Question

1. Country A and country B both have the production function Y = F(K,L)= VKL. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y=f(k)? (10 Points) 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. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker. (15 Points) What saving rate maximizes output per worker for each country? What saving rate maximizes consumption per worker for each country? And find the Golden Rule level of consumption, output, investment per worker for each country. (15 Points) 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 investment less depreciation, use a calculator or a computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A?

Answer 1

a.,b,c,d

DATE Y = √kol Increase K & L by t Y(t) = v ktL = t J K L = t. y i output also increase by t, then junction has CRS Y J K L production Y = UK (424 kk = k/ © duplication 8 = 5). savings SA = 10%. AB=20%. at steady state Ok= 0 s.y - Sk = 0 sy = 6k sk - Sk kes for A, R 1202 » (4) 2 = 16 for B R (10)2 = (232 = 04 yn _ S T6 24 YAM = U = 2 CAYA (1-8) = 4(1-0-1) -2 (1-0.2) = 3.6

DATE: (d) for Bath countries, savings rate of 1001 maximise output per worker. at steady stata K = (& 12 ya is maximum/ when 8 = 5% or 0.05) Yo bos or 205 So yo is maximum when sis I or 100% then y = 20x100 = 20. for consumption, c. (1-8)ys = (1-3) (2) 100 0.05 co = 20511-8) ce 208-201² max ce with respect to s de 220-2x20s =0 1-25=0 s = 1/2 = 0.5 or s=561. would meximise consumption in both nations. this will be the coolden rule. - 80 = Onos D. Ig = sg yg 11 0.05 - 005810 - 5 Cg = QSxo.5 - 5 Tositive.