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Assume that an economy described by the Solow model has the production function Y = K (LE) X , where all the variables are defined as in class. The saving rate is 36%, the capital depreciation rate is 1%, the population growth rate is 1%, and the rate of change in efficiency (E) is 2%. A. Derive the per-effective worker production function y = f(k). All derivations are required. You will lose points if you just give the final answer. (4 points) B. Write down the equation that represents the dynamics of lower-case k. (3 point) C. Suppose in the current year, capital per effective worker k is 1. Calculate what the level of k is in the next year. (3 points) D. Solve for the steady state levels of k*, y*, and c* (4 points) E. Does this economy always converge to the steady state? Why or why not? (3 points) F. What are the growth rates of k* and y* in the steady states? (2 point) G. What are the growth rates of K/L and Y/L in the steady state? Show all your derivations. You will lose points if you only give a final answer. (3 points) H. Compared with the Golden rule level, is this country saving too much, too little, or just right? First, offer a clear answer. Then, show all your derivations and calculations. Again, you will lose points if you only give a final answer (4 points) For this question, all your derivations, calculations, and graphs go on paper. Only your final answers (numbers, yes or no, one sentence answers) go in the text box. Assume that an economy described by the Solow model has the production function Y = K (LE) X , where all the variables are defined as in class. The saving rate is 36%, the capital depreciation rate is 1%, the population growth rate is 1%, and the rate of change in efficiency (E) is 2%. A. Derive the per-effective worker production function y = f(k). All derivations are required. You will lose points if you just give the final answer. (4 points) B. Write down the equation that represents the dynamics of lower-case k. (3 point) C. Suppose in the current year, capital per effective worker k is 1. Calculate what the level of k is in the next year. (3 points) D. Solve for the steady state levels of k*, y*, and c* (4 points) E. Does this economy always converge to the steady state? Why or why not? (3 points) F. What are the growth rates of k* and y* in the steady states? (2 point) G. What are the growth rates of K/L and Y/L in the steady state? Show all your derivations. You will lose points if you only give a final answer. (3 points) H. Compared with the Golden rule level, is this country saving too much, too little, or just right? First, offer a clear answer. Then, show all your derivations and calculations. Again, you will lose points if you only give a final answer (4 points) For this question, all your derivations, calculations, and graphs go on paper. Only your final answers (numbers, yes or no, one sentence answers) go in the text box

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