealth by $1: and rolling the die after the poison has been replaced by a harmless liquid\". Your answer is: 331'. Then he asks you \"suppose that instead of one glass with poison there had been four glasses with poison (and two with a harmless liquid}; what is the largest amount of money that you would be willing to pay to replace one glass with poison with a glass containing a harmless liquid (and thus roll the die with 3 glasses with poison and 3 with a harmless liquid)?" Your answer is: 33?. Show that if X 3':- 1' then you do not satisfy the aJnoms of Expected Utility Theory. [I-nt: think about what the basic outcomes are; assume that you do not care about how nu1ch money is left in your estate if you die and that, when alive, you prefer more money to less.] I Excell. Transition to equilibrium la. Fill out the table below. You need probably to make 2 tables to make room for all the numbers. 1b. Plot y, K/L, the real wage, and the real return to capital against time in diagrams. Plot In y against time in a diagram. Ic. Plot the growth rate of y against y in one diagram. Assume starting value: k(year=0)=2.00. Assume also: A=1, s=0.25, o = 0.1, 0=0.5, and n=0.02. N(year=0)=100 Year K y=ka ci 6.KA .k Ay A .k A . y Real K N K y wage 0 12 3 Note= r is real return to capital. r=MPK-depreciation rate. Briefly comment your results. 2A. Assume the parameter values above, and that the economy is in its steady state in period 0. Assume that in period 1 the parameter A increases to 2. Make a new table showing the transition to the new steady state. 2b. Plot In y against time. 2c. Plot the growth rate of y against y in one diagram. Briefly comment your results. 3. What happens if s increases? Assume that the economy in period O is in its equilibrium (described by the parameter values in exercise 1), and that s increases to 0.35. 4. Assume that the economy in period 0 is in its equilibrium (described by the parameter values in exercise 1), and that n increases to 0.04. Make a new table showing the transition to the new steady state. Compare the old equilibrium with the new equilibrium with respect to Y/L, K/L, the real wage, the real return to capital (r), K, and Y. Quantitative questions ch. 7 of Mankiw, which are relevant for B-macroeconomics, and economic growth course: Problem 7.1: Country A and B has the production function: Y = F(K, L) = KV2 . [2 A. Does this production function have constant returns to scale? B. What is the per-worker production function, Y/L=f(K/L) C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year, and country B saves 20 percent of output each year. Find the steady state level of capital per worker, the steady-state level of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is gross investment minus depreciation, calculate capital stock per worker, income per worker, and consumption per worker over time. How many years will it be before consumption per worker in Country B is higher than the level of consumption per worker in country A. Problem 7.2: In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not affect the capital stock, but that casualties reduce the labor force. A. What is the immediate impact on total output and on output per person? B. Assuming that the saving rate is unchanged and that the economy was in a steady state before the war, what happens subsequently to output per worker in the postwar economy? Is the growth rate of output per worker after the war smaller or greater than normal? Problem 7.3: Consider an economy described by the production function: Y = F(K, L) = K03 . ['.7 A. What is the per-worker production function? B. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. C. Assume that the depreciation rate is 10 percent per year. Make a table showing steady- state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, and 30 percent and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker? D. Use calculus to find the marginal product of capital. Add to your table the marginal product of capital net of depreciation for each of the saving rates.Problem 5.1: Use the model of the small open economy to predict what would happen to the trade balance, the real exchange rate, and the nominal exchange rate in response to each of the following events: A. A fall in consumer confidence about the future induces consumers to spend less and save more. B. The introduction of a stylish line of Toyotas makes some consumers prefer foreign cars over domestic cars. C. The introduction of automatic teller machines reduces the demand for money. Problem 5.2: Consider an economy described by the following equations: Y:C+I-|G+NX, Y:5[I, (3:10:00, Tzl, C';250+.?5*(Y-TL I=l-S*r, NX=5-5t}* a. A. In this economy, solve for national saving, investment, the trade balance, and the equilibrium exchange rate. B. Suppose now that G rises to 12511}. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain. Problem 5.3: The county of Leverett is a small open economy. Suddenly, a change in world fashions makes the exports of Leverett unpopular. A. What happens in leveret to saving, investment, net exports, the interest rate, and the exchange rate. B. The citizens of Ieveret like to travel abroad. How will this change in the exchange rate affect them? C. The fiscal policy makers of Leverett want to adjust taxes to maintain the exchange rate at its previous level. What should they do? If they do this, what are the overall effects on saving, investment, net exports, and the interest rate? Problem 5.5: What will happen to the trade balance and the real exchange rate of a small open economy when government purchases increase, such as during a war? Does your answer depend on whether this is a local war or a world war? Problem in: A case study in this chapter concludes that if poor nations offered better production efciency and legal protections, the trade balance in rich nations would move towards a surplus. Let's consider why this might be the case. A. If the world's poor nations offer better production efficiency and legal protection, what would happen to the investment demand function in those counu'ies? B. How would the change that you describe in A. affect the demand for loanable funds in world nancial markets? C. How would the change you describe in B affect the world interest rate? D. How would the change in the world interest rate you describe in C affect the trade balance in rich countries? Problem 53: The president is considering placing a tariff on the import of Japanese luxury cars. Discuss the economics and politics of such a policy. In particular, how would the policy affect the US trade decit? How would it affect the exchange rate? Who would be hurt by such a policy? Who would benefit? Problem 5.8:Suppose that some foreign countries begin to subsidize investment by instituting an investment tax credit. A. What happens to world investment demand as a function of the world interest rate? B. What happens to the world interest rate? C. What happens to invesunertt in our small open economy? D. What happens to our n'ade balance? E. What happens to our real exchange rate? Problem 5.9: Traveling in Mexico is much cheaper now than it was 10 years ago, says a friend. \"Because ten years ago, a dollar bought 10 pesos; this year, a dollar buys 15 pesos. Is your friend right or wrong? Given that total ination over this period was 2'5 percent in the US and 100 percent in Mexico, has it become more or less expensive to travel in Mexico? Problem 5.10: The nominal interest rate is 12 percent per year in Canada and 3 percent per year in the USA. Suppose that the real interest rate is the same in these two countries, and that purchasing-power parity holds. A. Use the Fischer equation {discussed in chapter 4.] what can you say about expected ination in Canada and in the USA? B. What can you say about the expected change in the exchange rate between the Canadian dollar and the US dollar? C. A friend proposes a get-rich-qnick scheme: borrow from a US bank at 8 percent, deposit the money in a Canadian bank at 12 percent, and make a 4 percent prot. What's wrong with this scheme? 1.Use the Mundell-Fleming model to predict what would happen to aggregate income, the exchange rate, and the trade balance under both floating and fixed exchange rates in response to each of the following shocks: A. A fall in consumer confidence about the future induces consumers to spend less and save more. B. The introduction of a stylish line of Toyotas makes some consumers prefer foreign cars over domestic cars. C. The introduction of automatic teller machines reduces the real demand for money. 2.A small open economy with a floating exchange rate is in recession with balanced trade. If policymakers want to reach full employment while maintaining balanced trade, what combination of monetary and fiscal policy should they choose ? 3. The Mundell-Fleming model takes the world interest rate r as an exogenous variable. Let's consider what happens when this variable changes? A. What might cause the world interest rate to rise? B. In the Mundell-Fleming model with a floating exchange rate, what happens to aggregate income, the exchange rate, and the trade balance when the world interest rate rises? 4. Business executives and policymakers are often concerned about the "competitiveness" of American industry (the ability of U.S. industries to sell their goods profitably in world markets). a. How would a change in the exchange rate affect competitiveness? b. Suppose you wanted to make domestic industries more competitive but did not want to alter aggregate income. According to the Mundell-Fleming model, what combination of monetary and fiscal policies should you pursue? 5. Suppose that higher income implies higher imports and thus lower net exports. That is, the net exports function is: NX=NX(e, Y). Examine the effects in a small open economy of a fiscal expansion on income and trade balance under a floating exchange rate. 7. Suppose that the price level relevant for money demand includes the price of imported goods and that the price of imported goods depends on the exchange rate. That is, the money market is described by M/P=L(r, Y) where P= 1 . P. + (1-1) - Pyle The parameter 1 is the share of domestic goods in the price index P. Assume that the price of domestic goods Pd and the price of foreign goods measured in foreign currency Pf are fixed. B.What is the effect of expansionary fiscal policy under floating exchange rates in this model? Explain. Contrast with the standard Mundell-Fleming model