Problem #1

1.Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. the prices of each unit of capital and labor are r and w, respectively. The output good y sells for $p per unit.

Firm A's production function is y = f_A(K,L) = K^1/4 L^1/4. The profit function is thus:

_A(K,L) = K^1/4 L^1/4 - rK -wL

a.Find the profit maximizing levels of K and L as functions of r, w, and p.

Suppose that r = w = $1 and p = $4. What is the profit maximizing level of output, y ?