UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT. MGEC02: Topics in Price Theory. Instructor: A. Mazaheri Sample Test-1 (Solutions)

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1 UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT MGEC02: Topics in Price Theory Instructor: A. Mazaheri Sample Test-1 (Solutions) Instructions: This is a closed book test. You have 2 Hours. Good Luck! Last Name: First Name: ID FOR MARKERS ONLY: Marks Earned Maximum Marks Possible Q1 Q2 Q3 Q4 Q5 Total Page 1 of 11

2 Answer all following 5 questions: Question-1 [25 Points] Answer the following Short Questions: a) [5 Points] Bookstores often offer annual memberships that allow customers to purchase books at a 10% discount. Explain why this may increase profits of the bookstore. Answer: This book club membership program is an example of a two-part tariff. If the consumer purchases a membership, they are able to purchase subsequent books at a discount to the price charged to non-members. This membership is in the best interest of the storeʹs profits if the consumers increase purchases at the store. That is, the loss in profit margin due to the discount is offset by the membership fee and the increased number of book purchases. If the consumer will not purchases any more books than without the membership and saves money by joining the club, then bookstore profits are reduced. The bookstore must believe that joining the book club will induce the consumer to purchase books more frequently at the bookstore or the membership fee will exceed the customerʹs savings. b) [5 Points] The outcome of Bertrand duopoly is efficient. True, False, Uncertain, Explain. Answer: Uncertain: The outcome of the Bertrand duopoly is efficient only if both players have similar marginal cost and if the good is not differentiated. Page 2 of 11

3 c) [10 Points] The market is characterized as a monopsony. Suppose the demand is P =10 Q, and the supply is given by P = Q 4. How much will the monopsonist buy? What price will it pay? What is the deadweight loss from monopsony power? Show on the clear graph the changes in producer and consumer surpluses when moving from competitive price and quantity to monopsony. MV = 10 Q AE = Q 4 TE = Q 2 4Q ME = 2Q 4 ME = MV => P = 14 / 3 4 = => 10 Q = 2Q 4 => Q = 14 / 3 2 / 3 MV = / 3 AE = MV DWL = (5.33 => 10 Q = Q 4 => Q = 7 2 / 3) (7 14 / 3) / /3 14/ Page 3 of 11

4 d) [5 Points] You own a family business. You are asked to determine the optimal monthly advertising expenditures for the business. Your total monthly cost is TC = 4Q Q 2 + A where A is the advertising expenditure. The firm s marginal revenue from advertising is constant at MRA = $4, and the advertising elasticity of demand is 0.4. Suppose you know the profit maximizing level of output is Q = 12,000 per month. What is the firm s optimal level of advertising expenditure? Q MRA = 4 = 1+ MC A => A = = 1+ ( Q ) E DA Q A = 1+ ( )0.4 A Page 4 of 11

5 Question-2 (20 Points): Grey provides bus service between two rural communities. It sells tickets to both adults and children. The demand functions for the two groups are given below. Adults: Q a = P a Children: Q c = 100-2P c The Q s are the number of trips demanded per day by the two groups and the P s are the fares. Assume that Grey is a constant cost third-degree price discriminator with TC = 20Q, where Q is the total number of trips taken per day by the two groups together. (Note that this says that the cost of a trip for a child is the same as for an adult.) a) [6 Points] What fare does Grey charge in the adult and children sub-market and how many tickets per day does it sell there? b) [6 Points] Compute the point elasticity for the both markets child market. c) [4 Points] What conclusion about third-degree price discriminators do you draw from your answers? d) [4 Points] What profit is Grey earning? a) P a = 200-5Q a MR a = Q a MC = ΔTC/ΔQ = 20 Set MC = MR and solve for Q. (Q a = 18). Plug your Q back into the demand curve. (P a = 110) Adult Ridership Dollars Quantity P c = Q c MR c = 50-Q c MC = ΔTC/ΔQ = 20 Set MC = MR and solve for Q. (Q c = 30). Plug your Q back into the demand curve. (P c = 35) Page 5 of 11

6 Children Ridership Dollars Quantity b) E D = (110/18)(-1/5) = Demand is elastic. A price reduction of 1% will increase ridership by 1.22%. E D = c) If the two demands are added up and the profit for the monopolist calculated the overall profit will definitely be less than what you get with price discrimination. Demand is more elastic in the child sub-market. The price discriminator should charge a higher price in the adult market, where demand is less elastic. d) Profit = (P a -20)Q a +(P c -20)Q c = 2070 Page 6 of 11

7 Question-3 (15 Points): Consider a telecommunications firm that offers both phone service and a high-speed internet service. It has two types of consumers who differ in their willingness to pay a monthly rental fee for either service: Talkers Hackers Phone Service $28 $a Internet Service $16 $22 where a > 0. There is a mass N of consumers. Half of these consumers are talkers, and the other half are hackers. The firm is not able to price discriminate. Costs are normalized to zero. a) [7.5 Points] Compute the firm's profit under separate pricing (i.e., under unbundling) as a function of a. b) [7.5 Points] Compute the firm's profit under pure bundling as a function of a. Pure bundling means that the firm is only selling the two services as a package. a) The firm maximizes profits by charging $16 for internet service, which yields $16N profit on internet sales. If a < 14, then the firm charges $28 and makes $14N on phone sales. If 14 < a < 28, the firm charges a for phone service and makes $an on phone sales. If 28 < a < 56, the firm charges $28 for phone service and makes $28N on phone sales. If a > 56, the firm charges a for phone service and makes (a/2)n on phone sales. b) There are three regions to consider: a < < a < 66 a > 66 Price 22 + a a Profits (22 + a)n 44N (11+a/2)N Page 7 of 11

8 Question-4 (15 Points): Two large diversified consumer products firms are about to enter the market for a new pain reliever. The two firms are very similar in terms of their costs, strategic approach, and market outlook. Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price. The market demand curve for the pain reliever is given as: Q = P. Both firms have constant long-run average costs of $2.00 per bottle. Patent protection insures that the two firms will operate as a duopoly for the foreseeable future. Price and quantity values are stated in per-bottle terms. a) (7.5 Points) If the firms act as Cournot duopolists, solve for the firm and market outputs and equilibrium prices. a) (7.5 Points) If the firms act as Stackelberg duopolists, solve for the firm and market outputs and equilibrium prices. a) Begin by solving for P. Q = P => Q = -400P => P = Q Denote the two firms A and B and solve for reaction functions. TRA = PA QA => TRA = ( Q)QA TRA = 6.5QA [(QA + QB)QA] = 6.5QA QA QAQB MRA = QA QB Set MRA = MC => QA QB = QA = QB QA = QB One can verify that: QB = QA Substitute expression for QB into QA QA = ( QA) = QA QA -0.25QA = QA(1-0.25) = 450 => QA = 450/0.75 = 600 Substitute expression for QA into QB QB = ( QB) QB= 600 QT = QA + QB QT = = 1200 P = (1200) = 3.5 Page 8 of 11

9 b) P = Q TRA = PA QA => TRA = ( Q)QA TRA = 6.5QA [(QA + QB)QA] = 6.5QA QA QAQB Substitute for QB by the reaction function: TRA= 6.5QA QA QA ( QA) = 4.25QA QA 2 MRA = QA Set MRA = MC => QA = 2 => QA = 900 Insert QA in the reaction function for B: QB = QA = 450 Page 9 of 11

10 Question-5 (15 Points): The market for an industrial chemical has a single dominant firm and a competitive fringe comprised of many firms that behave as price takers. The dominant firm has recently begun behaving as a price leader, setting price while the competitive fringe follows. The market demand curve and competitive fringe supply curve are given below. Marginal cost for the dominant firm is $0.75 per gallon. QM = 140,000-32,000P QF = 60, ,000P, where QM = market quantity demanded, and QF = the supply of the competitive fringe. Quantities are measured in gallons per week, and price is measured as a price per gallon. a) (7.5 Points) Determine the price and output that would prevail in the market under the conditions described above. Identify output for the dominant firm as well as the competitive fringe. b) (7.5 Points) Assume that the market demand curve shifts rightward by 40,000 units. Show that the dominant firm is indeed a price leader. What output (leader and follower) and market price will prevail after the change in demand? a) QM = 140,000-32,000P QF = 60, ,000P Denote dominant firm demand curve as QD. QD = QM - QF QD = 140,000-32,000P - (60, ,000P) QD = 80,000-40,000P Solve for P: QD - 80,000 = -40,000P P = QD MRD = QD Marginal cost for the dominant firm is $0.75. Equate MRD to MCD QD = QD = => QD = 25,000 P = (25,000) = = per gallon Fringe takes dominant firm price as given QF = 60, ,000(1.375) = 71,000 QT = 25, ,000 = 96,000 b) A 40,000 increase in demand curve to: QM = 180,000-32,000P = 60, ,000P QD = 180,000-72,000P - (60, P) = 120,000-40,000P Page 10 of 11

11 Solve for P QD - 120,000 = -40,000P PD = QD MRD = QD setting MRD = MCD QD = 0.75 => QD = => QD = 45,000 PD = (45,000) = = $1.875 Fringe again follows QF = 60, ,000(1.875) = 75,000 QT = 45, ,000 = 120,000 We can see that when demand changed, the dominant firm raised price. The competitive fringe took the new price as given and adjusted output accordingly. Page 11 of 11