2A. Assume the parameter values above, and that the economy is in its steady state in period 0. Assume that in period I 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 0 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 O 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) = K1/2. 1" 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 . LP-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.APPENDIX OF CHAPTER 8: GROWTH ACCOUNTING ("TILL VAXTBOKFORING") AND GROWTH RATES Problem 8.1: In an economy which is characterized by perfect competition in the goods and labor market, the owners of capital get two-thirds of national income, and the workers receive one-third. Assume a Cobb-Douglas aggregate production function. Problem 8.1A: The men stay at home in this economy, while the women work in factories. If some of the men started working outside the home so that the labor force increased by 5 percent, what would happen to the measured output of the economy? Does labor productivity (output per worker) increase, decrease or stay the same? Does total factor productivity (A) increase, decrease, or stay the same? One way to solve exercise., assume A=1, K=1, LO=1 and LI=1.05. Problem 8.1B: In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the labor input was 4, and output was 14. What happened to total factor productivity between the years? Problem 8.3: Assume an economy which is characterized by perfect competition in the goods and labor market, in which the owners of capital get one-third of national income, and the workers receive two-thirds. Assume a Cobb-Douglas aggregate production function. Assume that total output and total capital stock grow at 3.6 percent per year, and that labor input grows by one percent per year. Use the growth accounting equation to divide output growth into three sources - capital. labor. and total factor productivity - how much of output growth would you attribute to each source? Problem 8.4. If GDP per capita in Sweden (in 1995 prices) in 1995 and 2000 were 194 and 222 thousands of kronor, what was the average annual rate of economic growth during this 5- year period? Problem 8.5. If a variable during a 30-year period increases by 54 percent, what average annual growth rate does this correspond to? Problem 8.6. If the growth rate of GDP per capita was 2 percent between 1960 and 1990, and the population growth rate was 3 percent during the same period, what was the growth rate of GDP during this period? Problem 8.7: Assume that GDP per capita in Sweden and Zambia in 2002 were 16000 and 800 USD, respectively, and that the growth rate of GDP per capita in Sweden and Zambia is 1 and 7 percent, respectively. a) How does the absolute difference between the 2 countries develop over time? That is, GDP per capita in Sweden - GDP per capita in Zambia. b) How does the relative difference develop over time? That is, GDP per capita in Sweden/GDP per capita in Zambia. USE EXCEL to answer these questions. Problem 8.8: If your wage is 100 kronor and the growth rate is 5 percent, how many years does it take for your wage to double?5. THE CLASSICAL MODEL FOR THE SMALL OPEN ECONOMY= THE KEYNESIAN MODEL FOR THE SMALL OPEN ECONOMY IN THE LONG RUN 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=5000, G=1000, T=1000, C=250+0.75*(Y-T). 1=1000-50*r. NX=500-500* 2. A. In this economy, solve for national saving, investment, the trade balance, and the equilibrium exchange rate. B. Suppose now that G rises to 1250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain. Problem 5.3: The country 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 leveret 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 5.6: A case study in this chapter concludes that if poor nations offered better production efficiency 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 countries? B. How would the change that you describe in A. affect the demand for loanable funds in world financial 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 5.7: 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 deficit? 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 investment in our small open economy? D. What happens to our trade 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 inflation over this period was 25 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 8 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 inflation 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-quick scheme: borrow from a US bank at 8 percent, deposit the money in a Canadian bank at 12 percent, and make a 4 percent profit. What's wrong with this scheme?12. THE KEYNESIAN MODEL FOR THE SHORT RUN FOR A SMALL OPEN ECONOMY with a horizontal SRAS-curve. (The Mundell-Fleming model) Student should focus on floating exchange rates. I.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 ' 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-A). P, le The parameter A 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. 13. THE KEYNESIAN MODEL IN THE SHORT AND LONG RUN WITH A POSITIVELY SLOPED SRAS-CURVE. THE AS/AD-model. 2. Consider the following changes in the sticky-wage model. a. Suppose that labor contracts specify that the nominal wage be fully indexed for inflation. That is, the nominal wage is to be adjusted to fully compensate for changes in the consumer price index. How does full indexation alter the aggregate supply curve in this model? b. Suppose now that indexation is only partial. That is, for every increase in the CPI, the nominal wage rises, but by a smaller percentage. How does partial indexation alter the aggregate supply curve in this model? 3. Suppose that an economy has the Philips curve *= _, -05(1 -0.06) a. What is the natural rate of unemployment? b. Graph the short-run and long-run relationships between inflations and unemployment. c. How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? Using Okun's law, compute the sacrifice ratio, d. Inflation is running at 10 percent. The fed (=central bank in the US)wants to reduce it 10 5 percent. Give two scenarios that will achieve that goal