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

 

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.