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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?
b) Steady state output per worker depends positively on the saving (investment) rate and negatively on the population growth rate and depreciation rate.
c) If the saving rate decreases to say s',the saving curve shifts downwards to s'y and capital and output per worker falls since both the parameters depend positively on the saving (investment) rate. New steady state has lower capital per worker and output per worker.
d) Solow assumes technology as central for explaining the growth process but takes it as exogenous and does not offer any explanations for the same. His convergence hypothesis is majorly flawed and has no empirical validation.
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