# Ford School of Public Policy 555: Microeconomics A Fall 2010 Exam 3 December 13, 2010 Professor Kevin Stange

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2 3.  Medicare is paid for by a 2.9% tax on payroll, half of which is deducted out of workers paychecks and the other half is paid directly by their employers. True or false: If the tax were eliminated, workers and employers would benefit equally. That is, the net wage paid by employers would decrease by the same amount that the wage workers receive would increase. Explain briefly. False. The current incidence of the tax (and thus the benefit if it were eliminated) depends on the relative elasticity of labor supply and labor demand, not on who nominally pays the government for the tax. Only if these are exactly equal (which is unlikely) would the tax burden fall equally on workers (suppliers of labor) and employers (demanders of labor). Just because employers currently pay for half of the tax doesn t mean that half the burden falls on them. 4.  True or false: Regardless of whether firms in an oligopoly industry compete on price or quantity, if the product they sell is exactly the same, costs the same to produce, and if firms decisions are made simultaneously, equilibrium price will be pushed down to marginal cost. Explain briefly. False. It is true that if oligopolistic firms selling exactly the same product at the same cost were to set prices simultaneously, then price would be driven down to marginal cost (the Bertrand model). However, if the same firms competed by setting quantities rather than price (the Cournot model), then equilibrium price would be above marginal cost in equilibrium. 5.  The graph below plots the demand curve, marginal revenue curve, and marginal cost curve for a profit maximizing monopolist. Fill in the blanks with numbers: a. The firm will charge a price of \$8. b. The firm will produce where marginal cost equals \$4. c. If the firm were behaving competitively, it would set price equal to \$7. d. If a price ceiling of \$9 were implemented, the firm would set price equal to \$8. \$ per unit MC 8 6 Demand 4 2 MR q 2

3 6.  Taxing fake tans Assume that the indoor tanning industry is competitive, with demand function Q D = 140 2P and supply function is Q S = 40+3P. Q is the number of visits to tanning salons (in millions) and P is the price per visit. a.  On the graph below, draw the supply and demand curves. Label all intercepts. P Supply 70 Pc = 23 P* = 20 DWL Pp = 18 Demand 40 Q*= Qtax=94 Q b.  What is the equilibrium price and quantity? Label these P* and Q* on the graph. Remember that quantity is in millions. Set Qs = Qd: 40+3P = 140 2P 5P = 100 P*=20, Q* = 100 million One little known provision in the Patient Protection and Affordable Care Act of 2010 (also known as Health Reform ) is a tax on indoor tanning salons, which took effect this past summer. The tax aimed to both raise revenue and also to reduce the use of indoor tanning salons, which is believed to cause skin cancer. Assume that the government imposes a \$5 tax on each tanning salon visit. c.  Find the new price that consumers pay for each tanning salon visit (net of the tax) and the price that salon owners receive for each visit (net of the tax). Substitute Pp = Pc 5 into the supply equation and then set this equal to demand: 40 +3Pp = 140 2Pc (Pc 5) = 140 2Pc 5Pc = 115 Pc = 23, Pp = 18 3

4 d.  How many visits are sold now? (remember that quantity is in millions) Can substitute either Pc into the demand equation or Pp into the supply equation. I do the latter: Q = (18) = Qtax = 94 million e.  Show the effect of the tax on the supply and demand graphs you drew in part a. Be sure to label the price received by salon owners (P P ), price paid by consumers (P C ), and new quantity (Q TAX ). See graph. f.  How much revenue does the government raise? (remember that quantity is in millions) Revenue = (tax per unit)*(quantity) = (5)*(94) = \$470 million g.  Doe the subsidy generate deadweight loss? If so, calculate it and label it on your graph. Yes, the tax will generate deadweight loss because it will reduce output below the competitive equilibrium level. DWL = 0.5*(5)*(6) = \$15million h.  A spokesperson for the International Smart Tan Network (a Michigan based group representing tanning salons) said: The average cost of a tanning visit is going to rise by \$5 and this will hurt the small business salon owners. Why is this statement contradictory? [Note: this does not depend on your answers to the above questions] This statement makes two claims: (1) consumer s price will increase by the full amount of the tax; and (2) salon owners will be harmed by this. Both claims cannot be true. If the price consumers face raises by the full amount of the tax, this would mean that demand is perfectly inelastic (quantity demanded = 100 regardless of the price). If this is the case, salon owners will not be affected by the tax. That is, if demand is perfectly inelastic, quantity, revenue, producer surplus, and profits will not change when the tax is implemented. So either the price faced by consumers will increase by the full amount or producers will be affected, but both cannot be true. [Note: this is pretty close to an actual quote from a real person named Joseph Levy, vice president of the International Smart Tan Network] 4

5 7.  Colleges Collude Prior to 1991, a large group of elite U.S. colleges met annually to coordinate how much financial aid they were going to provide to students accepted to multiple institutions. The U.S. Department of Justice pursued antitrust litigation against them, accusing the colleges of colluding to charge higher prices (tuition minus aid) to the smartest students. Throughout, assume that colleges act so as to maximize profits (as the Department of Justice assumed).  Part 1: Monopoly Pricing First assume that the group of colleges acts as a monopolist in the market for higher education for smart students. The aggregate demand function is given by Q = 100 2P where Q is the number of students attending the colleges and P is the net price. The group s total cost function is given by TC = Q +2Q 2. a.  What is the marginal revenue function? Rearrange demand: 2P = 100 Q P = Q Revenue = P*Q = (50 0.5Q)*Q = 50Q 0.5Q*Q MR = drevenue/dq MR = 50 Q b.  What is the marginal cost function? MC = dcost/dq MC = Q c.  If the group maximized profits, what price will the colleges charge and how many students will attend? Set MR = MC 50 Q = Q 5Q = 40 Q = 8 Substitute this into the inverse demand function to get price: P = Q = (8) P = 46 d.  What is the monopolist s total profit? Profit = PQ Cost = (46)(8) [ (8) + 2(8*8)] = Profit = 60 5

6 e.  What would price and quantity be if the colleges instead acted to maximize total surplus? (Note: you will need a calculator for this. If you do not have one, fractions are fine). If the colleges were acting to maximize total surplus, they would enroll the number of students that equated price and marginal cost: MC = P Q = Q 4.5Q = 40 Q = 80/9 = 8.89 P = *(8.88) = f.  Briefly describe at least two policies (other than breaking up the monopoly) that would result in the efficient outcome calculated in part e and no deadweight loss. Be sure to explain briefly why each work. This should require minimal or no calculations. This could be accomplished by an appropriately sized price ceiling or subsidy. A price ceiling that dictated that the monopolist could not charge more than \$45.56 (the competitive price) would cause the monopolist to enroll the welfare maximizing number of students. Alternatively, a per student subsidy (you did not need to calculate the precise amount) could also accomplish this. The subsidy would result in a large welfare transfer from the government to the monopolist (which we may not like), but this transfer would not be inefficient. Though both price ceilings and subsidies generally create deadweight loss when applied to a competitive equilibrium, this is not true when the market is dominated by a monopolist with market power. 6

7  Part 2: Price Discrimination The college monopoly determines that there are two types of potential students rich kids and poor kids. The demand function for each is: Q Rich = 55 P Rich Q Poor = 45 P Poor Assume that the monopolist can perfectly distinguish between rich and poor students so is able to charge each group a different price (i.e. practice 3 rd degree price discrimination). g.  What price will it charge rich students? How many will attend the elite colleges? You need to set the MR for each group equal to the MC, where MC is calculated using the combined total quantity Q T =Q R + Q P. First find MR: P R = 55 Q R, so Revenue R = (55 Q R )Q R = 55 Q R Q R * Q R MR R = 55 2Q R From part c above, we found that Q T = 8, implying that MC = 10+4(8) = 42. Setting MR = MC: 55 2Q R = 42 Q R = 6.5 P R = 55 Q R = = 48.5 h.  What price will it charge poor students? How many will attend the elite colleges? First find MR: P P = 45 Q P, so Revenue P = (45 Q P )Q P = 45 Q P Q P * Q P MR P = 45 2Q P From part c above, we found that Q T = 8, implying that MC = 10+4(8) = 42. Setting MR = MC: 45 2Q P = 42 Q P = 1.5 P P = 45 Q P = = 43.5 i.  Explain what information the colleges would need to know about their potential students (and how they would need to use it) in order to turn all consumer surplus into profits. If the colleges knew each student s reservation price (the price at which a student would be indifferent between enrolling or not), they could charge each student this personalized price (or just a penny below it) and capture all the consumer surplus. This would be perfect first degree price discrimination. This would be impossible in practice. Note that it is not quite enough to know each student s income or ability to pay and charge based on that. Though income is probably strongly related to reservation prices, inevitably there would be some students that would actually be willing to pay more than charged if prices were based on income exclusively. Thus, the colleges would not be capturing all the consumer surplus from these students if income (or even ability to pay) was the only determinant of price. 7

8  Part 3: Oligopoly Now suppose the DOJ succeeded in breaking up the monopoly so that each college now makes pricing decisions independently and simultaneously, but the number of schools is sufficiently small that the market is an oligopoly. Simplify things by assuming there are only two colleges (Yale and Harvard) and that the product offered by each is differentiated. The demand function faced by each is: Q Y = 40 P Y +P H Q H = 40 P H +P Y where Q Y and Q H and P Y and P H are the demand and prices for Yale and Harvard, respectively. Also assume that the cost function for these colleges is the same: TC Y = Q Y TC H = Q H j.  What is each college s reaction function? (Yale s profit maximizing price as a function of Harvard s and Harvard s profit maximizing price as a function of Yale s) Since the colleges have identical cost structures and symmetric demands, their reaction functions will be symmetric. For Yale: Profit = P Y *Q Y TC Y = P Y *(40 P Y +P H ) (40 P Y +P H ) = 40P Y P Y *P Y + P Y *P H P Y 40P H = P Y P Y *P Y + P Y *P H 40P H dprofit/d P Y = 80 2 P Y + P H = 0 P Y = P H P H = P Y k.  What is the equilibrium price and quantity for each college? P Y = P H = ( P Y ) = P Y 0.75P Y = 60 P Y = 80, Similarly P H = 80 Q Y = 40, Q H = 40 l.  If the two colleges could collude and set prices to maximize their combined profits, what prices would they set? What would their profits be? Explain this result. If the two colleges were able to collude, they could set prices as high as they wanted and make infinite profits. Since demand only depends on the price difference, demand is inelastic when the two prices are the same 80 students want to attend regardless of the price. The general point that an unregulated monopoly can make huge profits if demand is inelastic is true and important. However, in reality it is unlikely that the colleges could raise their prices forever. Eventually the demand function would break down (i.e. demand would become somewhat elastic) or regulators would step in. 8