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An economy has the per-worker production function y = Akcx where y is output per worker and k is capital per worker; A = 8 and a = 0.4. Capital accumulation follows: k = sy- (n+8)k The saving rate s is 0.12, the depreciation rate & is 0.05, and the population growth rate n is 0.02. a. What are the steady state values of capital per worker, output per worker, and consumption per worker? b. Repeat Part (a) for a saving rate of 0.2 instead of 0.12. c. Repeat Part (a) for a population growth rate of 0.01 (with a saving rate of 0.12). d. Repeat Part (a) for a production function of y = 15k04 (with a saving rate of 0.12 and population growth rate of 0.02)

An economy has the per-worker production function y = Akcx where y is output per worker and k is capital per worker; A = 8 and a = 0.4. Capital accumulation follows: k = sy- (n+8)k The saving rate s is 0.12, the depreciation rate & is 0.05, and the population growth rate n is 0.02. a. What are the steady state values of capital per worker, output per worker, and consumption per worker? b. Repeat Part (a) for a saving rate of 0.2 instead of 0.12. c. Repeat Part (a) for a population growth rate of 0.01 (with a saving rate of 0.12). d. Repeat Part (a) for a production function of y = 15k04 (with a saving rate of 0.12 and population growth rate of 0.02)

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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a, b, c and if d is possible that would be great thank you

An economy has the per-worker production function y = Akax where y is output per worker and k is capital per worker; A = 8 and a = 0.4. Capital accumulation follows: k = sy - (n+8)k The saving rate s is 0.12, the depreciation rate & is 0.05, and the population growth rate n is 0.02. a. What are the steady state values of capital per worker, output per worker, and consumption per worker? b. Repeat Part (a) for a saving rate of 0.2 instead of 0.12. c. Repeat Part (a) for a population growth rate of 0.01 (with a saving rate of 0.12). d. Repeat Part (a) for a production function of y = 15k04 (with a saving rate of 0.12 and population growth rate of 0.02) e. Suppose the economy is not in the steady state currently. Write down the growth rate of capital per worker() along the transition path in terms of A, k, a, s, n and 8. Then draw as a function of k. Label the steady state capital-labour ratio as k*. (Hint: use the horizontal axis to represent k and the vertical axis to represent.) f. Show your answer to the following questions on the function diagram from part (e). What happens to when there is an increase in s? What happens to when there is an increase in n? Explain your intuition of the results.
Transcribed Image Text:An economy has the per-worker production function y = Akax where y is output per worker and k is capital per worker; A = 8 and a = 0.4. Capital accumulation follows: k = sy - (n+8)k The saving rate s is 0.12, the depreciation rate & is 0.05, and the population growth rate n is 0.02. a. What are the steady state values of capital per worker, output per worker, and consumption per worker? b. Repeat Part (a) for a saving rate of 0.2 instead of 0.12. c. Repeat Part (a) for a population growth rate of 0.01 (with a saving rate of 0.12). d. Repeat Part (a) for a production function of y = 15k04 (with a saving rate of 0.12 and population growth rate of 0.02) e. Suppose the economy is not in the steady state currently. Write down the growth rate of capital per worker() along the transition path in terms of A, k, a, s, n and 8. Then draw as a function of k. Label the steady state capital-labour ratio as k*. (Hint: use the horizontal axis to represent k and the vertical axis to represent.) f. Show your answer to the following questions on the function diagram from part (e). What happens to when there is an increase in s? What happens to when there is an increase in n? Explain your intuition of the results.
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