Question

Consider a version of the Solow model where population grows at the constant rate ? > 0 and labour efficiency grows at rate ?. Capital depreciates at rate ? each period and a fraction ? of income is invested in physical capital every period. Assume that the production function is given by:

?_{t} =
?_{t}^{a}(?_{t}?_{t}
)^{1-a}

Where ??(0,1), ?_{t} is output, ?_{t} is
capital, ?_{t} is labour and ?_{t} is labour
efficiency.

a. Show that the production function exhibits constant returns to scale, i.e. is homogenous of degree 1.

b. Derive an expression for the accumulation of capital per
worker in this economy, i.e. ∆?_{t}+1 where ?_{t} ≡
?_{t}/?_{t}?_{t} .

c. What is the steady-state condition in this economy? Explain the intuition behind the equilibrium condition and illustrate the steady state in a diagram.

d. What happens to capital and output per worker if the capital depreciation rate increases? Illustrate your answer in a diagram.

e. What is the steady state growth rate of ?_{t} ≡
?_{t}/?_{t}?_{t}?

Answer #1

The growth rate of yt is zero.

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