Question

Consider a firm with the following production function y = min{5xų,50x2} For the whole exercise let the price of input 1 be $10 and the price of input 2 be $50. a) Show that the production function has decreasing returns to scale. (4 points) b) Obtain the cost function. (6 points) C) Plot in the same graph the marginal cost and the average cost (4 points) d) Solve the profit maximization problem and calculate the profits of the firm when the output price is $12. (Hint: it might be a good idea to use the cost function you obtained before) (6 points)

Answer 1

Date ya Imeri(sx, 50 x₂) P. -10 P2=50 a) F (dx, dx₂) - min (six, so dx) = 1 - y Rey decreasing return to scale cainst At optimality sx, = 4² 50x2 - y² 2 2 x = & tra 392 2 Cost - P, x, + P2x2 = 3y² MC - ac sy = AL=39 by cast me =64 & Prefit is max when ACES Perice - Me →Y by = 12 y = 2 x₂ = To produced € x = The Qunit should be Resit 12 (2) - 3/2)² = 2n- 3/4 = 12 = 120 Profit