University of Victoria Winter Econ 203 Problem Set 3


 Mavis Wilkinson
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1 University of Victoria Winter 2017 Econ 203 Problem Set 3 Coverage: Some extra questions on Chapter 11 Perfect Competition ; Chapter 12 Monopoly ; Chapter 13A: Game Theory. There are also some Chapter 13B: Oligopoly for future reference. Many questions are from the Frank and Parker text. Instructions. Produce handwritten answers only. We expect you to work on the problem set in groups of 3 students who must be from your own course section (i.e. all in the group are from A01 or A02, no mix is permitted). 1 In addition, A02 students also have to be in the same lab, i.e. B04, B05, or B06. If you require help finding group members, or a third group member, please your instructor by Tuesday 14 th of March. This is also the final date to provide a reasoned request if you prefer to deviate from working in a group of 3 students. Handing in. Use the downloadable front page template for problem sets and staple together with the other pages. Your group hands in a single copy. Handin deadline: Monday 20 th 4:30pm in the Course Box for your lab section (e.g. B04) in the hall between BEC 360 and BEC 363. Late problem sets will normally not be accepted. Grading. About 6570% of your grade for the assignment will be for completeness, effort, and following instructions; and the remaining 3035% for correctness of answers. Correctness will be judged based on a small selection of the questions (1 or 2 questions). Section Coverage: Chapter 11 Perfect Competition (A couple more questions on this Chapter!); Question 1: The domestic supply and demand curves for lefthanded backscratchers (LHBs) are given by P = 10 + Q and P = 1002Q, respectively, where P is the price in dollars per LHB, and Q is the quantity in LHBs per year. Canada produces and consumes only a trivial fraction of the world s output of LHBs, so the current world price of $30/LHB is unaffected by events in the Canadian market. Transportation costs are negligible. a. How much will Canadian consumers pay for LHBs and how many LHBs per year will they consume? b. How will your answers to (a) change if the government imposes a tariff of $20/backscratcher? c. What total effect on domestic producer and consumer surplus will the tariff have? How much revenue will the tariff raise? 1 Doing a problem set together does not mean that you simply divvy up the questions. Each of the group members carries the responsibility for possible issues with answers, including possible issues of academic integrity.
2 Question 2: Mei is like all other managers in a perfectly competitive industry except in one respect: because of her great sense of humour, people are willing to work for her for half the going wage rate. All firms in the industry have cost curves given by C(Q) = M + 10Q + wq 2. Here Q represents units of output per day, M the salary paid to the manager, and w the regular wage rate in the industry. (a) If all firms in the industry face an output price of $28 per unit, the going wage rate is $2/labourday, and the market for managerial talent is competitive, then how much more will Mei be paid than the other managers in the industry? (b) The law of diminishing (marginal) returns is so important because often one factor of production is essentially fixed (or limited in supply after a certain quantity of output) at which stage it s applicable. In agriculture this could be the factor land. Discuss: What seems to be the fixed factor in this question? Does the law of diminishing returns apply? Question 3: For each of the following supply curves, calculate the level of output Q at which the elasticity of supply = 1, and indicate whether supply is elastic or inelastic at levels of Q less than this point and at levels of Q greater than this point: a. P = Q 2 b. P = 4 + Q, for Q 16 c. P = 6Q Section 2 Coverage: Chapter 12 Monopoly Question 4: (re. Section 12.9) Define and relate the following two terms: patents and monopoly. Figure out and clarify what is meant by a patent race. What s the relationship between drug prices and patents? Give a welfarebased argument for and also a welfarebased argument against allowing pharmaceutical companies to charge high drug prices. Question 5: a. Explain the difference between monopoly and monopoly power. In reality, do monopolists always have more monopoly power than firms in oligopolistic sectors? Why or why not? Give at least two arguments, with one that is based on the concept of limit pricing (see page 463) b. What is meant by the Lerner index and argue why it is a reasonable measure of the degree of monopoly power of a firm. c. Use the Lerner index to clarify (make more precise) the somewhat sloppy statement that Monopolists price high if the price elasticity of demand is low. d. The demand by senior citizens for screenings at a local movie house has a constant price elasticity of demand equal to 3. The demand curve for all other patrons has a constant priceelasticity equal to If the marginal cost of a person is $1.50, how much should the theatre charge members of each group?
3 Question 6: a. A monopolist has a demand curve given by P = Q and a total cost curve given by TC= 16 + Q 2. Find the monopolist's profitmaximizing quantity and price. How much economic profit will the monopolist earn? b. Now suppose the monopolist has double the fixed costs, so a total cost curve given by 32 + Q 2. Find the monopolist's profitmaximizing quantity and price. How much economic profit does the monopolist earn?  always first write up the monopolist s problem! Question 7: Suppose that, each period, a monopolist faces market demand P = Q and has constant marginal cost MC= 20 (with no fixed costs). a. If the monopolist can perfectly discriminate, how much does it sell? How much profit does the monopolist earn? What is the maximum perperiod licence fee the government could charge the firm it the government want it stay in business? b. Suppose now that this market consists of 100 identical consumers, each with individual demand P = 100 l000q. Suppose further that the monopolist may resort to a twopart tariff. What is the profitmaximizing twopart tariff? How much does the monopolist sell? How much profit does the monopolist earn? What is the deadweight loss due to monopoly power? c. Now suppose the market grows and that 50 additional identical consumers, each with individual demand P = q enter the market. What is the new optimal twopart tariff. How much does the monopolist sell now? And how much profit does she earn? Question 8: The drug company Fizehr sells a patented product CudoCuro in Canada and the US. The US demand for CudoCuro is P = Q and Canada's is given by P = Q, where Q is in millions of units and P the price in dollars. The cost of producing CudoCuro is 0.5Q 2. What price will be charged to each country? What is each country's priceelasticity of demand for CudoCuro at this point? Why would Fizehr possibly push for the regulator to allow the drug only to be sold after a doctor s prescription? Question 9: Crazy Harry, a monopolist, has a total cost curve given by C(Q) = 5Q + l5. He sets two prices for his product, a regular price, PH, and a discount price, PL. Everyone is eligible to purchase the product at PH. To be eligible to buy at PL it is necessary to present a copy of the latest Crazy Harry newspaper ad to the salesclerk. Suppose the only buyers who present the ad are those who would not have been willing to buy the product at PH (Hints: Figure out what is the problem of this monopolist. See the graph following this question. Note that in this graph we have inverse demand given by say: P=ABQ, and therefore: PH =ABQH and PL =AB(QH+QL)). a. If Crazy Harry's demand curve is given by P = 205Q, what are the profitmaximizing values of PH and PL. b. How much economic profit does Harry make? c. How much profit would he have made if he had been forced to charge the same price to all buyers? d. Are buyers better or worse off as a result of Harry's being able to charge two prices?
4 Question 10: Hardy Hurdley owns a clear spring, which produces mineral water that is viewed as having unique restorative properties. Hardy has no fixed costs, and the water is available at zero marginal cost. It is demanded by two groups, Group A and Group B, whose demand functions for the water take the following forms: Group A: P = 202QA Group B: P = 10  QB where Qi, i = A, B, is in liters per period and P is in dollars per liter. a. If Hardy sets a single price for the water, find: the price he will charge, the quantity purchased by Group A and by Group B, Hardy's profits, and the consumer surplus of Group A and of Group B. (Hint: first find Hardy's marginal revenue (MR) curve?) b. Hardy decides to charge two prices for the water, a "regular" price (PH), which involves no waiting, and a lower price (PL), which is available only after waiting one hour per liter purchased. (This is again an example of 2 nd degree price discrimination) Group A members assess the cost of the wait at $8/hour, while Group B members treat the waiting cost as zero. What prices would Hardy set if he knew the demand curves and the valuations of the cost of the wait? Calculate Hardy's profits and the consumer surplus of Group A and of Group B under this hurdlepricing system. c. Suppose that PH and PL are as in (b), but that now Group B members evaluate the waitingtime hurdle at a cost of $8 /hour, while Group A members treat the waiting cost as zero. Calculate Hardy's profits and the consumer surplus of Group A and of Group B in this situation. d. Compare the three situations. In which situation is the sum of consumer surplus and producer surplus greatest? In which situation is it smallest? How do these sums compare with the competitive outcome?
5 Section 3 Coverage: Chapter 13 Game Theory (GT); Question 11: Firm 1 and Firm 2 are automobile producers. Each has the option of producing either a big car or a small car. The payoffs to each of the four possible combinations of choices are as given in the payoff matrix below. Each firm must make its choice without knowing what the other has chosen. a. Does either firm have a dominant strategy? b. Identify the Nash equilibria. Question 12: Suppose we have the same payoff matrix as in Problem 13 except now Firm 1 gets to move first and knows that Firm 2 will see the results of this choice before deciding which type of car to build. a. Draw the game tree for this sequential game. b. Give the normalform representation for this sequential game. c. What are the Nash equilibria for this game? d. What are the Subgame Perfect Nash equilibria for this game? Is it better to move first or second?
6 Question 13: Consider the game tree below that describes a game between two politicians A and B. Politician A moves first and decides on her position in the policy spectrum: left (l), middle (m), or right (r). Next politician B decides whether to take position (L) left or right (R) of the position taken by A. The top entry of the payoff vector represents A s payoff and the bottom one B s payoff (a) Give the strategic form representation of the game above, and find all the Nash equilibria. Hint: be precise in defining the strategies of A and B. (b) (1) Find all the subgame perfect Nash equilibria. (2) Give an example of a noncredible threat made by B. Question 14. Do question Question 21 on Practice Final #1 on the course website <End of PS3, practice questions on Oligopoly follow below> Section 4: not to be handed in Coverage: Chapter 13 Oligopoly Theory ; Question 15: Consider a duopolistic market where demand is given by P = 363Q, where Q = Q1 + Q2. For each duopolist, the constant per unit marginal cost is $18/unit and fixed costs are zero. a. Assume first that the duopolists hold Cournot conjectures when they make their choices. Find the Cournot equilibrium price, quantity, and profits. b. Now find the equilibrium price, quantity, and profits assuming the duopolists compete a la Bertrand. c. Find the equilibrium price, quantity, and profit for each firm, assuming the firms act as a Stackelberg leader and follower, with Firm 1 as the leader.
7 Question 16: Augie and Corinne are mineral spring duopolists facing a market demand given by the equation P = 24  Q. Fixed costs are zero for both, but Augie has a constant marginal cost of $6 per unit, while Corinne's marginal cost is zero. a. If they both behave as Cournot duopolists, give the equations for the two reaction curves, equilibrium levels of output, the market price, the profits of each, and the value of consumer surplus. b. Suppose instead that they both behave as noncooperative Bertrand duopolists, and calculate the market price, the levels of output and profits of each, and the value of consumer surplus. c. If Corinne could effectively bribe Augie to shut down his production completely, regardless of the market price, so that she supplied the entire market, what is the maximum amount she would be willing to pay? What is the minimum amount he would accept? Answer this question twice, for Cournot competition and for Bertrand competition. Question 17: Assume annual market demand for UVic coffee mugs is given by P=20Q, where P is the price, and Q is the quantity of these fancy collector s items. In this market, consider the firm Dominant with cost function C1(Q1)=Q1+25, where Q1 is the Dominant s quantity. Let Dominant initially be a monopolist. (a) Derive the monopoly price and quantity of Dominant both graphically and mathematically. In your graph show what are Dominant s monopoly profits. Now assume that a potential competitor DifficultToDominate (DTD) with cost function C2(Q2)= 3Q2+16 considers entering the market. If DTD indeed enters, then both firm next arrive at a subgame in which they compete a la Cournot (that is, in the subgame both firms choose their quantities simultaneously, while each firm holds Cournot conjectures regarding its rival s behaviour). If DTD does not enter then Dominant charges the monopoly price. DTD gets a payoff of zero then. (b) Present the game tree of the game between Dominant and DTD. [Hint: If you cannot answer this question fully, at least sketch the Cournot subgame carefully.] (c) Assume in this part of the question that DTD has indeed entered, so that the Cournot subgame referred to in (b) applies. Derive the socalled best response functions of Dominant and DTD. Derive the Nash equilibrium to the Cournot subgame. Add a stage to the game and assume that Dominant makes a preannouncement regarding her production amount before the entry decision of DTD. (d) Derive the limit quantity, that is, derive the minimum quantity that Dominant has to preannounce in order to successfully impede entry of DTD. In this question, assume that Dominant s announcement sounds fully credible to DTD.