Let Q=F(K,L)=K1/4 L1/4 denoted a production function with K as capital input and L as labour input. The price per unit of output isp, the price per unit of capital isr, and the price per unit of labor is w.

(a) Write down the profit function .

(b) Write down thefirst-order conditions for maximum profit.

(c) Find the choices K* = K*(p, r, w) of K and L* = L*(p, r, w) of L that maximize .

(d) Let *(p, r, w)= (K*, L*, p, r,w) be the optimal profit as a function of(p, r,w). Show that */p=F(K*,L*)=Q*. (Special case ofHotelling's lemma.)