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Problem 3.1: 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 3.1A: 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? Dne way to solve exercise, assume A='I, K=1, L3=1 and L1 =1 .35. Problem 3.13: In year 1, the capital stock was 5, the labor input was 3, and output was 12. In year 2, the capital stock was ?, the labor input was 4, and output was 14. What happened to total factor productivity between the years? Problem 3.3: 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 3.5 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 3.4. If GDP per capita in Sweden [in 1995 prices) in 1995 and 2333 were 194 and 222 thousands of kronor, what was the average annual rate of economic growth during this 5-year period? Problem 3.5. If a variable during a 33-year period increases by 54 percent, what average annual growth rate does this correspond to? Problem 3.5. If the growth rate of GDP per capita was 2 percent between 1953 and 1993, and the population growth rate was 3 percent during the same period, what was the growth rate of GDP during this period? Problem 3?: Assume that GDP per capita in Sweden and Zambia in 2332 were 15333 and 333 USD, respectively, and that the growth rate of GDP per capita in Sweden and Zambia is 1 and ? 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 SwedenJ'GDP per capita in Zambia. USE EXCEL to answer these questions. Problem 3.3: If your wage is 133 kronor and the growth rate is 5 percent, how many years does it take for your wage to double? 1a. Fill out the table below. You need probably to make 2 tables to make room for all the numbers. 1b. Plot y=Y/L, k= K/L, the real wage, and the real return to capital against time in diagrams. Plot In y against time in a diagram. 1c. 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, a=0.5, and n=0.02. N(year=0)=100 Year K y =kaci OK A . K A y A . K A . y Real R Y K N K wage 0 1 2 3 OO Note= R is real return to capital. R=MPK-depreciation rate. Briefly comment your results. - Page Break - - A question you may ask yourselves: Why is r + depreciation rate = MPK? Answer: Perfect competition is assumed in the Solow model: Perfect competition implies that profit-maximizing firms employ K and L so that W/P=MPL and R/P=MPK, which are equal to W = P*MPL and R = P*MPK, where P is the product price, and W is nominal cost per worker and R the rental cost per unit of capital. Assume that the capital is owned by firms that rent out the capital to firms that produce goods that are both a consumption good and a capital good. What rent should the firms that own the capital charge? It should charge at least P*r, where P is the price per unit of capital. r is the real interest rate or the real return on capital. P*r is the opportunity cost of holding capital. The firm should also account for the fact that when it rent out capital the value of capital depreciates by P*depreciation rate. Thus, R= P*(r+deprecitation rate). This rental price of capital implies that the capital-owning firms do not make a profit. In other words, P*(r+depreciation rate) is the COST PER UNIT OF CAPITAL PER PERIOD OF TIME 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 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 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.The problem below is a simulation exercise for the SOLOW MODEL with on-going technological change. That is, we assume that A(t) = A(0) . es Students do not have to do this problem. To be handed in: Deadline: XXXXXX. Allow for long-run technological progress: (A1): Y (1) = K(1) " . (A(t) . L(1) )1-2, A( t) = A(0) . e9 Explaining the transition to the equilibrium growth path: Assume: A(0)=1, s=0.25, and (n+g+d)=0.1, g=0.015, n=0.015, d=0.07, a =0.5. N(year=0)=100, the starting value: k(0) =2. Fill out the table. Yea C= k A . K A . y Real Y K K= y. A (t) E . A(1) 7 . A(D) K wage K/L 0 1 2 3 4 00 Note: r is real return to capital. r=MPK-depreciation rate. K = K ( t ) / A ( t ) . L ( t ) . y = Y ( t) / A (t) . L (t) , y = Y (t) / L (t ). cti= y = (1 - s) y+s. y A.Plot In y against time, as well as the equilibrium growth path of Iny. Briefly comment your results. B1. What happens to the growth rate and to the equilibrium growth path if s increases? Assume that the economy in period 0 is on its equilibrium growth path (described by the parameter values above), and that s increases to 0.35. B2. A make a new table similar to the one above showing the transition to the new steady state growth path. B3. Plot In y against time, as well as the old and new equilibrium growth paths of Iny. Briefly comment your results. C1. What happens to the growth rate and to the equilibrium growth path if total factor productivity improves (due to less corruption and more education) increases? Assume that the economy in period 0 is on its equilibrium growth path (described by the initial parameter values above), and that A(0) increases to 2. C2. A make a new table similar to the one above showing the transition to the new steady state growth path. C3. Plot In y against time, as well as the old and new equilibrium growth paths of Iny. Briefly comment your results