Question 1 (16 points) The aggregate production function in the Romer model describes how the capital...

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Question 1 (16 points) The aggregate production function in the Romer model describes how the capital stock, K, and labor, Ly, combine to produce output, Y, using the stock of ideas, A: YK" (ALy)¹ (1) O 0 < a < 1. o L-Ly + LA=(1-SR)L+SRL (labor force to produce output + labor force to produce ideas). O SR is a constant fraction of the labor force. Labor grows exponentially at some constant and exogenous rate: = n o Along a balanced growth path, <=9A O Capital accumulates as people forego consumption at some given rate, Sk, and depreciates at the exogenous rate d. K = SY-dk (2) The production function for ideas: A = OLA where is the rate at which new ideas are discovered. CLIC (3) 1) From equation (3), explain why the rate of technological progress along the balanced growth path, L to labor growth rate, = n (such that gA =n) 2) Find the steady state value of capital per effective worker, k K AL 3) Find the steady state values of output per effective worker, y = Y AL =9A, is equal (2 points) (3 points) and I per worker (discuss the determinants of the output per worker). (3 points) (2 points) 4) Find the steady state values of investment and consumption per worker. 5) What happens if the share of the population engaged in research, Sp, increases permanently due to a government subsidy for R&D (growth effects versus level effects)? Draw graphs for the rate of technological progress and the level of technology over time. (2 points) 6) Prove that gy =9k=9A=n (2 points). Question 1 (16 points) The aggregate production function in the Romer model describes how the capital stock, K, and labor, Ly, combine to produce output, Y, using the stock of ideas, A: YK" (ALy)¹ (1) O 0 < a < 1. o L-Ly + LA=(1-SR)L+SRL (labor force to produce output + labor force to produce ideas). O SR is a constant fraction of the labor force. Labor grows exponentially at some constant and exogenous rate: = n o Along a balanced growth path, <=9A O Capital accumulates as people forego consumption at some given rate, Sk, and depreciates at the exogenous rate d. K = SY-dk (2) The production function for ideas: A = OLA where is the rate at which new ideas are discovered. CLIC (3) 1) From equation (3), explain why the rate of technological progress along the balanced growth path, L to labor growth rate, = n (such that gA =n) 2) Find the steady state value of capital per effective worker, k K AL 3) Find the steady state values of output per effective worker, y = Y AL =9A, is equal (2 points) (3 points) and I per worker (discuss the determinants of the output per worker). (3 points) (2 points) 4) Find the steady state values of investment and consumption per worker. 5) What happens if the share of the population engaged in research, Sp, increases permanently due to a government subsidy for R&D (growth effects versus level effects)? Draw graphs for the rate of technological progress and the level of technology over time. (2 points) 6) Prove that gy =9k=9A=n (2 points).

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Lets break down the questions one by one 1 From equation 3 explain why the rate of technological progress along the balanced growth path g equals the labor force growth rate gL 2 points From equation ... View the full answer