Solow Model Practice - Calculate the Steady State & Compare Economies with Varying Saving Rates

In this problem we'll work through a rather simple version of the Solow Model. We'll then calculate the steady values of per-worker capital, investment, consumption and production. Then, we'll compare two economies - one with a relatively high savings rate and one with a relatively low savings rate -- and we'll see how the dynamics of these two countries differ. More Macro Problems: https://sites.google.com/site/curtisk... _________________________________________ Given a parameterization, solving for the steady state values of per-worker capital, investment, consumption and production. Country A and country B both have the production function Y=K^0.5 L^0.5 0:55 a. Does this production function have constant returns to scale? 3:55 b. What is the per-worker production function, y=f(k)? 9:20 c. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and steady state condition that investment equals depreciation, find the steady state level of capital per worker for each country. Then find the steady state levels of income per worker and consumption per worker. 18:10 d. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker?. Remembering that the change in the capital stock is investment less depreciation, use a calculator or computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A. from Mankiw's Macroeconomics, Chapter on Economic Growth Part 1 (Chapter 8) - Problem 1 -------------------------------------------------------------------