A country produces output using a production function:Y = F(K, L) = AxK0.5 L0.5 where L is labour, K is capital and A is total factor productivity. Prove that this function exhibits constant returns to scale.Assume that A = 3 and its growth rate is zero. The country has a population growth of 1.5% per year (0.015) and capital depreciates at a rate of 10% (0.10) per year. If the country saves 30% (0.3) of national income, find the steady state levels of capital per worker, as well as consumption and income per worker in the Solow growth model corresponding to this country. What would be the rate of growth of GDP per capita in steady state? Calculate the “Golden Rule” level of capital stock in steady state. Is this economy dynamically efficient?

The steady state is reached where the per capita variables no longer undergo the change. Economies…

Answered: A country produces output using a…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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A country produces output using a production function:

Y = F(K, L) = AxK^0.5 L^0.5

where L is labour, K is capital and A is total factor productivity.

Prove that this function exhibits constant returns to scale.
Assume that A = 3 and its growth rate is zero. The country has a population growth of 1.5% per year (0.015) and capital depreciates at a rate of 10% (0.10) per year. If the country saves 30% (0.3) of national income, find the steady state levels of capital per worker, as well as consumption and income per worker in the Solow growth model corresponding to this country. What would be the rate of growth of GDP per capita in steady state?
Calculate the “Golden Rule” level of capital stock in steady state. Is this economy dynamically efficient?

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