Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1...

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Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that n = 0.02, i.e., A =(1+0.1) At-1, and Lt (1+0.02) Lt-1- Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Y is given by Recall that efficient units of labor are given by Assume that 8=0.1, s = 0.2, and a = 0.3. 1. What is the growth rate of Lt, i.e., find 2. Recall that capital per-efficient worker kt = YA,KL. L = A = Lt. = It Lt-1 - 1. K/L varies over time according to k1+1 = (1- () kr + sko 1+2 Use this equation to show that the steady state level of capital per efficient worker is given by 1 (2) 1-a S = Replace the numbers for s, 8, and a to find the value of capital per efficient worker in steady state. 3. Use the production function (2) to show that output per efficient worker, t = Y/Lt, is given by y = kg. What is output per-efficient worker if capital per-efficient worker is at its steady-state value? 4. If capital per-efficient worker is at its steady state value, does output per efficient worker grow over time? Recall that output per worker is given by yt = Y/Lt. Use our definition of output per-efficient worker to replace Y and write What is the growth rate of output per worker Yt = t Lt Yt gy 1 Yt-1 if capital per-efficient worker is at its steady-state value? Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that n = 0.02, i.e., A =(1+0.1) At-1, and Lt (1+0.02) Lt-1- Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Y is given by Recall that efficient units of labor are given by Assume that 8=0.1, s = 0.2, and a = 0.3. 1. What is the growth rate of Lt, i.e., find 2. Recall that capital per-efficient worker kt = YA,KL. L = A = Lt. = It Lt-1 - 1. K/L varies over time according to k1+1 = (1- () kr + sko 1+2 Use this equation to show that the steady state level of capital per efficient worker is given by 1 (2) 1-a S = Replace the numbers for s, 8, and a to find the value of capital per efficient worker in steady state. 3. Use the production function (2) to show that output per efficient worker, t = Y/Lt, is given by y = kg. What is output per-efficient worker if capital per-efficient worker is at its steady-state value? 4. If capital per-efficient worker is at its steady state value, does output per efficient worker grow over time? Recall that output per worker is given by yt = Y/Lt. Use our definition of output per-efficient worker to replace Y and write What is the growth rate of output per worker Yt = t Lt Yt gy 1 Yt-1 if capital per-efficient worker is at its steady-state value?

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To find the growth rate of L we use the formula L1nL1 where n is the population growth rate In this ... View the full answer