Do not open this exam until told to do so. Solution

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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, Fall 003 Final (Version): Intermediate Microeconomics (ECON30) Solution

2 Final (Version ) ECON30/Fall 003/Annen PART : Monopoly and Monopoly Behavior ) Since a monopoly charges a price higher than marginal cost, it will produce an inefficient amount of output. ) A monopolist will always equate marginal revenue and marginal cost when maximizing profit. 3) A monopolist who is not able to price discriminate will never operate where demand is elastic.. b) False. ( points) 4) A monopolist faces the inverse demand curve p = 0 6q and marginal costs MC =. Calculate the output and the price that maximize the monopolist s profit. MC = MR = 0 q 08 = q q = 9 p = 0 6*9 = 66 m = 9 p m = 66 (4 points) 5) Consider the monopolist in 4) and assume that this monopolist behaves perfectly competitive (i.e. it takes price as given). Calculate the output and the price that maximize the monopolist s profit under this assumption. MC = MR = 0 6q 08 = 6q q = 8 c = 8 p c = (4 points) 6) Consider the monopolist in 4) and 5). Calculate the deadweight loss in this market that is due to the fact that this monopolist has market power. ( 8 9)(66 ) / = 43 Final Answer: Deadweight Loss= $43 (4 points) 7) In a market with a monopolist who is maintaining third-degree price discrimination the consumer surplus is necessarily zero.. b) False. ( points) 8) Bulk-discount is an example of third-degree price discrimination.. b) False. ( points)

3 Final (Version ) ECON30/Fall 003/Annen 3 9) A monopolist has decreasing average costs as output increases. If the monopolist sets price equal to average cost, it will (Hint: If the average cost curve is decreasing, remember where the marginal cost curve must be). a) produce too much output from the standpoint of efficiency. b) lose money. c) produce too little output from the standpoint of efficiency. d) maximize its profits. e) face excess demand. (4 points) PART : Oligopoly 0) A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist.. b) False. ( points) ) The monopoly outcome in a given market generates a higher total industry output than the Cournot outcome in this market. ) The negative slope of the reaction function of a firm in a duopoly means that the profit-maximizing output of one firm increases as the output of the other firm increases. 3) 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 6 4( q + q ), where q and q is firm s and firm s output respectively. Marginal costs are MC =. Calculate the Cournot equilibrium quantity and price for firm and in this market. (Note that firm s marginal revenue equals MR = 6 8q 4q and that firm s marginal revenue equals MR = 6 8q 4q.) Reaction Function Firm : 6 8q 4q = q = 0 / q. Since firms are symmetric, the reaction function of Firm is q = 0 / q. The Cournot outcome is given where the two reaction functions intersect. Thus, q = 0 / (0 / q ) q = / 4q 3/ 4q = 0 q = 40/ 3 = q p = 6 4(80 /3) = (486 30) / 3 = 66 / 3 = _40/3 q = 40/3_ p = 66/3 (4 points) 4) Consider firm in exercise 3). Assume that firm produces first and firm produces second. Firm (= follower) observes that firm (= leader) produced an output of q = 0. Calculate the output for firm that maximizes its output given firm s output.

4 Final (Version ) ECON30/Fall 003/Annen 4 Firm s reaction function is q = q Thus, q = 0 0.5*0 = 5. = 5. ( points) PART 3: Game Theory 5) In a Nash equilibrium, everyone must be playing a dominant strategy. 6) In the prisoner's dilemma game, if each prisoner believed that the other prisoner would deny the crime, then both would deny the crime. 7) In the game matrix below, the first payoff in each pair goes to player A who chooses the row, and the second payoff goes to player B, who chooses the column. Let a, b, c and d be positive constants. If player A chooses Bottom and player B chooses Right in a Nash equilibrium, then we know that a) b > and d <. b) c < and b <. c) b < and c < d. d) b < c and d <. e) a < and b < a. (4 points) 8) In Nash equilibrium, each player is making an optimal choice for herself, given the choices of the other players. 9) John and Tommy share a room in a dorm together. Both of them can or cannot contribute to the cleaning. Both get a payoff of 0 when the room is clean and a payoff of 3 when the room is dirty. To clean the room has a payoff cost of 4. If John and Tommy both clean, this cost is shared. (i) Analyze this situation as a game and write down the payoff matrix. (ii) (iii) Tommy Clean N Clean Clean 8,8 6,0 John N Clean 0,6 3,3 Compute all pure Nash equilibria in this game: Answer: (N Clean, Clean) and (Clean, N Clean). Does Tommy have a dominant strategy? Answer: Yes / No (Circle the right answer).

5 Final (Version ) ECON30/Fall 003/Annen 5 (iv) Is John s threat not to clean the room when Tommy does not help to clean the room credible? Answer: Yes / No (Circle the right answer). (8 points) PART 4: Asymmetric Information 0) 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. ) In a market where there is a pooling equilibrium, different types of agents choose the same action. ) 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 are willing to pay $300 for a lemon and $,900 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). For a buyer, the expected value of a used car is 0.5* *900=00. Since this is lower than $500, no good cars will sell. The price of used cars is therefore $300. Final Answer: p = $300. (ii.) What is the price of a used car if q = 0. (Assume that sellers get the whole exchange surplus). The expected value of a used car is 0.* *900=740. Since this is higher than $500 good cars and lemons will be sold. The price is this expected value. Answer: p = _$740. (6 points) PART 5: Externalities 3) A trade between two people is an example of an externality. 4) If your consumption of music produces a negative externality for your neighbors (which you ignore), then you are consuming more music than is Pareto optimal.

6 Final (Version ) ECON30/Fall 003/Annen 6 5) A noisy production plant disturbing your leisurely TV evening is an example of a production externality. 6) Firm produces output x with a cost function c ( x) = x + 0. Firm produces output y with a cost function c ( y, x) = y + x. Thus, the more that firm produces, the greater are firm 's costs. Firm cannot influence the production decision of firm. Thus, firm s production imposes a negative externality of firm. Both firms face competitive product markets. The competitive price of x is $0 and the competitive price of y is $40. No new firms can enter the industry and the old ones must remain. (i) Calculate firm s profit maximizing output. MC = MR MC = x; MR = p = 0 x = 0 x = 0 (ii) (iii) Final Answer: x = 0. (3 points) Assume that the two firms merge. Calculate the profit maximizing output x of the new merged firm. The marginal cost is now x +. Each unit of x produced increases production costs of y by. MR = MC p = x + = 0 = x + x = 9 Final Answer: x = 9. (3 points) Assume that the two firms are separated again. The government wants to impose a tax on the production of x in order to internalize the negative externality. Calculate the optimal tax t that reaches the Pareto efficient outcome. (Hint: Remember from the lecture that the c ( y, x) optimal tax equals t = ). x The marginal cost of the production of y with respect to x is equal. So the tax should be equal to. Final Answer: t =. ( points) PART 6: Extra-Point Question 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

7 Final (Version ) ECON30/Fall 003/Annen 7 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)

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