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 ie. 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.
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 ie. 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.
Chapter1: Making Economics Decisions
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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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