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1 Do not open this exam until told to do so. Department of Economics College of Social and Applied Human Sciences K. Annen, Winter 004 Final (Version ): Intermediate Microeconomics (ECON30) Solutions

2 Final (Version ) ECON30/Winter004/Annen PART : Monopoly and Monopoly Behavior ) In a market with a monopolist who is maintaining second-degree price discrimination the consumer surplus is necessarily zero.. b) False. ( points) ) If he produces anything at all, a profit-maximizing monopolist with some fixed costs and no variable costs will set price and output so as to maximize revenue. 3) If a supplier has a monopoly in a market, the outcome is necessarily inefficient. 4) A market is characterized by imperfect competition if firms are price takers.. b) False. ( points) 5) A monopolist with the cost function c ( q) = 0 + q faces the inverse demand curve p = 80 4q. Calculate the output and the price that maximize the monopolist s profit. Calculate the monopolist s profit. Calculation: MC=q; MR=80-8q; q=80-8q; 0q=80; q=8; p=08 Profit=R-C=8*08-0-8^=600 m = _8 p m = 08 π m = 600_ (3 points) 6) Consider the monopolist in 5) and assume that this monopolist behaves perfectly competitive. Calculate the output and the price that maximize the monopolist s profit, and calculate its profit under this assumption. Calculation: MC=q MR=80-4q; q=80-4q; 6q=80; q=30; p=60 Profit=R-C=30* ^=880 c = _30 p c = 60 π c = _880 (3 points) 7) Consider the monopolist in 5) and 6). Calculate the deadweight loss in this market that is due to the fact that this monopolist has market power. Calculation: (*4)/+(*48)/=43 Final Answer: Deadweight Loss= 43 (4 points) 8) Bulk-discount is an example of second-degree price discrimination.. b) False. ( points)

3 Final (Version ) ECON30/Winter004/Annen 3 9) A monopolist has decreasing average costs as output increases. If the monopolist sets price equal to average cost, it will produce too much output from the standpoint of efficiency. 0) Isabel has just written an interesting new book. Her publisher estimates that the demand for her book among students will be D S ( p) = 500 0p, and the demand among other people will be D o ( p) = p. The publisher has a cost function of c( q) = 0 + 4q. Calculate the output and price that maximize the publisher s profit if the publisher has to charge the same price for students and other people. Calculation: Total Demand = p; Inverse demand: p=0-/40 q; MC=4; MR=0-/0 q; 4=0-/0 q; 6=/0 q; q=30; p= = _30 p = (4 points) ) Consider the same situation than in question 0). But assume now that the publisher can charge a different price for students and other people. Calculate the output and price that maximize the publisher s profit in the market with students and in the market with other people. Calculation: Students: MC=4; MR=5-/0 q; 4=5-/0 q=; 0=q; p=5-/0*0=9/ Other people: MC=4; MR=5-/0 q; 4=5-/0 q; =/0 q; q=0; p=5- /0 0=9.5 S = _0 p S = 4.5 q o = _0 p o = 9.5_(4 points) ) A firm has discovered a new kind of nonfattening, nonhabitforming dessert called zwiffle. It doesn't taste very good, but some people like it and it can be produced from old newspapers at zero marginal cost. Before any zwiffle could be produced, the firm would have to spend a fixed cost of $ F. Demand for zwiffle is given by the equation q = p. The firm has a patent on zwiffle, so it can have a monopoly in this market. a) The firm will produce zwiffle only if F is less than or equal to 36. b) The firm will not produce zwiffle if F >. c) The firm will produce units of zwiffle. d) The firm will produce 9 units of zwiffle. e) None of the above. (4 points) 3) A monopolist that produces a positive amount of output maximizes profits where marginal revenue equals marginal cost.

4 Final (Version ) ECON30/Winter004/Annen 4 PART : Oligopoly 4) A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist.. b) False. ( points) 5) The monopoly outcome in a given market generates a higher total industry output than the Stackelberg outcome in this market. 6) The reaction function of firm measures profits for any given level of output of firm and output of firm. 7) There are two major producers of corncob pipes in the world, both located in Herman, Missouri. Suppose that the inverse demand function for corncob pipes is described by 0 6( q + q ), where q and q is firm s and firm s output respectively. Marginal costs are MC = for both firms. Calculate Cournot equilibrium in this market. Calculation: Reaction function firm : MC=; R=0q-6q^-6q*q; MR=0- q-6 q. =0- q 6 q; q=59/6-/ q. In equilibrium, q=q=q since firms are symmetric. q=59/6 -/ q;.5 q=59/6; q=6.556 = _6.556 q = (4 points) 8) Consider again the market in exercise 7). Calculate the Stackelberg outcome assuming that firm can move first and firm second. Calculation: Reaction function firm : q=59/6-/q; MR of firm : R=0 q 6 q^ 6 q (59/6 -/ q); MR=0 q q; 6-6 q; =6 6 q; q = 59/6=9.833; q=59/6-9.5/6=4.9 = _9.833 q = _4.9 (4 points) 9) The situation in which firms in an oligopoly compete with respect to prices is called Bertrand competition. PART 3: Game Theory 0) A two-person game in which each person has access to only two possible strategies will have at most one Nash equilibrium.

5 Final (Version ) ECON30/Winter004/Annen 5 ) A general has the two possible pure strategies, sending all of his troops by land or sending all of his troops by sea. An example of a mixed strategy is where he sends /4 of his troops by land and 3/4 of his troops by sea. ) Consider the static game as described by the following payoff matrix. (i) (ii) (iii) L R T -,, B -3,5 0,0 The Row player has a dominant strategy. b) False The Column player has a dominant strategy. b) False Find all pure strategy Nash equilibria in this game. Final Answer: (T,L) (6 points) 3) A dominant strategy equilibrium is a set of choices such that each player's choices are optimal regardless of what the other players choose. 4) Consider a revised version of the game Rock, Paper, Scissors. In this revised version each of the two players has a forth option which is called Dynamite. The rule is that Dynamite beats Rock, Paper, and Scissors. Assume that the winner gets a payoff of ; looser gets a payoff of -; and in case of a tie, both get 0. (i) Analyze this situation as a game and write down the payoff matrix. Rock Paper Sci Dy Rock 0,0 -,,- -, Paper,- 0,0 -, -, Sci -,,- 0,0 -, Dyn,-,-,- 0,0 (ii) (iii) Indicate whether the Row and/or the Column player have a dominant strategy. If yes, what is the dominant strategy? Final answer:_dyn is a dominant strategy for both players. Compute all pure Nash equilibria in this game: Final answer: (Dyn, Dyn) (6 points)

6 Final (Version ) ECON30/Winter004/Annen 6 5) The Prisoner s dilemma has one dominant strategy equilibrium. PART 4: Asymmetric Information 6) The fact that an insurance company must be concerned about the possibility that someone will buy fire insurance on a building and then set fire to it is an example of adverse selection. 7) A firm hires two kinds of workers, alphas and betas. The population at large has equal number of alphas and betas. One can't tell a beta from an alpha by looking at her, but an alpha will produce $3,000 worth of output per month and a beta will produce $,500 worth of output in a month. The firm decides to distinguish alphas from betas by having workers take an examination. A worker will be paid $3,000 if she gets at least 60 answers right and $,500 otherwise. For each question that they get right on the exam, alphas have to spend / hour studying and betas have to spend hour. For either type, an hour's studying is as bad as giving up $0 of income per month. This scheme leads to a) a separating equilibrium where alphas score 60 and betas score 0. b) a pooling equilibrium where alphas score 60 and betas score 0. c) a pooling equilibrium where everybody scores 60. d) a pooling equilibrium where everybody scores 0. e) a separating equilibrium where everybody scores 60. (4 points) 8) In a market where there is signaling, a separating equilibrium occurs when economic agents separate their actions as consumers from their actions as producers. 9) In Guelph, Ontario, there are many used cars for sale; the fraction q of these cars are good and the fraction q of them are lemons. Owners of lemons are willing to sell them for $00. Owners of good used cars are willing to sell them for prices above $,500 but will keep them if the price is lower than $,500. There is a large number of potential buyers who is willing to pay $400 for a lemon and $,500 for a good car. Buyers can't tell good cars from bad, but original owners know. (i.) What is the price of a used car if q = 0. 5 (Assume that sellers get the whole exchange surplus). Calculation: < 500; owners of good cars won t sell. Final Answer: p = $400. (ii.) What is the price of a used car if q = 0. (Assume that sellers get the whole exchange surplus). Calculation: $40+ $50=90>500; owners of good cars will sell. Final Answer: p = _90. (4 points)

7 Final (Version ) ECON30/Winter004/Annen 7 30) An example of adverse selection is the situation where someone chooses a car that is not as good as it is claimed to be. PART 5: Externalities 3) If your consumption of toothpaste produces positive externalities for your neighbors (which you ignore), then you are consuming less toothpaste than is Pareto optimal. 3) A noisy production plant disturbing a professor when writing a research paper with profound insights is an example of a consumption externality. 33) A trade between two people is an example of an externality. 34) Suppose that in Halifax the cost of operating a lobster boat is $4,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is 000(x x ). (i) If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then how many boats will enter? Calculation: 000 (-x)=4000; -x = 4; x=8 (ii) Final answer: x = 8 (3 points) If the number of boats that operate in the bay is regulated to maximize total profits, then how many boats will enter? Calculation: 000 ( x) = 4000; x=4 Final answer: x = 4 (3 points) PART 6: Extra-Point Question 35) Find the mixed strategy Nash equilibrium in the static game described by the payoff matrix below. L R T,0 0, B 0,,0 Final Answer: (r=/3, c=/3) where r= prob of playing T and c= prob of playing L. (4 points)

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