Consider the Solow growth model with technological progress at the rate g, population growth at the rate n, and capital depreciation rate at the rate δ. The savings rate is denoted by s and the production function is given by: Y = Kα (AL)1-α , 0 < α < 1. Y is aggregate output, K is aggregate capital, L is aggregate labour, A is technology and AL is effective labour. (a) Let ݇k = K/AL which denotes capital per unit of effective labour. Obtain the production function in terms of capital per unit of effective labour. Explain the properties this production function satisfies. (b) Derive the key equation that governs the evolution of capital per unit of effective labour in this Solow model. Provide the steady state value of capital and output in per unit of effective labour terms. What are the growth rates of capital per unit of labour and output per unit of labour in the steady state? (c) Analyse the effect of a decrease in the population growth rate on the steady state values of endogenous variables. Illustrate your result. (d) What are the important predictions obtained from the basic Solow model? How do the qualitative and quantitative predictions measure up to reality?
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Consider the Solow growth model with technological progress at the rate g, population growth at the rate n, and capital
Y = Kα (AL)1-α , 0 < α < 1.
Y is
(a) Let ݇k = K/AL which denotes capital per unit of effective labour. Obtain the production function in terms of capital per unit of effective labour. Explain the properties this production function satisfies.
(b) Derive the key equation that governs the evolution of capital per unit of effective labour in this Solow model. Provide the steady state value of capital and output in per unit of effective labour terms. What are the growth rates of capital per unit of labour and output per unit of labour in the steady state?
(c) Analyse the effect of a decrease in the population growth rate on the steady state values of endogenous variables. Illustrate your result.
(d) What are the important predictions obtained from the basic Solow model?
How do the qualitative and quantitative predictions measure up to reality?
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