A firm produces two products, X and Y. The production technology displays the following costs, where C(i, j) represents the cost of producing i units of X and j units of Y: C(0, 50) = 100 C(5, 0) = 150
C(0, 100) = 210 C(10, 0) = 320
C(5, 50) = 240 C(10, 100) = 500

Required:
Does this production technology display economies of scale?

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?