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Problem 1. Production: cost minimization and profit maximization (11 points) In class we introduced two different characterizations of firm decisions: cost minimization and profit maximization. In this exercise you are asked to show that the two optimization problems are equivalent ways of solving the same problem. Consider a mango farm in the Philippines. The farm has a production function y = f (L, K, F) . where L is labor, K is capital, and F is farm land. The price of labor is w, the price of capital is r, the price of land is s, with all of the prices positive. Assume also f/ >0 and ff, 1 and plot the marginal cost c (w, r, s, y, F) and the average cost c (w, r, s, y, F) /y as a function of y. How does the supply curve for the firm look like? (3 points) 8. We now consider market supply and demand for the only well-behaved case, that is, for a + 8