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econ11practice4 - Practice Problem Set 4 ECON 11...

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Practice Problem Set 4 ECON 11 Summer Session C 2010 Microeconomic Theory Yong Yang (You may not use calculators in the exam. The exam questions will have simpler numbers.) 1. Let P = 50 is given and fixed, so a firm can sell infinite amount of its product at the price. Suppose the firm’s cost function is C = 100 + 20 Q + Q 2 . (a) How many units of Q would maximize the firm’s profit? (b) Calculate the profit. Is it positive or negative? (c) Find the firm’s variable costs and derive the average variable cost. (d) Find the marginal cost and depict it with the average variable cost. (e) Would the firm produce positive amount of its product when P = 30? If so, how much would the firm’s profit? What if P = 10? (f) At which level of P or below would the firm shut down? (g) Verify that the firm’s profit becomes 0 when P = 40 and the firm adjusts Q to maximize its profit. Suppose all the firms in the market have the same cost function and face the same price. Would firms enter or exit at P = 50? Would they enter or exit at P = 40, at P = 30, and at P = 10? (h) Make a comment on the following statement: “In the long run, the price would be determined at P = 40 by firms’ entry and exit as long as C = 100 + 20 Q + Q 2 .” 2. Let P K = 25 and P L = 4. Production function is given by Q = LK . Assume the firm has a fixed input K = 4 in the short run. (a) Find the firm’s short run cost function.( Hint : Recall Question 4 from Problem Set 3.) (b) Find the variables costs, the average cost, the average variable cost, and the marginal cost. (c) Show that the average cost is minimized at Q = 10. Show also that MC = AC when Q = 10. (d) If the price of the firm’s product is given by P = 40, what level of Q maximizes the profit? Find also L to produce that level of Q and compute the total cost. How much is the profit?
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