Question 2: Convergence (xx points) Suppose that you work in the World Bank and you are carrying out an economic report analyzing and comparing the economy of two neighboring countries: A and B. The macroeconomic magnitudes of both economies are characterized by the same equations, which are the following: Y = K0.5 p0.5 (1) Kt+1 = (1 - 0)K+ + It (2) Y = C+ + It (3) It = sY (4) where the subscript t denotes time, which is measured in years; Y is output, K is the capital stock at the beginning of the period, N is the number of workers (which is assumed to be exogenous and constant over time, so we drop the subscript t), I is investment, and C is consumption. d is the depreciation rate, which is equal for both economies, 8 = 0.1. s is the saving rate, and it is also equal for both economies, s = 0.2. The two countries differ only on their initial (say, t = 0) capital stock, which is KA 100 for country A; and KB = 900 for country B. N = 100 in both countries. = NN and Y YB NN. = (a) Write the production function as a relation between output per worker and capital per worker. (xx points) (b) Does output per worker double when capital per worker dou- bles? why? (xx points) (c) Compute output per worker at the beginning of year t = 1 and t = 2 for each country. Call them YA, YA, (xx points) (d) Compute the percentage change of output per worker between periods t = 0 and t 1, and periods t = 1 and t = 2 for each country. Call them 44,0-1, A4,1-2, and 48,0-1, 42,1-2 (xx points) (e) Compare the percentage change across countries and within the same time periods (that is, compare A9,01 with AB,01; and compare A4,1-2 with AB,1-2). Why are they different? explain in economic terms, you can make use of a graph. (xx points) (f) Compare the percentage change within countries and across time periods (that is, compare A4,0-1 with 44,1-2; and com- pare AB,0-1 with AB,1-2). Why are they different? explain in economic terms, you can make use of a graph. (xx points) Y (g) Compute capital per worker in the steady state for both coun- tries (i.e. at the point where capital per worker is constant over time). (xx points) (h) Compute output per worker in the steady state for both coun- tries. (xx points) 4 (i) The government of country A is studying the possibility of - plying certain policies to increase the saving rate to s = 0.4. They argue that, this way, the country would catch up earlier with the standards of living of neighboring countries. Analyze how such a policy would affect consumption per worker in the long-run. Without doing any calculation, can you guess what would happen to consumption per worker in the short-run? Question 2: Convergence (xx points) Suppose that you work in the World Bank and you are carrying out an economic report analyzing and comparing the economy of two neighboring countries: A and B. The macroeconomic magnitudes of both economies are characterized by the same equations, which are the following: Y = K0.5 p0.5 (1) Kt+1 = (1 - 0)K+ + It (2) Y = C+ + It (3) It = sY (4) where the subscript t denotes time, which is measured in years; Y is output, K is the capital stock at the beginning of the period, N is the number of workers (which is assumed to be exogenous and constant over time, so we drop the subscript t), I is investment, and C is consumption. d is the depreciation rate, which is equal for both economies, 8 = 0.1. s is the saving rate, and it is also equal for both economies, s = 0.2. The two countries differ only on their initial (say, t = 0) capital stock, which is KA 100 for country A; and KB = 900 for country B. N = 100 in both countries. = NN and Y YB NN. = (a) Write the production function as a relation between output per worker and capital per worker. (xx points) (b) Does output per worker double when capital per worker dou- bles? why? (xx points) (c) Compute output per worker at the beginning of year t = 1 and t = 2 for each country. Call them YA, YA, (xx points) (d) Compute the percentage change of output per worker between periods t = 0 and t 1, and periods t = 1 and t = 2 for each country. Call them 44,0-1, A4,1-2, and 48,0-1, 42,1-2 (xx points) (e) Compare the percentage change across countries and within the same time periods (that is, compare A9,01 with AB,01; and compare A4,1-2 with AB,1-2). Why are they different? explain in economic terms, you can make use of a graph. (xx points) (f) Compare the percentage change within countries and across time periods (that is, compare A4,0-1 with 44,1-2; and com- pare AB,0-1 with AB,1-2). Why are they different? explain in economic terms, you can make use of a graph. (xx points) Y (g) Compute capital per worker in the steady state for both coun- tries (i.e. at the point where capital per worker is constant over time). (xx points) (h) Compute output per worker in the steady state for both coun- tries. (xx points) 4 (i) The government of country A is studying the possibility of - plying certain policies to increase the saving rate to s = 0.4. They argue that, this way, the country would catch up earlier with the standards of living of neighboring countries. Analyze how such a policy would affect consumption per worker in the long-run. Without doing any calculation, can you guess what would happen to consumption per worker in the short-run