Question

Consider the Solow growth model with the following production function where y is output. K is capital, s is the productivity and is labor. Assume that 0 < α < 1 Further, suppose that labor grows at a constant rate n. That is. 1 + n. Also, assume that capital depreciates at rate d and that gross investment in capital is fraction s of output. a Letting k-N, obtain the law of motion for capital accumulation per unit of workers, k. Hint: Solve until no more substitutions are possible in the law of motion for capital) b Solve for the equations characterizing the steady-state values and determine the steady-state values of capital, k. output, y, investment, i, and consumption, c, all per unit of workers Determine what the growth rates of aggregate output. Y, capital. K, investment, I and consumption, C, are. c What is the effect of an increase in investment rate of capital, s, on aggregate capital, output nd consumption, both in the short-run (before the final steady-state) and the long-run (after the final steady state)? d What is the effect of an increase in the productivity, z, on aggregate capital, output and consumption, both in the short-run (before the final steady-state) and the long-run (after the final steady state)? e Discuss which policy is more effective: an increase in saving rate s or an increase in produc tivity. Explain your answers.

A and B only

Answer 1

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