5. A firm operates using the production technology f(L,K) = √(LK). The wage rate is w = 1, the rental rate of capital is r = 3, and the price of the output is p = 10.
5(a). (23 points) Show that the firm’s short-run demand for labor as a function of the fixed level of capital K > 0 satisfies
L(K) = 25K.
(b). (20 points) What is the effect of a marginal change in K on the profit of the firm?