_ 1 1 . . Let Q = F(K, L) = 5K1\" + L1/2 denote a CES production function with K as capital Input and L as labour Input. The price per unit of output Is p, the price per unit of capital' Is r, and the price per unit of labor Is w. (3) Write down the prot function It (b) Write down the rstorder 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 7t. (d) Let Jt * (p, r, W): 7t(K * L * , p, r, w) be the optimal profit as a function of (P. r, w). Show that an * lar - K * and 67: * law = - L * .(Special cases of Hotelling' s lemma.) mum"... _