Consider Problem 1.10. Suppose there is a marginal increase in K. (a) Derive an expression (in terms of K/Y, , the marginal product of capital

Consider Problem 1.10.

Suppose there is a marginal increase in K.

(a) Derive an expression (in terms of K/Y, δ, the marginal product of capital FK, and the elasticity of substitution between capital and effective labor in the gross production function F (•)) that determines whether a marginal increase in K increases, reduces, or has no effect on the share of net capital income in net output.

(b) Suppose the capital-output ratio is 3, δ = 3%, and the rate of return on capital

(FK − δ) = 5%. How large must the elasticity of substitution in the gross production function be for the share of net capital income in net output to rise when K rises?