HW3Answerkey

HW3Answerkey - ECO 420 Homework 3 Due in class on October...

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Homework 3 Due in class on October 8 th , 2008 1. Country A and country B both have the production function: Y=F(K,L)=K 1/2 L 1/2 a. What is the per-worker production function? Y=k 1/2 b. 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 the 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. In steady state, sf(k) = δk s k 1/2 = δk k = (s/δ) 2 k* in Country A = (0.10/0.05) 2 = 4 k* in Country B = (0.20/0.05) 2 = 16 c. 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 a 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 consumption in country B is higher than the consumption in country A? 5 years – SEE BELOW.
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This document was uploaded on 10/28/2011 for the course ECON 420 at UNC.

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HW3Answerkey - ECO 420 Homework 3 Due in class on October...

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