申論題

三、A firm produces a product to sell in a competitive market using capital and labor. Given the production function Y=f(K,L)= where Y is output, K is capital input and L is labor input. Suppose that p, r and w are prices of output (Y), capital (K) and labor (L), respectively. Assume that p, r, w are exogeneous and α＞0 and β＞0 and α+β＜1.

(b) What are the first order conditions for this maximization problem? (10 分)