Assume That a Country's Production Function Is Y = AK^{0 $M P K$}

Essay

Assume that a country's production function is Y = AK^0.3L^0.7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. a. What is the marginal product of capital in this situati on? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital-output ratio or by using the fact that capital's share equals $M P K$ multiplied by $K$ divided by $Y$ .)
b. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by $Y$ must provide for gross growth of $( \delta + n + g ) K$ , where $\delta$ is the depreciation rate.)
c. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital?
d. What must the saving rate be to achieve the Golden Rule level of capital?