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Consider a version of the Solow model where the population growth rate is 0.05. There is...

Consider a version of the Solow model where the population growth rate is 0.05. There is no technological progress. 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 = ?t1/2 ?t1/2

where ?t is output, ?t is capital and ?t is labour.

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

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

c. What happens to capital and output per worker if the saving rate decreases? Illustrate your answer in a diagram and explain the mechanisms behind the transition to the new steady state.

d. What is the main criticism of the Solow model?

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