1 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 CEVAPLAR 1. Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for $100 per thousand. Conigan's total and marginal cost curves are: TC = 3,000,000 + 0.001Q 2 MC = 0.002Q where Q is measured in thousand box bundles per year. a. Calculate Conigan's profit maximizing quantity. Is the firm earning a profit? b. Analyze Conigan's position in terms of the shutdown condition. Should Conigan operate or shut down in the short-run? Solution: a. Given the competitive nature of the industry, Conigan should equate P to MC. 100 = 0.002Q Q = 50,000 To determine profit: π = TR - TC TR = PQ TR = $100 50,000 TR = 5,000,000 TC = 3,000,000 + 0.001(50,000) TC = 3,000,000 + 2,500,000 TC = 5,500,000 π = 5,000,000-5,500,000 π = -500,000 Conigan is losing 500,000 per year. 2
2 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 b. To determine if the firm should operate or shutdown, we must compare P to AVC. TVC AVC = Q TVC = TC - TFC TVC = 5,500,000-3,000,000 TVC = 2,500,000 2,500,000 AVC = = $50 50,000 AVC = 50; P = $100 The firm should operate since P > AVC. 4 2. Homer's Boat Manufacturing cost function is: C ( q) = q + 10, 240. The 75 128 75 3 marginal cost function is: MC ( q) = q. If Homer can sell all the boats he 32 produces for $1,200, what is his optimal output? Calculate Homer's profit or loss. Solution: The profit maximizing output level is where the market price equals marginal cost (providing the price exceeds the average variable cost). To determine the optimal output level, we need to first equate marginal cost to the market price. 75 3 That is, MC ( q) = q = P = 1, 200 q = 8. The average variable cost at this 32 75 3 75( 512) output level is: AVC ( 8) = ( 8) = = 300. Since P > AVC ( 8 ), Homer will 128 128 maximize profits at 8 units. Homer's profits are: 75( 8) 4 π = Pq C ( q) = 1, 200( 8) + 10,240 = 3,040. Homer will produce and 128 make a loss as losing $3,040 is better than not producing and losing $10,240.
3 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 3. The market for wheat consists of 500 identical firms, each with the total and marginal cost functions shown: TC = 90,000 + 0.00001Q 2 MC = 0.00002Q, where Q is measured in bushels per year. The market demand curve for wheat is Q = 90,000,000-20,000,000P, 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. b. Calculate the profit maximizing quantity for the individual firm. Calculate the firm's short-run profit (loss) at that quantity. c. Assume that the short-run profit or loss is representative of the current long-run prospects in this market. You may further assume that there are no barriers to entry or exit in the market. Describe the expected long-run response to the conditions described in part b. (The TC function for the firm may be regarded as an economic cost function that captures all implicit and explicit costs.) Solution: a. Market supply is horizontal sum of individual firm supply (firms MC curve). Firm's TC = 90,000 + 0.00001Q 2 MC = 0.00002Q = P. Solve for Q in terms of P to express as supply curve P = 0.00002Q Q = 50,000P Market supply curve is horizontal sum of firm supply curve or N-times the firm supply curve (N is the number of firms). Q S = 500(50,000)P Q S = 25,000,000P
4 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 equate Q S and Q D to determine price and quantity 25,000,000P = 90,000,000-20,000,000P 45,000,000P = 90,000,000 P = $2.00 Q = 25,000,000P Q = 25,000,000(2) Q = 50,000,000 b. To determine the firm's output, equate price and marginal cost - Firm's MC = 0.00002Q. P = 2 = 0.00002Q Q = 100,000 Firm's π = TR - TC TR = 2.00(100,000) TR = 200,000 TC = 90,000 + 0.00001Q TC = 90,000 + 0.00001(100,000) TC = 190,000 π = 200,000-190,000 = 10,000 2 2 c. Firms are earning economic profit so we would expect entry to occur, causing the market supply curve to shift rightward. As the market supply curve shifts rightward, price falls, which in turn causes each firm to reduce its output. This will continue until we reach long-run equilibrium at zero profit.
5 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 4. The elected officials in a west coast university town are concerned about the "exploitative" rents being charged to college students. The town council is contemplating the imposition of a $350 per month rent ceiling on apartments in the city. An economist at the university estimates the demand and supply curves as: Q D = 5600-8P Q S = 500 + 4P, where P = monthly rent, and Q = number of apartments available for rent. For purposes of this analysis, apartments can be treated as identical. a. Calculate the equilibrium price and quantity that would prevail without the price ceiling. Calculate producer and consumer surplus at this equilibrium (sketch a diagram showing both). b. What quantity will eventually be available if the rent ceiling is imposed? Calculate any gains or losses in consumer and/or producer surplus. c. Does the proposed rent ceiling result in net welfare gains? Would you advise the town council to implement the policy? Solution: a. To calculate equilibrium set Q D = Q S and solve for P. 5600-8P = 500 + 4P 5100 = 12P P = 425 Substitute P into Q D to solve for Q Q D = 5600-8(425) Q = 2200 Q = 5600 8P P = 700 0.125Q Q = 500 4P P = 125+ 0.25Q C.S. = area A D S D
6 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 C.S. = 0.5(700-425) x 2200 C.S. = 302,500 P.S. = area B P.S. = 0.5(425-125) x 2200 P.S. = 330,000 Sum of producer and consumer surplus is: 302,500 + 330,000 = 632,500 b. Eventually the market will settle at the quantity supplied corresponding to $350 rent. Q S = 500 + 4(350) Q S = 1900 Q D at P = 350 Q D = 5600-8(350) = 2800 There will be a shortage of 900 apartments. Gain = Consumer surplus is area A Area A = (425-350) x 1900 = 142,500
7 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 Area B = loss in consumer surplus To find area B, first find consumer reservation price corresponding to an output of 1900. P = 700-0.125(1900) = 462.50 Difference Q = 2200-1900 = 300 Area B = 0.5(462.50-425) x (2200-1900) Area B = 5625 Loss in consumer surplus is 5625. c. Area C is loss in producer surplus not offset by gain in consumer surplus. Area C = 0.5(425-350) x (2200-1900) Area C = 11,250 Area A is a gain in consumer surplus, but it is offset by a loss in producer surplus. The net changes are thus B (lost C.S.) and C (lost P.S.). The policy thus results in a deadweight loss. The deadweight loss = lost C.S. + lost P.S. or 5625 + 11250 = 16,875. Deadweight loss = 16,875 5. Tad's bait shop has a monopoly on the bait market at Sanderson's Lake. The demand curve for bait is revenue function is: MR ( Q) D 1 = 56 8 = 7 D. 8 1 = 7. 4 Q P P Q This implies the marginal Q Tad has two employees he can use to search for bait. The marginal cost of using Amanda to search for bait is: 1 4 3 = 8 MC ( Q ) = Q. The marginal cost of using Andrew to search for bait is: M M M MC ( Q ) Q. Determine how many units of bait each employee should N N N gather. What is the price Tad receives for selling the bait? Solution: We can think of Tad's employees as two different plants that Tad owns. We can then determine the individual plant supply and aggregate to determine Tad's total output. This is done as follows: ( ) 3 8 8 3 8 = M + N = 4 M + N. 3 20 Q =. 3 1 MCM QM = QM QM = 4 MC M. 4 Also, MC ( Q ) = Q Q = MC. This implies that Tad's aggregate supply N N N N N is: Q Q Q MC MC Since marginal costs will be equivalent across plants, MC Tad's marginal cost as a function of output at both plants is:
8 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 3 MC ( Q) = Q. Since Tad is a monopolist, he will set marginal revenue equal 20 to marginal cost to determine optimal output. This is: 3 1 20 4 MC ( Q) = Q = MR ( Q) = 7 Q Q = 17.5. At this output level, Tad's marginal cost is $2.63. This means that Amanda is gathering 10.5 units of bait while Andrew gathers 7 units of bait. Tad receives $4.81 per unit of bait.