please answer every step of this question with work showing! I am very confused!! thank you!! Question

please answer every step of this question with work showing! I am very confused!! thank you!!

 

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Question II Solow Model with Population or Technology Growth - 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 L =(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 = 0.1, s = 0.2, and a = 0.3. 1. What is the growth rate of Lt, i.e., find Y = AKL. 1 1-a = A Lt. (2) = Lt Lt-1 - 1. 2. Recall that capital per-efficient worker k = K/L varies over time according to ke+1 = (1-8) k + sko 1 +2 Use this equation to show that the steady state level of capital per efficient worker is given by 1 1-a S 8 +2 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 I = ko. 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 y = 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 = Yt Lt Yt 1 gy Yt-1 if capital per-efficient worker is at its steady-state value? 5. Suppose that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of capital per-efficient worker? Is it higher, lower, the same? 6. Continue assuming that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of output per-efficient worker? Is it higher, lower, the same? 7. Recompute the growth rate of output per worker gy with the higher savings rate s = 0.3. Is it higher, lower, the same? Use your results to comment on how does the savings rate affect the growth rate of output per capita in this model. Question II Solow Model with Population or Technology Growth - 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 L =(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 = 0.1, s = 0.2, and a = 0.3. 1. What is the growth rate of Lt, i.e., find Y = AKL. 1 1-a = A Lt. (2) = Lt Lt-1 - 1. 2. Recall that capital per-efficient worker k = K/L varies over time according to ke+1 = (1-8) k + sko 1 +2 Use this equation to show that the steady state level of capital per efficient worker is given by 1 1-a S 8 +2 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 I = ko. 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 y = 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 = Yt Lt Yt 1 gy Yt-1 if capital per-efficient worker is at its steady-state value? 5. Suppose that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of capital per-efficient worker? Is it higher, lower, the same? 6. Continue assuming that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of output per-efficient worker? Is it higher, lower, the same? 7. Recompute the growth rate of output per worker gy with the higher savings rate s = 0.3. Is it higher, lower, the same? Use your results to comment on how does the savings rate affect the growth rate of output per capita in this model.