Consider the following Solow growth model in which households save a constant fraction of their income....

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Consider the following Solow growth model in which households save a constant fraction of their income. Let N be the population (also the labor force) in the current period. Assume that the population follows N = (1+n)N where N'is the population in the future period, and n is the net population growth rate. Assume that the output is produced according to the production function Y= ZAK, N), where z is the total factor productivity, K is capital stock, and RK, N) exhibits constant returns to scale. Capital depreciates at the rate d where o < d < 1. The capital stock changes over time according to K'= (1 - d)K + / where / is the investment level. (a) Derive the equation that determines the future capital-per-worker in competitive equilibrium. Here is some additional information for parts (5b), (5c), and (5d). Suppose that the economy is initially in steady state, and experiences a natural disaster (e.g. the recent quake and tsunami in Japan in 2011) that destroys some of the capital stock. (For simplicity, assume that population does not decrease as result of the disaster.) (b) Determine the short-run effects of this disaster on capital per worker, and output per worker. Does the economy grow in terms of output per worker in the short run? Explain. (C) Determine the long-run effects of this disaster on capital per worker, and output per worker. Does the economy grow in terms of output per worker in the long run? Explain. (d) Based on the reaction of the economy you discussed in (5b), some politicians conclude that natural disasters are "good" for the economy. Explain clearly why such a conclusion is or is not wrong. Consider the following Solow growth model in which households save a constant fraction of their income. Let N be the population (also the labor force) in the current period. Assume that the population follows N = (1+n)N where N'is the population in the future period, and n is the net population growth rate. Assume that the output is produced according to the production function Y= ZAK, N), where z is the total factor productivity, K is capital stock, and RK, N) exhibits constant returns to scale. Capital depreciates at the rate d where o < d < 1. The capital stock changes over time according to K'= (1 - d)K + / where / is the investment level. (a) Derive the equation that determines the future capital-per-worker in competitive equilibrium. Here is some additional information for parts (5b), (5c), and (5d). Suppose that the economy is initially in steady state, and experiences a natural disaster (e.g. the recent quake and tsunami in Japan in 2011) that destroys some of the capital stock. (For simplicity, assume that population does not decrease as result of the disaster.) (b) Determine the short-run effects of this disaster on capital per worker, and output per worker. Does the economy grow in terms of output per worker in the short run? Explain. (C) Determine the long-run effects of this disaster on capital per worker, and output per worker. Does the economy grow in terms of output per worker in the long run? Explain. (d) Based on the reaction of the economy you discussed in (5b), some politicians conclude that natural disasters are "good" for the economy. Explain clearly why such a conclusion is or is not wrong.

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Explanation 1 The populace develops at a steady rate g Subsequently the current populace addressed by N and future populace addressed by N are connect... View the full answer