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30 Apr 2019

Suppose that the production function is y=ka, where y and k denote production per unit of effective labor and capital per unit of effective labor, respectively. Suppose also that the saving rate, the depreciation rate, the growth rate of the population and the rate of technological progress are s, q, n and g, respectively.

a) what is the condition that characterizes the steady-state?

b) What are the growth rates of production per unit of effective labour, of production per worker, and of total production in steady-state?

c)If a=0.3, q=0.05, n=0.02, g=0.03, k/y=3, and the econmy is in steady-state, what is the saving rate?

d0 What is the marginal product of capital?

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Suppose the output per effective worker is production function is y=10k1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.

a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.

b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state.(Hint: Capital and labor each earn a constant share of the economy's income ).

c) Prove, at the steady state, (i) the capital-output ratio is constant;(ii) the real wage grows at the rate of 2 percent.

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