4. Consider the steady state of the Solow model with population growth and technological progress. The...

  

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4. Consider the steady state of the Solow model with population growth and technological progress. The production function is Y = F(K,EL), and the per capita production function is f(k) = F(k,1), where k is defined as K/EL. E grows at the rate g, while L grows at the rate n. = a. (Optional) The marginal product of capital is defined as partial derivative of F(K,EL) with respect to K. Demonstrate that it also equals f'(k), that is, derivative of the function f(k). If you cannot demonstrate it, just proceed with the new definition MPK = f'(k). b. Using the result in (a), demonstrate that the share of capital income in the economy (and therefore share of labor income as well) stays constant on the steady state growth path. C. From here demonstrate at which rate the real rental price of capital and the real wage should grow in the steady state. d. Let us get back to the equation MPK = PK/P(r+8). In the long run, the prices of investment and consumption goods should equalize, so PK/P=1. In that case, what does the Solow model predict about long-run behavior of the real interest rate? 4. Consider the steady state of the Solow model with population growth and technological progress. The production function is Y = F(K,EL), and the per capita production function is f(k) = F(k,1), where k is defined as K/EL. E grows at the rate g, while L grows at the rate n. = a. (Optional) The marginal product of capital is defined as partial derivative of F(K,EL) with respect to K. Demonstrate that it also equals f'(k), that is, derivative of the function f(k). If you cannot demonstrate it, just proceed with the new definition MPK = f'(k). b. Using the result in (a), demonstrate that the share of capital income in the economy (and therefore share of labor income as well) stays constant on the steady state growth path. C. From here demonstrate at which rate the real rental price of capital and the real wage should grow in the steady state. d. Let us get back to the equation MPK = PK/P(r+8). In the long run, the prices of investment and consumption goods should equalize, so PK/P=1. In that case, what does the Solow model predict about long-run behavior of the real interest rate?