Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium c
Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale.
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(a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the equa- tion how the k evolves over time. At what rate does
aggregate output , aggregate consumption, aggregate investment, and per capita income grow at steady state? -
(b) Suppose that β increases. Discuss the impact of this change on the quantity of capital per efficieny units of labor, k, in steady state and on the growth rate in per capita income. Does the economic well being increase? Explain.
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(c) Suppose that n increases. Discuss the impact of this change on the quantity of capital per efficieny units of labor, k, in steady state and on the growth rate in per capita income. Does the economic well being increase?
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