ba415_ps2key3 - zmir University of Economics Faculty of...

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1 İzmir University of Economics Faculty of Economics and Administrative Sciences Department of Business Administration Surname, Name: Student No: BA 415 PROBLEM SET II KEY (January 20, 2011) 1) Suppose that a competitive firm’s marginal cost of producing output q is given by () 3 2 MC q q = + . Assume that the market price of the firm’s product is $9. a) What level of output will the firm produce? Solution: q = 3. b) What is the firm’s producer surplus? Solution: producer surplus = 9. 2) A number of stores offer film developing as a service to their customers. Suppose that each store that offers this service has a cost function 2 ( ) 50 0.5 0.08 Cq q q = ++ . If the going rate for developing a roll of film is $8.50, is the industry in long run equilibrium? If not find the price associated with long run equilibrium. Solution: The industry is not in long run equilibrium because profit is greater than zero. P=4.50. 3) A firm faces the following average revenue (demand) curve 120 0.02 PQ = where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by 60 25000 CQ = + . Assume that the firm maximizes profits. a) What is the level of production, price, and total profit per week? Solution: Q = 1500 P = 90 cents Profit = 200 b) If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit? Solution: Q = 1150 P* = 83 cents ( )( ) ( ) ( ) 83 1,150 60 1,150 25,000 1450 π = += 4) Suppose that an industry is characterized as follows: 2 100 2 Firm total cost function 90 2 Industry demand curve = + = a) If there is only one firm in the industry, find the monopoly price, quantity, and level of profit. Solution: Q=11.25 P=67.50 The level of profit =406.25 b) Find the price, quantity, and level of profit if the industry is competitive. Solution: Q=15 P=60 The level of profit =350. 5) The market for wheat consists of 50 identical firms, each with the total cost function shown as 2 90 0.01 TC Q = + where Q is measured in bushels per year. The market demand curve for wheat is 9000 2000 QP = , where Q is again measured in bushels and P is the price per bushel. a) Determine the short run equilibrium price and quantity that would exist in the market. Solution: Market supply Q = 50P P = 2.00 Q= 5000 b) Calculate the profit maximizing quantity for the individual firm. Calculate the firm’s short run profit (loss) at that quantity.
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2 Solution: P = 2 = 0.02Q so Q = 100 Firm’s profit = TR – TC = 2000 - 190 = 1810 c) Analyze the individual firm’s position in terms of the shutdown condition. Should this specific firm operate or shut down in the short run? Solution: AVC=1.9 at p=2 q=100 so The firm should operate since p larger than AVC 6) Answer the following questions using the above diagram. Justify your answers. a) At P=$80, what is the profit-maximizing output in the short run? Solution: 39 b) At P=$80, how much is profit in the short run?
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ba415_ps2key3 - zmir University of Economics Faculty of...

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