Industrial Organization Lecture 4: Monopoly

Transcription

1 Industrial Organization Lecture 4: Monopoly Nicolas Schutz Nicolas Schutz Monopoly 1 / 59

2 Definition Definition: A firm is a monopoly if it is the only supplier of a product in a market. A monopolist s demand curve slopes down because firm demand equals industry demand. Roadmap: 1 Base case (one price, perishable good, non-increasing returns to scale) Extension: the dominant firm model. 2 Natural monopoly. 3 Discrimination: First-degree price discrimination: personalized pricing. Third-degree price discrimination: group pricing. Second-degree price discrimination: non-linear pricing. 4 Bundling. 5 Durable goods. Nicolas Schutz Monopoly 2 / 59

3 Examples Microsoft, market for operating systems. Market share 90%. Tyco, market for plastic hangers. Market share 70 80%. IBM, computers market, from 1960 to Gillette, razor blades market, 72% market share. Google: 70% of US web searches. 70% of online advertising market. Utilities (electricity, water, telephone, rail, etc.) Nicolas Schutz Monopoly 3 / 59

4 Monopoly: Base Case Consider a monopoly with market demand P(Q) and cost function C(Q). Profit: π(q) = P(Q)Q C(Q) = R(Q) C(Q). Remark: Choosing P or choosing Q makes no difference, because we have the strictly decreasing relation P(Q). This will not be true when we consider oligopoly problems. Differentiate π w.r.t. Q: R (Q) = C (Q). Marginal revenue = Marginal cost. Marginal revenue: MR(Q) = P(Q) + P (Q)Q. Increasing Q has two effects on the monopolist s revenue: The monopolist sells an additional unit at price P(Q). It s the P(Q)(> 0) term. The price of all infra-marginal units decreases: P (Q)Q < 0. Nicolas Schutz Monopoly 4 / 59

5 Marginal Revenue: Illustration P P 1 P 2 0 Q 1 Q 2 P(Q) Q Nicolas Schutz Monopoly 5 / 59

6 Marginal Revenue In general, when should we expect MR to be positive? MR(Q) = P(Q) + dp dq Q ( = P(Q) 1 + dp ) Q dq P = P(Q)(1 1 ) ε D Therefore, MR(Q) > 0 iff ε D (P) > 1. non-negative number.] Intuition? [Remember that ε D (P) is defined as a Linear demand: P(Q) = a bq. R = Q(a bq) = aq bq 2 MR = dr/dq = a 2bQ Compare MR(Q) and P(Q). MR: same intercept, and twice the slope. Nicolas Schutz Monopoly 6 / 59

7 Monopoly Outcome Putting things together: P MC(Q) P M 0 Q M MR(Q) P(Q) Q Compared to the perfect competition outcome, the monopoly produces less and charges a higher price. Intuition? Nicolas Schutz Monopoly 7 / 59

8 The Inverse Elasticity Rule Price cost margin, markup, or Lerner index is: L P MC P. Monopolist s first-order condition: ( ) 1 P(Q) 1 = dc ε D (P(Q)) dq The inverse elasticity rule: P MC P = 1 ε D > 0 Example with a constant elasticity demand function: Q(P) = ap σ, with σ > 0. Elasticity of demand: for all P ε D (P) = dq/q dp/p = d log Q d log P = σ Inverse elasticity rule: L = 1 σ, i.e., less elastic demand (lower σ) higher markup. Nicolas Schutz Monopoly 8 / 59

9 Welfare P MC(Q) P M 0 Q M MR(Q) P(Q) Q The red triangle (Harberger triangle) is the dead weight loss. Flatter demand higher ε D (holding P and Q fixed) smaller dead weight loss. Nicolas Schutz Monopoly 9 / 59

10 Welfare A monopoly may generate social costs which may be bigger than the dead weight loss: Rent-seeking behavior (lobbying costs). Cost of deterring entry: excessive advertising, overinvestment in capacity (more on this in a couple of weeks). Excessive R&D to acquire monopoly power. On the other hand, the prospect to obtain monopoly power may provide good incentives to innovate. Nicolas Schutz Monopoly 10 / 59

11 The Dominant Firm Model Two types of firms: A big, unconstrained and strategic firm, with marginal cost c: The dominant firm. A fringe of perfectly competitive firms, with marginal cost c. Assumptions: The fringe is capacity constrained, i.e., it cannot produce more than K. The fringe is small: K << Q(c). The dominant firm has no incentives to set a quantity Q such that P(Q) c, i.e., it has no incentives to exclude the fringe. The fringe will always sell K in equilibrium. The dominant firm, since it is strategic, knows that. The dominant firm focuses on the residual demand, i.e., Q R (P) = Q(P) K. For instance, with linear demand, P R (Q) = a b(q + K) = (a bk) bq. If we replace ε D by ε R, we can still use the inverse elasticity formula to D derive the dominant firm s behavior. Nicolas Schutz Monopoly 11 / 59

12 The Dominant Firm Model Qualitatively, a dominant firm behaves the same way as a monopoly. The monopoly model can be readily applied to think about firms (such as Tyco, Microsoft, AT&T after telecoms deregulation, Gillette, etc.) holding a dominant position. Nicolas Schutz Monopoly 12 / 59

13 Natural Monopoly Definition: A firm is a natural monopoly if it can produce the market quantity Q, at lower cost than two or more firms. To argue for a natural monopoly, have to establish subadditivity of cost function: C(Q) < N i=1 C(q i), where Q = N i=1 q i. Example of such cost functions? If AC is decreasing everywhere, then subadditivity is satisfied. However, the reverse is not always true, i.e., economies of scale is a sufficient, but not necessary condition for natural monopoly. Examples of natural monopolies? Electrical, gas, telephone and other utilities. Nicolas Schutz Monopoly 13 / 59

14 Natural Monopoly and Essential Facility Recent shift in regulatory practices: Identify the essential facility (or upstream bottleneck). Example: Market for telephony services (1990s): Local access (the local loop) is an essential facility, and should be operated by a (regulated) monopoly. Competition can develop in the market for long-distance calls. Broadband market: Local access = essential facility. New broadband operators can build national network, and obtain access to the incumbent s local loop. Electricity: Transmission network = essential facility. Competition b/w electric power plants can develop. Nicolas Schutz Monopoly 14 / 59

15 Natural Monopoly P P M AC(Q) P C MC(Q) 0 Q M MR(Q) Q C Q P(Q) Monopoly will maximize profits at (Q M, P M ). (Q C, P C ) would be welfare-maximizing, but a firm would make a loss in this case. How would you regulate a natural monopoly? Nicolas Schutz Monopoly 15 / 59

16 Natural Monopoly: Regulation How to regulate a natural monopoly? Pay a subsidy to the firm to cover losses, or have firms bid based on price: franchise bidding, or, even better, have firms bid based on both a fee to operate, but also the price they will charge consumers. We ll come back to regulation theory. Nicolas Schutz Monopoly 16 / 59

17 Price discrimination We distinguish b/w three types of price discrimination: First degree price discrimination (i.e., perfect price discrimination, or personalized pricing). Second degree price discrimination (i.e., non-linear pricing, such as quantity discounts). Third degree price discrimination (i.e., market segmentation). In any case, price discrimination requires the absence of resale. Price discrimination always increases profit, but its impact on consumer surplus is ambiguous. Nicolas Schutz Monopoly 17 / 59

18 First-Degree Price Discrimination The monopolist can charge a different price to each consumer. This price does not need to be linear. First example: N consumers, with unit demand, and willingness-to-pay θ i, i = 1..n. Utility of consumer i: u i = θ i P i. Monopolist with constant unit cost c. The monopolist knows the θ of each consumer. What should he do? For each consumer, set P i = θ i if θ i c, and P i = + otherwise. Is this efficient? First-degree price discrimination maximizes social welfare. (A consumer consumes iff its willingness-to-pay marginal cost) But consumers are left with 0 surplus! Nicolas Schutz Monopoly 18 / 59

19 First-Degree Price Discrimination Another example: N consumers, with demands P i (Q), i = 1..N. Monopolist with constant unit cost c. Assume P i (0) > c i for simplicity. The monopolist knows each consumer s demand, and is free to use non-linear pricing. What should he do? For each consumer: Compute Q i, such that P i (Q i ) = c. Charge: T i (q) = cq + Q i (P 0 i ( q) c)d q. T i (.) is a two-part tariff, with fixed fee Q i (P 0 i (q) c)dq and variable part c. Nicolas Schutz Monopoly 19 / 59

20 First-Degree Price Discrimination Consumer i with contract T i (q) = cq + Q i (P 0 i ( q) c)d q. P 0 Q i c Q P i (Q) Again, this improves firm s profit, maximizes efficiency, but consumers get no surplus. First-degree price discrimination can be observed in some input markets. Example: Aircraft manufacturer charge a different non-linear tarif to each airline. Nicolas Schutz Monopoly 20 / 59

21 Third-Degree Price Discrimination The seller divides buyers into groups, and sets a different price for each group. Examples? Prices of prescription drugs are different in Canada and in the US. Survey on 45 prescription drugs: the median product was priced 45% cheaper in Canada than in the US. These price differences cannot be explained by costs. Pharmaceutical companies have been fighting hard to prevent their consumers from exporting / importing drugs. In the European car market, markups for the same car model vary widely across countries. Academic journals charge a higher price to libraries than to individuals. Discounts for students / the elderly. Nicolas Schutz Monopoly 21 / 59

22 Third-Degree Price Discrimination Versioning can be a simple means to implement 3rd-degree price discrimination, when groups of buyers are hard to identify. The idea is to offer different products to make sure that consumers self-select into groups. Examples: Paperback vs. hard cover books. Airlines: requirement of a Saturday night stay to get cheaper fares. Discriminates b/w tourists and business persons. IBM s LaserPrinter vs LaserPrinter E. LaserPrinter vs LaserPrinter E are almost identical. There is an additional component in LaserPrinter E, which limits its speed. IBM incurs an extra cost to damage its good, to segment the market. Nicolas Schutz Monopoly 22 / 59

23 Third-Degree Price Discrimination Two segments: max q1,q 2 π(q 1, q 2 ) = TR(q 1 ) + TR(q 2 ) TC(q 1 + q 2 ) MR 1 (q 1 ) = MC(q 1 + q 2 ) MR 2 (q 2 ) = MC(q 1 + q 2 ) Profit maximization implies that marginal revenues should be equal across segments. Why? Marginal revenues may be the same, but not the resulting prices. We get: p m 1 (1 1 ε 1 ) = p m 2 (1 1 ε 2 ). The price should be higher in the segment w/ less elastic demand. Nicolas Schutz Monopoly 23 / 59

24 Third-Degree Price Discrimination: Welfare To obtain welfare implications, let s specify the demand functions: In segment a, P a = a Q a. In segment b, P b = b Q b. Assume a > b, i.e., segment a is the high-demand, low-elasticity segment. For simplicity, normalize costs to zero, so that Profits = Total revenue. Discrimination: Monopoly chooses Q a and Q b such that MR a (Q a ) = MR b (Q b ) = 0. a 2Q a = b 2Q b = 0, i.e., Q a = a/2 and Q b = b/2. P a = a/2 and P b = b/2, and Π D = a2 +b 2 4. CS D = a2 +b 2 8, therefore, W D = 3 8 (a2 + b 2 ). Nicolas Schutz Monopoly 24 / 59

25 Third-Degree Price Discrimination: Welfare Assume discrimination is forbidden: Let us first compute the total demand at price P: a + b 2P If P b Q(P) Q a (P) + Q b (P) = a P If b P a 0 otherwise For convenience, we will work with Q(P) (instead of P(Q)). Warning: Total demand is kinked at point P = b. Intuition? Marginal revenue (MR(p)) and marginal profit (dπ/dp) are discontinuous at point P = b. We need to be careful when using first-order conditions. Nicolas Schutz Monopoly 25 / 59

26 Third-Degree Price Discrimination: Welfare Let s compute marginal revenue (= marginal profit): { a + b 4P If P b MR(P) = a 2P If b P a How big is the discontinuity in MR at point b? lim P b MR(P) = a 3b, lim P b + MR(P) = a 2b > a 3b. MR(P) 0 a 2b 0 a 3b Where s the zero? 0 b P Nicolas Schutz Monopoly 26 / 59

27 Third-Degree Price Discrimination: Welfare MR(P) 0 a 2b a 3b MR(P) a 2b a 3b 0 a+b 4 b b a 2 P P Assume a < 2b: Profit-maximizing price solves a + b 4P = 0 P = a+b 4, Q = a+b 2. Π ND = (a+b)2 8, CS ND = 1 16 (5(a2 +b 2 ) 6ab) and W ND = Π ND + CS ND. Assume a > 3b: Profit-maximizing price solves a 2P = 0 P = a 2, Q = a 2. The low-demand segment is not supplied. Π ND = a2 4, CSND = a2 8 and WND = 3 8 a2. Nicolas Schutz Monopoly 27 / 59

28 Third-Degree Price Discrimination: Welfare MR(P) a 2b 0 a 3b Assume 2b < a < 3b: Two local maxima: P = a+b 2 and P = a 2. Which one is better? a+b 4 a 2 P Π(a/2) > Π((a + b)/4) a2 (a + b)2 > a > b 2.4b. 2 1 P = a/2 (resp. P = (a + b)/2) maximizes profits when a is high enough (resp. low enough). In any case, we can reuse the values of Π ND, W ND and CS ND that we computed before. Nicolas Schutz Monopoly 28 / 59

29 Third-Degree Price Discrimination: Welfare Welfare and consumer surplus comparisons: If a < b 2 1, after some algebra: CS ND CS D = 3 16 (a b)2 > 0. W ND W D = 1 16 (a b)2 > 0. If a > b 2 1 : CS ND CS D = b2 8 < 0. W ND W D = 3b2 8 < 0. Nicolas Schutz Monopoly 29 / 59

30 Third-Degree Price Discrimination: Welfare Conclusion: If a < b (i.e., if submarket b is not too small): 2 1 Both segments of the market are supplied under non-discrimination. Pb < P ND < P a : High-demand (resp. low-demand) consumers are better off (resp. worse off) if discrimination is forbidden. CS ND > CS D : overall, consumer surplus is higher under non-discrimination. W ND > W D : banning discrimination improves social welfare. Intuition: Non-discrimination reduces monopoly distortions in the highdemand segment. If a > b 2 1 (i.e., submarket b is very small): Only the high-demand segment is supplied under non-discrimination. Pb < P ND = P a : all consumers are worse off under non-discrimination. W ND < W D : Profits and CS, i.e., non-discrimination degrades social welfare. Intuition: discrimination does not affect high-demand consumers, but it enables low-demand consumers to consume. Nicolas Schutz Monopoly 30 / 59

31 Second-Degree Price Discrimination Second-Degree Price Discrimination: The monopolist knows the distribution of willingness-to-pay among consumers. However, he has no way to know which consumers belong to which group. First- or third-degree price discrimination cannot work here. Instead, the monopolist offers a menu of contracts (or pricing plans, or tariffs) to all consumers. Each consumer then chooses the contract he prefers. The idea is to induce consumers to reveal their private information through their contract s choice. Examples? Cell phone plans. Quantity discounts. Much harder problem to analyze. Nicolas Schutz Monopoly 31 / 59

32 Second-Degree Price Discrimination Two-type example: Consumer surplus from drinking q ounces of coffee and paying t is given by: θ i q t where i = L; H; with (λ, 1 λ) percent of each type in population θ L < θ H, i.e. θ H people get higher marginal utility from each ounce of coffee ( H types). Monopolist offers two sizes of coffee: (q L, t L ), (q H, t H ) and corresponding pricing. Maximization problem: max λ(t L C(q L )) + (1 λ)(t H C(q H )) {(q L,t L ),(q H,t H )} such that people (a) buy, (b) and buy the bundle they are supposed to θ L q L t L 0 (IR-L) θ H q H t H 0 (IR-H) θ L q L t L θ L q H t H (IC-L) θ H q H t H θ H q L t L (IC-H) Nicolas Schutz Monopoly 32 / 59

33 Second-Degree Price Discrimination Let s get rid of some of these constraints: 1 Claim: IR-L and IC-H automatically imply IR-H. Proof : θ H q H t H θ H q L t L (IC-H) > θ L q L t L (since θ H > θ L ) > 0 (IR-L) 2 Claim: IR-L binds at an optimum. Proof : Suppose not. If monopolist increases t L and t H by ε, he still satisfies IR-L. IC-L and IC-H are unchanged (ε cancels from both sides), and IR-H continues to hold. But then monopolist increases profit (price increased by ε, so we can t be at an optimum. Contradiction. 3 Claim: IC-H binds. Proof : Suppose not. Increase t H by ε such that IC-H still holds. IR-L not affected, so IR-H still holds. IC-L holds even more. So once again monopolist increased profits! Contradiction. 4 Claim: IC-L is satisfied automatically given other constraints. Assume for now and verify at optimum. Nicolas Schutz Monopoly 33 / 59

34 Second-Degree Price Discrimination Simplified Maximization problem: max { λ ( t L C(q L ) ) + (1 λ)(t H C(q H )) } s.t. t L = θ L q L t H t L = θ H q H θ H q L Plugging the constraints into the maximand, we get: max λ ( θ L q L C(q L ) ) + (1 λ)(θ H q H + (θ L θ H )q L C(q H )) (q L,q H ) First-order conditions: θ L (1 λ)θ H = λc (q L ) θ H = C ( q H ) Nicolas Schutz Monopoly 34 / 59

35 Second-Degree Price Discrimination For H-types, large coffee size is socially optimal For L-types, suboptimal: θ L (1 λ)θ H < θ L (1 λ)θ L = λθ L, so θ L > C (q L ). Small coffee size is too small. Intuition? The monopolist has to distort ql downward, to prevent H-consumers from purchasing the small quantity. Notice also that q L < q H. Moreover, L-types enjoy zero surplus: θ L q L t L = 0, and are just indifferent between buying coffee and not. H-types enjoy surplus: θ H q H t H 0. Proof: Use IC-H and IR-L. If λ is too close to zero, θ L (1 λ)θ H < 0. In this case, the firm sets t L = q L = 0, C (q H ) = θ H and t H = θ H q H. Intuition? Providing incentives to type-h consumers is costly. If λ is small, the expected profit from selling something to type-l consumers is small. In this case, it s better to focus on type-h consumers. Nicolas Schutz Monopoly 35 / 59

36 Second-Degree Price Discrimination Verify IC-L: θ H q H t H = θ H q L t L Using IC H (θ H θ L )q H + θ L q H t H = θ H q L θ L q L Using IR L θ L q H t H = (θ H θ L )(q L q H ) < 0 Therefore, θ L q H t H < 0 = θ L q L t L, and IC L is satisfied. Nicolas Schutz Monopoly 36 / 59

37 Second-Degree Price Discrimination Welfare: With quadratic cost function, C(q) = q 2, second-degree price discrimination always improves social welfare. There exists an interval [λ, λ], such that, if λ [λ, λ], then, price discrimination makes everybody better off. More than 2 types of consumers: If there are K types, θ 1 < θ 2 < θ 3 <... < θ K 1 Optimality at the top. Marginal cost of largest coffee cup is equal to marginal benefit of H types. 2 Lowest type gets no surplus 3 All other types enjoy some surplus 4 Only downward IC constraints matter, i.e. t i t i 1 = θ i q i θ i 1 q i 1 5 q i > q i 1 Nicolas Schutz Monopoly 37 / 59

38 Bundling Bundling: Selling goods A and B in a package, in fixed proportions. Movie distributors force theaters to acquire bad movies if they want to show good ones. Photocopier manufacturers offer several goods: the copier, maintenance, and a package of both together. Microsoft Office. Menus in restaurants. Tie-in sales: Similar to bundling, but the firm does not control the proportions. IBM required the buyers of its tabulating machines to purchase IBM tabulating cards. HP cartridges won t fit Canon printers. Nicolas Schutz Monopoly 38 / 59

39 Bundling Example 1: Two types of consumers, unit-inelastic demand, no complementarity between products: WTP AB = WTP A + WTP B Assume MC =0 Type 1 WTP Type 2 WTP A B AB If sell separately, p A = 9000, p B = π A +π B = 2(9000)+2(2000) = If sell AB, p AB = 12000, π AB = Nicolas Schutz Monopoly 39 / 59

40 Bundling Example 2: Type 1 WTP Type 2 WTP A B AB If sell separately, p A = 9000, p B = π A + π B = 2(9000) = If sell AB, p AB = π AB = What s different? In the first example, type 1 has higher demand for B, type 2 has higher demand for A. In the second example, type 2 has higher demand for both goods Intuition: bundling works when there is heterogeneity in preferences across goods. Nicolas Schutz Monopoly 40 / 59

41 Bundling Example 3: Type 1 WTP Type 2 WTP Type 3 WTP A B AB If sell separately, p A = 3000, p B = π A + π B = 3000 x 4 = If sell AB, p AB = π AB = If sell A and B and AB (mixed bundling), p A = 4000, p B = 4000, p AB = 6000, π mixed = In this example, consumer type 2 has a fairly low valuation for the 2 products separately but a much higher valuation for the 2 together. In contrast, consumers 1 and 3 only value one of the two products. Firm can extract all surplus from all consumers through mixed tying (design one package to appeal to each type of consumer). In examples 1 and 3 bundling is used as a means to implement price discrimination. Nicolas Schutz Monopoly 41 / 59

42 Bundling Bakos and Brynjolffson (1999): Bundling of Information Goods Should AOL price services separately, or sell bundles? Intuition: Separate monopoly pricing of goods means exclusion of consumers with low valuations and also loses revenues from those with very high values. With bundling, valuations are averaged with much fewer extreme values. Hence, can extract higher profits from all customers If number of goods being bundled is large enough, and the valuations for goods are not too positively correlated, pure bundling is a good idea too. Nicolas Schutz Monopoly 42 / 59

43 Bundling and Foreclosure Antitrust laws prohibit bundling when it leads to reduced competition. Does it make sense? Traditional foreclosure theory: If firm M has monopoly power in market A, it may try to extend its market power to market B by selling an A B bundle. This would foreclose its competitors in (previously competitive) market B. Chicago School criticism (1970 s): You can t leverage market power from market A to market B. Nicolas Schutz Monopoly 43 / 59

44 Bundling and Foreclosure A simple model to formalize the Chicago School criticism: Two products: A and B. Mass 1 of consumers w/ unit demand for both products and identical preferences. Market A: Firm M is a monopoly, w/ constant unit cost a. Consumers WTP: A. Market B: A and B are complements. Product B is worthless if not combined with product A. Competitive fringe of suppliers: infinitely elastic supply at price ˆb. Consumers WTP for the fringe s product: ˆB > ˆb. M produces good B w/ constant unit cost b > ˆb. Consumers WTP: B < ˆB. Nicolas Schutz Monopoly 44 / 59

45 Bundling and Foreclosure Unbundling: M doesn t sell product B in equilibrium. P B = ˆb. If a consumer purchases good A, it also purchase good B, since ˆB > P B. Consumer s utility: { A + ( ˆB U = ˆb) P A if purchases good A 0 otherwise Therefore, P A = A + ( ˆB ˆb), and the monopolist earns Π NB = A + ( ˆB ˆb) a. Bundling: If M chooses to bundle products A and B, consumer s utility is U = A + B P AB. Therefore, P AB = A + B, and the monopolist earns Π B = A + B a b < Π NB. Nicolas Schutz Monopoly 45 / 59

46 Bundling and Foreclosure Conclusion: Even though bundling leads to the foreclosure of M s rivals in market B, it is not profitable. Under unbundling, M can already extract consumers surplus through its pricing in market A. M has no interest in trying to exclude low-cost / high quality products in market B, which increase consumers WTP for its product A. Nicolas Schutz Monopoly 46 / 59

47 Bundling and Foreclosure October 2000: $42 billion merger announced between General Electric and Honeywell. GE: revenues over $125 billion. Businesses included plastics, television (NBC), financial services, power systems, lighting. Also aviation: produces aircraft engines (e.g. Boeing 777, 767, 747 and Airbus A300, A310, A330 planes). Honeywell: $23 billion of revenues. Included heating, environmental controls, avionics (= aviation electronics). About half of revenues came from avionics. Why did they want to merge? What are the arguments against the merger? Nicolas Schutz Monopoly 47 / 59

48 Bundling and Foreclosure US Department of Justice approved the merger. July : European Commission blocked it. Reasons: GE had a dominant position in aircraft engines for large commercial aircraft. Honeywell had a leading position in avionics. The proposed merger would allow the new firm to bundle these complementary products. This advantage would lead to the exit of rivals and thus ultimately to strengthening the dominance of GE. EU Final Decision (paragraph 355): Because of their lack of ability to match the bundle offer, these component suppliers will lose market shares to the benefit of the merged entity and experience an immediate damaging profit shrinkage. As a result, the merger is likely to lead to market foreclosure on the existing aircraft platforms and subsequently to the elimination of competition in these areas. Nicolas Schutz Monopoly 48 / 59

49 Bundling and Foreclosure The Chicago School argument may not work in the following situations: If products A and B are not complements, bundling may deter entry in segment B. If entry in market B facilitates entry in market A, it can be profitable to deter entry in B to deter entry in A. (More on this in a couple of lectures.) The European Commission s decision may not be misguided after all. Nicolas Schutz Monopoly 49 / 59

50 Durable Goods Monopoly Definition of a Durable Good: goods that are bought only once in a long time and can be used for a long time. Examples: cars, houses, land. (The typical analysis uses perishable or flowgoods.) Since the typical analysis uses perishable goods, we can use static models to understand pricing decisions. With durable goods, we need to take the future into account, and we need dynamic models to understand pricing decisions. (Note that durability is a relative concept: there are many different degrees of durability. Definition by U.S. Census: 3 years.) Nicolas Schutz Monopoly 50 / 59

51 Durable Goods Monopoly Coase Conjecture: Consider the example of a monopolist who owns all the land in the world and wants to sell it at the largest discounted profit. In year 1, the monopolist sets a monopoly price and sells half the land. (Think of a linear demand curve with marginal cost at zero.) In year 2, the monopolist will want to do the same with the remaining land, but unless the population is growing very quickly, demand for land will be lower. Thus, the monopoly land price in year 2 will be lower. Coase conjecture: if consumers do not discount time too heavily and if consumers expect price to fall in future periods, current demand facing the monopolist will fall, implying that the monopoly will charge a lower price (compared to a perishable good). Nicolas Schutz Monopoly 51 / 59

52 Durable Goods Monopoly Crucial assumptions: 1 Durable good. 2 Demand does not grow quickly over time. 3 Consumers anticipate price cuts. As we will see, the assumption of a downward sloping demand (with a continuum of consumers) is also a crucial assumption. Nicolas Schutz Monopoly 52 / 59

53 Durable Goods Monopoly Model I: Continuum of consumers, downward sloping demand. Assumptions: Consumers live for 2 periods. Product lasts for 2 periods. Production cost normalized to 0. The aggregate one-period demand for the services of the good is p = 100 q. Define a game: 1 Set of players: seller and buyers. 2 Set of actions/strategies for each player: Seller chooses quantity in period 1, and quantity in period 2 (as a function of q 1 ). Buyers choose whether to buy in each period as a function of price. 3 Pay-off function (producer and consumer surplus). No discounting. Nicolas Schutz Monopoly 53 / 59

54 Durable Goods Monopoly We look for the equilibria of this game. Which solution concept should we use? Subgame-perfect equilibrium, since it s a multistage game. How should we look for equilibria? Since there s a finite number of periods, we can (and should) use backward induction. Let s start with period 2. Assume that q 1 units were sold in period 1: People who bought in period 1 do not need to buy again. Demand in stage 2 is: p 2 = 100 q 1 q 2. As usual, MR = MC(= 0), i.e., 100 q 1 2q 2 = 0. q 2 = 50 q 1 2 and π 2 = p 2 q 2 = (50 q 1 2 )2. Nicolas Schutz Monopoly 54 / 59

55 Durable Goods Monopoly Assume the monopolist sells q 1 units in period 1. What is the maximum price he can charge? The marginal buyer (in period 1) should be indifferent between purchasing today and purchasing tomorrow. Payoff of the marginal buyer if purchases today: 2(100 q1 ) p 1. If purchases tomorrow: (100 q1 ) p 2 = (100 q 1 ) (50 q 1 ). 2 This gives us the demand curve faced by the monopolist in period 1: p 1 = q 1 2. Now we can write the firm s profit maximization problem as a function of q 1 only: ( max(π 1 + π 2 ) = 150 3q ) ( 1 q q ) 2 1 q Take F.O.C. and solve... We find q 1 = 40; q 2 = 30; p 2 = 30; p 1 = 90. This implies that total profits for both periods are 4, 500. Nicolas Schutz Monopoly 55 / 59

56 Durable Goods Monopoly An alternative strategy set: Rent (Example: Xerox in the 1960 s, when it had substantial market power in the photocopiers market). Selling means charging a single price for an indefinite period... Renting means charging a price for using the product for a limited time period. How does the firm maximize profits if it rents out the good? Recall that the aggregate one-period demand for the services of the good is p = 100 q. Therefore, solve the static model twice (a repeated game). F.O.C. (MR = MC) imply p t = 50 = π t = 2, 500 = π 1 + π 2 = 5, 000. The firm does better by renting out the product. When it sells its products, a durable good monopolist is its own competitor. NB: If the monopoly sells the product, the total two-period price is 90. If he sells it, it is 50 2 = 100. Nicolas Schutz Monopoly 56 / 59

57 Durable Goods Monopoly Choosing a lower relative level of durability is one way of solving the problem of consumers expectations. Other ways include: 1 Renting (we just did that). 2 Planned obsolescence (new car models, new fashions... as long as costs are not too high). 3 Capacity constraints (numbered prints). 4 Announcements/advertising future prices. 5 Lowest-price guarantee. Nicolas Schutz Monopoly 57 / 59

58 Durable Goods Monopoly Durable goods monopoly w/ discrete demand: Two consumers: Utility per period: Ui = θ i P. Assume θh > 2θ L, i.e., consumers are different enough. Renting: Two periods. Costs normalized to zero. Again, all we need to do is solve the static profit maximization problem. If p t = θ H, then, π t = θ H. If p t = θ L, then, π t = 2θ L. Since θ H > 2θ L, the monopolist charges θ H at each period and makes total profits Π R = 2θ H. Nicolas Schutz Monopoly 58 / 59

59 Durable Goods Monopoly Selling: Start with period 2: If consumers H and L are still there, we know that p2 = θ H maximizes the static profit. π 2 = θ H, CS H = CS L = 0. If consumer H is still there, again, p2 = θ H. π 2 = θ H, CS H = 0. If consumer L is still there, p2 = θ L. π 2 = θ L, CS L = 0. Period 1: Consumer H accepts any offer below 2θH (since he will get 0 surplus if he waits until period 2). Similarly, consumer L accepts any offer below 2θL. In equilibrium, the monopolist offers p1 = 2θ H and p 2 = θ L. This yields Π S = 2θ H + θ L > Π R. The Coase conjecture doesn t work when demand is discrete and consumers are different enough. In this case, selling the durable good is a means to discriminate between consumers. Nicolas Schutz Monopoly 59 / 59