Consider a firm that produces output using a Cobb Douglas combination of capital and labour:Y=KL1 , 0<<1

Suppose that the firm's price is fixed in the short run; thus, it takes both the price of its product, P,

and the quantity, Y, as given. Input markets are competitive; thus, the firm takes the wage, W, and the rental

price of capital, rk as given.

What is the first-order condition for the profit-maximizing choice of K. Is the second-order condition

satisfied?