Suppose the production function is Y = K(e EL) 1, 0

Suppose the production function is Y = Kα(e φEL)

1−α, 0 <α< 1. E is the amount of education workers receive; the rest of the notation is standard. Assume that there is perfect capital mobility. In particular, K always adjusts so that the marginal product of capital equals the world rate of return, r ∗.

(a) Find an expression for the marginal product of capital as a function of K, E, L, and the parameters of the production function.

(b) Use the equation you derived in

(a) to find K as a function of r ∗, E, L, and the parameters of the production function.

(c) Use your answer in

(b) to find an expression for d(lnY)/dE, incorporating the effect of E on Y via K.

(d) Explain intuitively how capital mobility affects the impact of the change in E on output.