# Final Examination Suggested Solution ECON 201

Size: px
Start display at page:

Transcription

1 Final Examination Suggested Solution ECON 201 Beomsoo Kim Spring (16 points, 4 points each)write down the definition of the following terms a) Positive Externality Action by either a producer or consumer which affects other producers or consumers, but is not accounted for in the market price. Positive externality shows positive effects to the party. b) Dominant strategy Strategy that is optimal no matter what an opponent does c) Adverse selection Market failure resulting when products of different qualities are sold at a single price because of asymmetric information, so that too much of the low-quality product and too little of the high-quality product are sold. d) Nash Equilibrium No player can do better by unilaterally changing his or her strategy. 2. (26 points)suppose long-run production of automobile per day is given by q A= K 0.5 L 0.5. a) (7 points)in the short run (holding K fixed) does this production function exhibit diminishing marginal returns, constant marginal returns, or increasing marginal returns? (Explain your answer with an example, like K =5) For example, let s suppose K=4. Short run production function : q A =2L 0.5 MPP d q dl L. so, d MPP 0.5 L. 0foreveryL 0 dl diminishing marginal returns Partial: MPPL 3points; reasoning 3points; conclusion 1point Note: Even if your conclusion was right, you got no partial credit for conclusion part unless you used correct logic to reach the conclusion.

2 b) (7 points)in the long run (allowing both K and L to change) does this production function exhibit decreasing returns to scale, constant returns to scale, or increasing returns or scale? (Explain your answer with an example.) When K=4, L=25, then q A =10, When K=8, L=50, then q A =20 => doubling inputs, there comes exact double output => constant returns to scale Partial: reasoning 5points; conclusion 2points c) (12 points)here is another production function. Q=AL α K ß Describe the situation when constant, increasing, or decreasing returns to scale. If α β 1, then this production function is decreasing returns to scale. If α β 1, then this production function is constant returns to scale. If α β 1, then this production function is increasing returns to scale. Partial: CRS 4points; IRS 4points; DRS 4points 3. (45 points, 7 points each unless specified)suppose a stream is discovered whose water has remarkable healing powers. You decide to bottle the liquid and sell it. The market demand curve is linear and is given as follows: P = 30 Q The marginal cost to produce this new drink is \$3. a) What price would this new drink sell for if it sold in a competitive market? In a competitive market, MC=P P C = 3 b) What is the monopoly price of this new drink? Demand : P=30-Q TR P Q 30 Q Q MR dtr dq 30 2Q Profit maximization happens where MR=MC 30 2Q 3 Q 13.5 P M = 16.5

3 c) What will be the price of this new drink in the long run if the industry is a Cournot duopoly? TR P Q 30 Q Q Q MR 30 2Q Q In Cournot model, output level is determined where MR 1 =MC 30 2Q Q 3 Q Q Based on the symmetry, Q Q substituting Q 2 for Q 1, Q Q Q 9, by symmetry Q 9 Q Q Q 18 Plug Q=18 into market demand curve, then P DC = 12 Partial: Derivation of reaction (or best response) functions for firm 1 and 2 4points; price 3points d) (10 points)what will be the price of this new drink in the long run if the industry is a Stackelberg duopoly? Tell me separate price for the leader and the follower. Suppose that firm 1 is a leader and firm 2 is a follower. In the condition of MR 2 =MC, Q Q TR P Q 30 Q Q Q 30 Q Q Q Q Q MR 16.5 Q Output level is determined where MR 1 =MC 16.5 Q 3 Q 13.5 and Q 6.75 Q Q Q Plug Q=20.25 into market demand curve, then P DS = 9.75 Partial: equilibrium quantity for the leader and the follower 5points; price 5points e) What will be the price of this new drink in the long run if the industry is a Bertrand duopoly?

4 Bertrand equilibrium price equals MC (as in competition) because of incentive to undercut. P DB = 3 f) What will be the price of this new drink in the long run if the firms in the industry collude with one another to maximize joint profit? Collusion price equals monopoly-price because this group plays same role as one monopoly firm. P collusion = (32 points, 7 points each unless specified)suppose that all firms in a constant-cost industry have the following long-run cost curve: c(q) = 5q q The demand in this market is given by QD = p. To produce firms need to have a permit and there are only50 permits a) Derive the supply curve in this situation. Find the market equilibrium price and quantity with the restriction. In the condition of MC=P, P 10q 100 q P We know that there are 50 firms out there, Q 50q 5P 500 Equate to demand: 5P P P = 250, Q = 750 Partial: Supply curve 3points; eq. price 2points; eq. quantity 2points b) If firms are allowed to buy and sell these permits in an open market, what will be the rental price of permits? Will firm s that own permits make profit? Firms will not earn profits but RENTS. The rent will equate the firm s profits to zero: q Profit P q TC Rent 625 Partial: Rental price 4points; Will firm s that own permits make profit? 3points c) (10 points) Due to deregulation policy of the new government the permit

5 requirement in this market has been abolished. What will be the new price in this market? What will be the market equilibrium quantity? Without permits, the market price will fall to the break-even price: AC 5q q MC 10q 100 In the condition of AC=MC, q 10, P 200 Q = 1000 Partial: eq. price 5points; eq. quantity 5points d) (8 points) How much deadweight loss is generated by the permit system? Show your work DWL (21 points, 7 points each) Merriwell Corporation has a virtual monopoly in the ultra highh speed computer market. Merriwell has recently introduced a new computer that will be used by satellite installations around the world. The installations have identical demands for the computers. Merriwell s managers have decided to lease rather than sell the computer, but they have been unable to decide whether to use a single hourly rental charge or a two-part tariff. Under the two-part tariff, users would be levied an access charge plus an hourly rental rate. Merriwell s marketing staff estimates the demand and marginal revenue curves below for each potential user: P = Q MR = Q, where P = price per hour of computer time, and Q = the number of hours of computer time leased per month. Merriwell offers their users extensive maintenance assistance and technical support. The firm s engineers estimate that marginal cost is \$30 per computer hour.

6 a) Assuming that Merriwell chooses to set a single price, what are the firm s profitmaximizing price and output? As a simple monopolist, the firm would set MR=MC : Q 30 Q 300 P TR b) Assuming that Merriwell uses a two-part tariff, what access charge and hourly rental fee should the firm set? Under a two-part tariff with identical consumers, price and outpu are determined where P=MC Q 30 Q 600 P To find access charge, must find the consumer surplus which is area A. area A Partial: Access charge 4points; hourly rental fee 3points c) Compare the firm s revenues under the options in (a) and (b). Set access charge of \$4500 and a \$30 hourly fee. TR TR doubles with a two-part tariff as compared with the single hourly rental charge option. Partial: TR of (a) 3.5points; TR of (b) 3.5 points Note: If you did not get TR of (a), (b) explicitly, but you correctly compared the magnitudes then you get 3 points.

7 6. (30 points, 10 points each)the market for used cars in a particular region includes both high quality and low quality cars. High quality cars are sold primarily to quality sensitive customers, while low quality cars are sold to price sensitive buyers. The submarkets for high quality and low quality cars can be described by the supply and demand curves: QD H = 160, P H QS H = - 48, P H QD L = 110, P L QS L = 20, P L, where QD H, QS H refer to the quantities demanded and supplied of high quality cars, QD L, QS L refer to the quantities demanded and supplied of low quality cars, P H and P L refer to the prices of high quality and low quality cars. All quantities are measured in cars per month, prices are measured in dollars. a) Assuming that buyers and sellers are both able to distinguish low quality and high quality cars, determine the equilibrium price and quantity in each submarket. If we assume perfect information by buyers and sellers, buyers correctly appraise quality. Supply and demand equated in each submarket: QD QS and QD QS In the QD H = QS H, P P P 8000 Q In the QD L = QS L, P P P 4000 Q Partial: equilibrium price of low quality, equilibrium quantity of low quality, equilibrium price of high quality, equilibrium quantity of high quality 2.5points each b) Examine the case where sellers are able to accurately determine used car quality but buyers are not. You may assume that buyers assume that all cars are of average quality so that an average demand curve is appropriate. Determine the price and quantity in each submarket. With imperfect information, buyers treat all cars as average. Let QD A represent average demand :

8 QD QD QD P P P In order to determine prices and quantities in submarkets, equate QD A to QS H and QS L. In the QD A = QS H, P P P Q In the QD A = QS L, P P P Q c) Make a conjecture what will happen in the market until final long run equilibrium is reached. You must describe the eventual outcome, but no calculations are required for this part of the problem. In part (b), buyers initially believed that there were equal numbers of high and low quality cars. However, low quality cars are more numerous. Buyers began to adjust their expectations of quality to something less than average. This shifts high quality supply further to the left. Furthermore, it would shift demand towards the low quality demand curve as buyers assume that a car will be of low quality. Shifts continue until only low quality cars are available.