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Question 2 Assume an economy's aggregate production function has the following form Y = AK³L¹-* Where a = 0.25 and where output Y is produced using capital K and labour L, and A is total factor productivity. The population growth rate n is 1.5% per year. The depre- ciation rate of capital is 10%. Total factor productivity equals 20 i.e. A = 20 and we assume the growth rate of A is zero. a) Show that the production function displays constant returns to scale. b) Show that the production function displays diminishing returns to capital. c) If the country's savings rates is 20%, find its steady state capital stock per capita, income per capita, consumption per capita, and investment per capita. d) What is the optimal i.e. Golden Rule capital stock per capita in this economy in steady state? Is this economy dynamically efficient? Explain your answer.

Question 2 Assume an economy's aggregate production function has the following form Y = AK³L¹-* Where a = 0.25 and where output Y is produced using capital K and labour L, and A is total factor productivity. The population growth rate n is 1.5% per year. The depre- ciation rate of capital is 10%. Total factor productivity equals 20 i.e. A = 20 and we assume the growth rate of A is zero. a) Show that the production function displays constant returns to scale. b) Show that the production function displays diminishing returns to capital. c) If the country's savings rates is 20%, find its steady state capital stock per capita, income per capita, consumption per capita, and investment per capita. d) What is the optimal i.e. Golden Rule capital stock per capita in this economy in steady state? Is this economy dynamically efficient? Explain your answer.

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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Question 2 Assume an economy's aggregate production function has the following form Y = AK"L?- Where a = 0.25 and where output Y is produced using capital K and labour L, and A is total factor productivity. The population growth rate n is 1.5% per year. The depre- ciation rate of capital is 10%. Total factor productivity equals 20 i.e. A = 20 and we assume the growth rate of A is zero. a) Show that the production function displays constant returns to scale. b) Show that the production function displays diminishing returns to capital. c) If the country's savings rate s is 20%, find its steady state capital stock per capita, income per capita, consumption per capita, and investment per capita. d) What is the optimal i.e. Golden Rule capital stock per capita in this economy in steady state? Is this economy dynamically efficient? Explain your answer.
Transcribed Image Text:Question 2 Assume an economy's aggregate production function has the following form Y = AK"L?- Where a = 0.25 and where output Y is produced using capital K and labour L, and A is total factor productivity. The population growth rate n is 1.5% per year. The depre- ciation rate of capital is 10%. Total factor productivity equals 20 i.e. A = 20 and we assume the growth rate of A is zero. a) Show that the production function displays constant returns to scale. b) Show that the production function displays diminishing returns to capital. c) If the country's savings rate s is 20%, find its steady state capital stock per capita, income per capita, consumption per capita, and investment per capita. d) What is the optimal i.e. Golden Rule capital stock per capita in this economy in steady state? Is this economy dynamically efficient? Explain your answer.
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