Industrial Organization Lecture 12: Vertical Relations

Size: px
Start display at page:

Download "Industrial Organization Lecture 12: Vertical Relations"

Transcription

1 Industrial Organization Lecture 12: Vertical Relations Nicolas Schutz Nicolas Schutz Vertical Relations 1 / 71

2 Introduction Production and distribution chains are often made up of different firms. Manufacturers (upstream firms) rarely supply final consumers directly. Retailers (downstream firms) often make important decisions regarding the product. 1 Determination of final price. 2 Promotional effort. 3 Placement of product on store shelves. 4 Promotion and placement of competing products. 5 Technological inputs. Nicolas Schutz Vertical Relations 2 / 71

3 Introduction Why don t firms always vertically integrate? Costs to VI: As firm size and scope increases, becomes harder to manage Explicit transaction costs to vertical mergers (lawyer and investment banker fees, regulatory constraints) Why do firms sometimes vertically integrate? Non-integrated vertical partner does not always have the incentive to do what is best for the vertical coalition. Integration is a way to get around this misalignment of incentives problem. Caution: most of the time, however, integration is a costly alternative to wellwritten contracts. Nicolas Schutz Vertical Relations 3 / 71

4 The Hold-Up Problem Whenever firms in a production chain have to make relationship-specific investments that can not be completely contracted on, a possibility for investment hold-up arises. Model: Timing: An upstream firm, a downstream firm and a final consumer. Quality of the downstream product depends on investment made by the upstream firm. Final consumer s willingness to pay for the downstream good is v(i), with v (I) > 0 and v (I) < 0. Investment costs I dollars per unit. All other costs are normalized to zero. Downstream firm is a monopoly, and sells good to consumers at v(i) > 0. 1 Upstream firm makes investment choice. 2 Upstream firm makes product; Downstream firm sells at v(i). Set unit input payment from Downstream to Upstream firm p(i), so that the ex post surplus is shared evenly. Nicolas Schutz Vertical Relations 4 / 71

5 The Hold-Up Problem Solve by backward induction. Second stage of game, the surplus is split evenly. Extreme assumptions: If firms do not reach an agreement, then the upstream firm cannot sell its input elsewhere. If firms do not reach an agreement, then the downstream firm cannot purchase the input from another supplier. The surplus for the upstream firm is therefore p(i) 0 = p(i). [Notice that we do not include the I in the surplus, since this cost was sunk in the previous period] The surplus for the downstream firm is: v(i) p(i) 0 = v(i) p(i). Surplus is shared evenly: v(i) p(i) = p(i) p(i) = v(i) 2 Nicolas Schutz Vertical Relations 5 / 71

6 The Hold-Up Problem Back to the first stage: Upstream firm s investment decision: max p(i) I = v(i) I 2 I First-order condition: v (I)/2 1 = 0, i.e., v (I ) = 2. But the optimization problem of an integrated firm would have been different: First-order condition: v (I ) = 1. max(v(i) I) I Since v > 0 and v < 0, I < I, i.e., the upstream firm invests too little. Intuition? Nicolas Schutz Vertical Relations 6 / 71

7 The Hold-Up Problem Back to the first stage: Upstream firm s investment decision: max p(i) I = v(i) I 2 I First-order condition: v (I)/2 1 = 0, i.e., v (I ) = 2. But the optimization problem of an integrated firm would have been different: First-order condition: v (I ) = 1. max(v(i) I) I Since v > 0 and v < 0, I < I, i.e., the upstream firm invests too little. Intuition? The upstream firm incurs the whole investment cost, but it gets only 1/2 of the benefits. Less incentives to invest. This is the hold-up problem. Nicolas Schutz Vertical Relations 6 / 71

8 The Hold-Up Problem In general, the activities of the downstream / upstream firm may affect the profits of the upstream / downstream firm. Two possible solutions to this (some subject to legal constraints): Vertical integration. Contracts and other vertical restraints. Examples: At time 0, sign a contract which specifies a transfer b/w the two firms, and an investment level (here, I ). Or, at time 0, sign a contract which specifies: a transfer b/w the firms (at time 0) and a price p(i) (say, p(i) = v(i)) for period 2 payments. At a deeper level, though, what is the difference between writing contracts with the manager/employees of the downstream as opposed to writing contracts across firm boundaries? We won t touch on this, but the question of how to provide incentives within a firm is an important one. Nicolas Schutz Vertical Relations 7 / 71

9 Vertical Restraints Let s focus on contractual solutions from now on. Main message is: One can cut through many possible inefficiencies and conflicts-of-interest through the use of well thought-out contracts. Of course, this is conditional on the enforceability of those contracts. Nicolas Schutz Vertical Relations 8 / 71

10 Vertical Restraints Types of contracts / vertical restraints: Transactional restraints / contracts: Franchise fees. Profit/revenue sharing arrangements. Resale Price Maintenance: a dealer commits to a retail price or a range of retail prices for the product. This can take the form of either minimum resale price maintenance or maximum resale price maintenance. Quantity forcing / quantity rationing. Full-line forcing : a dealer is committed to sell all the varieties of the manufacturer s products rather than a limited selection. (i.e., the upstream firm ties all its products when selling to the downstream firm). Organizational restraints: Exclusive Territories: a dealer / distributor / retailer is assigned a (usually geographic) territory by the manufacturer / upstream firm and given monopoly rights to sell in that area. Exclusive Dealing: a dealer / distributor / retailer is not allowed to carry the brands of a competing upstream firm. Nicolas Schutz Vertical Relations 9 / 71

11 The Double Marginalization Problem Basic Problem of Vertical Control: Simple model: homogeneous good with (inverse) demand given by p = a Q. Suppose we have a monopolistic manufacturer and we have given exclusive rights to a dealer to sell the product of the manufacturer, so both the upstream and downstream firms are monopolistic. The downstream firm has marginal cost of selling d which is equal to the wholesale cost of purchasing the product from the manufacturer, and the manufacturer has marginal cost of producing the good equal to c. Assume the following timing: 1 Manufacturer sets price d. 2 The dealer sets its downstream price (or quantity). Nicolas Schutz Vertical Relations 10 / 71

12 The Double Marginalization Problem Dealer maximizes his profit given by π d = p(q)q dq = (a Q)Q dq F.O.C.: π d Q = 0 = a 2Q d Q = a d 2 p = a + d 2 Manufacturer maximizes profit given by π d = (a d)2 4 π m = (d c)q = (d c) a d 2 F.O.C.: π m d d = a + c 2 = 0 = a 2d + c = 0 π m = (a c)2 8 Nicolas Schutz Vertical Relations 11 / 71

13 The Double Marginalization Problem Note that we can now substitute into the dealer s solutions (for d) and get: Q = a c 4 p = 3a + c 4 π d = (a c)2 16 Now, assume that the industry is vertically integrated. Vertically integrated firm maximizes (a c Q)Q. This yields Q VI = a c 2 p VI = a + c 2 π VI = (a c)2 4 Nicolas Schutz Vertical Relations 12 / 71

14 The Double Marginalization Problem Summary: 1 The manufacturer earns a higher profit than the dealer 2 The manufacturer could earn a higher profit if he did the selling himself. Total industry profit in this case is lower than the vertically integrated profit: π VI = (a c)2 4 > π d + π m = 3(a c) Output is higher and final price is lower when the two firms are vertically integrated. Intuition for these results? Nicolas Schutz Vertical Relations 13 / 71

15 The Double Marginalization Problem Summary: 1 The manufacturer earns a higher profit than the dealer 2 The manufacturer could earn a higher profit if he did the selling himself. Total industry profit in this case is lower than the vertically integrated profit: π VI = (a c)2 4 > π d + π m = 3(a c) Output is higher and final price is lower when the two firms are vertically integrated. Intuition for these results? The presence of two markups causes this distortion. This basic fact is called: Double-monopoly markup problem, successive monopolies problem, or double marginalization. Nicolas Schutz Vertical Relations 13 / 71

16 The Double Marginalization Problem How to solve this double marginalization problem: A first solution: non-linear pricing. The manufacturer offers a two-part tariff T(Q) = (a c)2 4 + cq Put differently, the manufacturer sets franchise fee φ = (a c)2 4, and a unit price of d = c to dealer. In this case, the retailer sets the monopoly quantity, earns the monopoly profits, and these profits are extracted by the manufacturer through the franchise fee. This kind of two-part pricing arrangement is specified in most franchising agreements (hotel, restaurant, fast-food, business services industries, etc.) Nicolas Schutz Vertical Relations 14 / 71

17 The Double Marginalization Problem Some problems with non-linear pricing: In the case where demand is uncertain, retailer absorbs all risk. Giving the retailer a discount on franchise fee, but charging a price above c may provide some insurance, but introduces some double marginalization problem. One can think of uncertainty case with franchise fee and & marginal cost pricing as the pure profit-sharing case. The insurance motive, in effect, leads to partial profit sharing between manufacturer and retailer. Retailer may have private info about true demand for product (a), and it might be tough for manufacturer to set correct franchise fee. One solution: offer a menu of franchise contracts to induce correct selfselection. This will still leave some information rents to retailer, but will improve upon having a single contract. Nicolas Schutz Vertical Relations 15 / 71

18 The Double Marginalization Problem If there are multiple retailers, setting d = c may not result in correct incentives. If retailers compete in prices with perfectly homogenous products, the double markup problem disappears. Manufacturer can just set an input price equal to the monopoly price. Price competition w/ differentiated products: d should be between c and the monopoly price. Optimal d decreases as products become more differentiated. What if there are multiple manufacturers and a single dealer? Nicolas Schutz Vertical Relations 16 / 71

19 Resale Price Maintenance Another solution: Resale Price Maintenance: Requires retailers to maintain a minimum price, a maximum price, or a fixed price. Examples: Windows 98, Windows XP, books, many many retail products. Two goals: 1 Partially solve the double marginalization problem 2 Can induce dealers or retailers to allocate resources for promoting the product, or exerting other forms of effort in distributing the product. Nicolas Schutz Vertical Relations 17 / 71

20 Resale Price Maintenance Consider the example of promotions or advertising. Assume (inverse) demand is given by p = A Q The manufacturer sells to two dealers at wholesale price d. Then, retailers set their advertising expenditures A 1 and A 2 simultaneously. This yields A = A 1 + A 2. Finally, retailers compete in prices with homogenous products. First result: For any given d, no dealer will engage in advertising and demand will shrink to zero, with no sales. Why? Nicolas Schutz Vertical Relations 18 / 71

21 Resale Price Maintenance Consider the example of promotions or advertising. Assume (inverse) demand is given by p = A Q The manufacturer sells to two dealers at wholesale price d. Then, retailers set their advertising expenditures A 1 and A 2 simultaneously. This yields A = A 1 + A 2. Finally, retailers compete in prices with homogenous products. First result: For any given d, no dealer will engage in advertising and demand will shrink to zero, with no sales. Why? Firms compete in price, and they sell a homogeneous product. What does p equal in this case?? Nicolas Schutz Vertical Relations 18 / 71

22 Resale Price Maintenance What can Resale Price Maintenance do? Minimum Resale Price Maintenance: p = p f d Now demand is Q = (A 1 + A 2 ) p f Assume that quantity demanded is split evenly between the two retailers. The only strategic variable for the retailers is A. Thus, writing profits as a function of A and finding the F.O.C. yields: π i = (Ai + A j ) p f (p f d) A i 2 F.O.C.: 0 = π i p f d = A i 4 (A i + A j ) 1 Nicolas Schutz Vertical Relations 19 / 71

23 Resale Price Maintenance Therefore, (A 1 + A 2 ) = (pf d) Note that we can only identify the sum of A 1 +A 2 and not A 1 and A 2 individually. But the idea is that retailers will compete on promotion now. As long as p f > d then at least one retailer has an incentive to advertise, and the total dollars spent on ads increases with the markup. In this model, retailers free ride on their rivals advertising expenditures. Imposing a minimum price allows the manufacturer to increase retailers incentives to advertise, and hence, to partially solve the free-riding / public good problem. This model illustrates nicely the tradeoff faced by competition authorities when deciding whether to challenge a vertical restraint: On the one hand, resale price maintenance allows the manufacturer to solve the free-riding problem, which creates some economic surplus. On the other hand, it softens downstream competition, and raises downstream prices. Nicolas Schutz Vertical Relations 20 / 71

24 Resale Price Maintenance A similar story for retail services: Suppose you want to buy a book (or a PC, or a stereo equipment, etc.) If you go to your local bookstore, you will certainly get some valuable and personalized advice. But then, other firms, such as Amazon.com may have incentives to free ride on your local bookstore s efforts. You would get recommandations at your local bookstore, and purchase at a low price at Amazon. In France, minimum resale price maintenance is mandatory for books. Nicolas Schutz Vertical Relations 21 / 71

25 Exclusive Territories Note that one problem in the last example was that competition between the retailers initially resulted in too much competition downstream, so that firms could not afford to advertise as a vertically-integrated firm would choose to do. Another way around that: Exclusive Territories or Territorial Dealerships. With exclusive territories, the manufacturer chooses a dealer, and gives him exclusive rights to sell its product in a specific submarket. Nicolas Schutz Vertical Relations 22 / 71

26 Exclusive Territories A simple model of territorial dealerships: A manufacturer, firm M, must choose whether to grant dealerships to one or two dealers. A similar literature looks at these decisions in the context of licensing for inventors (i.e., when I invent a new product, do I want to sell it myself, license it exclusively to a retailer / distributor, or license it to many competing retailers?). M s production cost is c = 0. M sets a wholesale (linear) price d. There is a fixed cost (paid by the dealer) to setting up a dealership given by F > 0. Consider a spatial model of differentiated products with two consumers located at the extremities of a segment: Consumer 1 Consumer 2 Length 2T Nicolas Schutz Vertical Relations 23 / 71

27 Exclusive Territories The manufacturer must decide whether to license a single dealer in the center of town: Consumer 1 Dealer Consumer 2 Or two dealerships at the edges of town: T Consumer 1 Dealer 1 2T Consumer 2 Dealer 2 The travel costs for a consumer of travelling from either edge of town to the center are T. Consumers have the same basic value for the product, = B. Nicolas Schutz Vertical Relations 24 / 71

28 Exclusive Territories Thus, the utility functions of the consumers are: B T p if buy from a center dealer u i B p = i if buy from local (edge) dealer B 2T p j if buy from other side of town 0 otherwise. Now, let s be a bit more precise about the timing: 1 Firm M decides how many dealers to license. 2 Firm M sets its wholesale tariff d. Dealers decide whether to start producing, and pay the set-up cost F. 3 Dealers set their prices simultaneously. Nicolas Schutz Vertical Relations 25 / 71

29 Exclusive Territories Solve by backward induction. If the manufacturer has granted only one license, then we have an exclusive town-center dealer. Each consumer s net utility is max{b T p, 0}. The dealer fully extracts the consumer surplus by charging the highest price possible: p = B T. His total profit is therefore: π d = 2(p d) F = 2(B T d) F Now, go back to stage 2: Firm M sets d so as to maximize its profit, π m = d Q, subject to the dealer s participation constraint: π d = 2(B T d) F 0 Nicolas Schutz Vertical Relations 26 / 71

30 Exclusive Territories The manufacturer will saturate this constraint (i.e., fully extract the dealer s profit): π d = 0 d = B T F 2 This yields π m = 2 (B T F 2 ) = 2(B T) F Now, assume that firm M granted two licenses in period 1: As it turns out, we have to distinguish two cases: large town, and small town (or, equivalently, towns with high / low transportation costs, or towns with high / low search costs for consumers... ) Case 1: Large town Define a large town as one in which T > F 4 (and small town: T < F 4 ). You should remember from David s recitations that a Nash equilibrium (in pure strategies) may fail to exist in spatial models of product differentiation. To get around this issue, we will use a weaker solution concept, which Shy calls undercut-proof equilibrium. Nicolas Schutz Vertical Relations 27 / 71

31 Exclusive Territories We want to find an equilibrium in which the two dealers do not undercut each others prices. Thus, we want to find an equilibrium such that: π 1 = p 1 d F 2((p 2 2T) d) F i.e., profit to firm 1 is higher if they don t undercut firm 2 and take all of firm 2 s customers. π 2 = p 2 d F 2((p 1 2T) d) F same requirement for firm 2. These are the requirements for an undercut-proof equilibrium. [If we wanted to find a Nash equilibrium, which condition(s) should we add?] Assume the manufacturer sets d = B F (we will show later on that this is the best thing firm M can do). Let us show that there exists an undercut-proof equilibrium, in which both dealers set a price equal to B. Nicolas Schutz Vertical Relations 28 / 71

32 Exclusive Territories If both dealers charge B, then they both earn (B (B F)) 1 F = 0. If dealer i undercuts, the best thing he can do is set p i = p j 2T = B 2T. In this case, he earns (B 2T d) 2 F = 2(B 2T (B F)) F = F 4T, which is negative, since the town is large. Therefore, p 1 = p 2 = B is an undercut-proof equilibrium. The manufacturer earns: 2d = 2(B F). Notice that the dealers are fully extracting the consumer surplus. In turn, the manufacturer is fully extracting the dealers surplus. This means that the manufacturer is earning the whole monopoly profit of the industry. There is no way for the manufacturer to improve on this. We can conclude that, in equilibrium, firm M charges d = B F, and earns 2(B F). Nicolas Schutz Vertical Relations 29 / 71

33 Exclusive Territories So, what should the manufacturer do in stage 1? Set up one dealership and earn 2(B T) F? Or set up two dealerships and earns 2(B F)? [Remember that we are still assuming that the town is large] A single dealership is more profitable iff Conclusion (for the large town): 2(B T) F > 2(B F) F < 2T If F < 0 < 2T, then, two dealerships. If 2T < F < 4T, then, one dealership. Intuition: Setting up two dealerships is costly... But this also enables the manufacturer to (indirectly) price discriminate b/w the two consumers. The second effect dominates as long as F is not too large. Nicolas Schutz Vertical Relations 30 / 71

34 Exclusive Territories Now, suppose that the town is small, i.e., F > 4T. Remember the conditions for an undercut-proof equilibrium: Simplify a bit, and plug (2) into (1): p 1 d 2((p 2 2T) d) (1) p 2 d 2((p 1 2T) d) (2) p 1 2 ( 2(p 1 2T) d 2T ) d 0 3p 1 12T 3d p 1 4T + d So in an undercut-proof equilibrium, p 1 and p 2 have to be lower than d + 4T. This puts an upper bound on dealers profits: π i = p i d F 4T + d d F = 4T F, which is strictly negative, since the town is small. Conclusion: When the town is small, there is no undercut-proof equilibrium in which dealers make non-negative profits. When the town is small, the manufacturer grants a single dealership. Nicolas Schutz Vertical Relations 31 / 71

35 Exclusive Territories In a small town: Setting up two dealerships enables the manufacturer to (indirectly) price discriminate b/w the two consumers, But this is costly, and price competition between retailers makes it tougher for them to survive. In a small town, the last two negative effects dominate the price discrimination effect, and it is never profitable to set up two dealerships. Nicolas Schutz Vertical Relations 32 / 71

36 Exclusive Territories One contractual way to get around this problem is to set up exclusive territories so that 2 dealerships are simply not allowed to compete with each other (i.e., we contract around the problem of intrabrand competition). In the previous example, each dealer becomes a monopolist on his half of the linear market. Each dealer charges the monopoly price B, and makes π d = B d F. As in the large town case, the manufacturer can then set d = B F, and earn the industry monopoly profit. As it turns out, even if the manufacturer can enforce exclusive territories, he will still choose to grant a single dealership when the town is small (so it s not such a great model... ) Still, the main point is that, when a manufacturer has granted several licenses, he may want to limit competition by imposing exclusive territories, so as to make sure that all its dealers can pay their fixed costs and survive. Example of exclusive territories: car dealerships in European countries. Nicolas Schutz Vertical Relations 33 / 71

37 Vertical Restraints: Legal Issues There are a lot of ambiguities in legal treatment of vertical contracts. Until the 1970s, resale price maintenance and exclusive territories were per se illegal under Sherman Act. Although price fixing remains per se illegal, it s not always applied in vertical settings because it conflicts with free trade notions between manufacturers and their distributors. Courts seem to be more receptive to vertical arrangements that do not involve price fixing (e.g., exclusive territories). Given our analysis, in which exclusive territories and resale price maintenance were often substitutes, it is not clear that these two types of vertical restraints should be treated asymmetrically. Nicolas Schutz Vertical Relations 34 / 71

38 Vertical Mergers Why do firms sometimes merge vertically, and what should antitrust authorities think about vertical mergers? As usual, vertical mergers may create efficiency gains. A vertical merger can generate synergies. After a vertical merger, the upstream unit may be better able to tailor its input for the downstream unit. We also know that, in vertically related markets, upstream-downstream externalities are important: There may be a double marginalization problem, Retailers may free ride on each other for the provision of advertising / retail services, etc. Competition between retailers may be too fierce to allow them to survive. We have seen contractual solutions (i.e., vertical restraints) for these problems. But vertical integration would also do the job. In most cases, such a vertical merger would be welfare improving. Nicolas Schutz Vertical Relations 35 / 71

39 Vertical Mergers But it is often argued that vertical mergers can have anticompetitive effects. The traditional foreclosure theory (or raise your rival s cost theory), which was influential in antitrust decisions in the 60s/70s, states that: 1 Firms like to face poorly competitive / high-cost rivals. 2 A vertically integrated firm has the ability to raise its downstream rivals costs Either by increasing its input price, Or simply by refusing to deal with unintegrated downstream firms. 3 Ergo, a vertical merger raises input prices, and hence, final prices. Distinction b/w partial and complete foreclosure: Complete foreclosure: After a vertical merger, unintegrated downstream firms can no longer purchase the input. Partial foreclosure: After a vertical merger, unintegrated downstream still purchase the input, but at a higher price. Nicolas Schutz Vertical Relations 36 / 71

40 Vertical Mergers The traditional foreclosure theory was forcefully criticized by Chicago School authors in the 70s. One way to summarize the Chicago School criticism: firms cannot leverage / extend market power from one market to another. To (over)simplify, Chicago authors said that: Vertically integrated firms do not necessarily have incentives to raise their rivals costs. The single monopoly profit criticism. Even if they do have such incentives, this does not annihilate the competitive pressure on the upstream market. The upstream competition criticism. If these points are taken seriously (which competition authorities have done since the beginning of the 80s), then a vertical merger is competitively neutral or pro-competitive. If a merger is observed, it must be driven by efficiency motivations. Nicolas Schutz Vertical Relations 37 / 71

41 Vertical Mergers More recently, a new approach, the post-chicago approach, has developed. Main objective: try to shed light on the debate b/w the traditional foreclosure theory and the Chicago School criticism, by using modern game-theoretical tools. In the following, we will cover both the single monopoly profit argument and the upstream competition criticisms. We will also check whether these arguments survive to the Post-Chicago approach. Nicolas Schutz Vertical Relations 38 / 71

42 The Single Monopoly Profit Criticism We consider the upstream bottleneck framework: D1 U D2 One manufacturer U and two retailers D1 and D2. All marginal costs are normalized to zero. Retailers compete à la Cournot on the final market, with inverse demand function P(Q) = 1 Q. Manufacturer offers non-discriminatory two-part tariff contracts (w, T) to the retailers. Timing: Final consumers 1 U announces (w, T). 2 Downstream firms decide whether to accept the offer. 3 Downstream firms compete in quantities on the downstream market. We will restrict our attention to two-part tariff offers such that both downstream firms find it profitable to accept the contract in period 2. As we will see, this restriction is without loss of generality. Nicolas Schutz Vertical Relations 39 / 71

43 The Single Monopoly Profit Criticism We look for the subgame-perfect equilibria of this three-stage game, and solve by backward induction. Start at period 2, and assume both retailers accepted the supplier s offer in period 1. Retailer Di s profit is given by: π i (q 1, q 2 ) = (P(q i + q j ) w)q i T = (1 q i q j w)q i T This is a simple quantity-setting game. Firm Di s first-order condition is: 1 q j w 2q i = 0 This yields firm Di s best response: R i (q j ) = 1 w q j 2. Solving for the intersection of these best-response functions, we get the Nash equilibrium of the subgame: q i (w) = q j (w) = 1 w 3 Nicolas Schutz Vertical Relations 40 / 71

44 The Single Monopoly Profit Criticism Plugging these equilibrium quantities into firms profit functions, we obtain the retailers profits at the equilibrium of the subgame: π i (w, T) = (1 q i (w) q j (w) w)q i (w) T = (1 w)2 9 Similarly, the manufacturer s profit at the equilibrium of this subgame is π U (w, T) = w(q i (w) + q j (w)) + 2T = 2(w 1 w 3 + T) Now, go back to period 2: retailer Di will accept the contract as long as he expects a non-negative profit from it, i.e., as long as T (1 w) 2 9 T Nicolas Schutz Vertical Relations 41 / 71

45 The Single Monopoly Profit Criticism Back to period 1. Remember that we restrict ourselves to upstream contracts which will be accepted by both downstream firms. Therefore, firm U maximizes its profit π U (w, T) = 2(w 1 w 3 + T) in (w, T) subject to the constraint that both retailers participate, i.e., π i (w, T) = (1 w)2 9 T 0. Of course, the constraint will be binding at the manufacturer s optimum. (if it were not, firm U could just increase the fixed fee by ε. Both retailers would still participate, and the manufacturer would make more profits). We can plug T = (1 w)2 9 into the manufacturer s profit function: π U (w, T) = 2(wq i (w) + T) = 2(wq i (w) + (P(q i (w) + q j (w)) w)q i (w)) = 2P(Q(w))q i (w) = P(Q(w))Q(w) The above equation tells us that the manufacturer sets w so as to maximize the industry s total profit. He will then use the fixed fees to extract retailers profits. Nicolas Schutz Vertical Relations 42 / 71

46 The Single Monopoly Profit Criticism Plugging in the values of Q(w) and P(Q(w)), we get: π U (w, T) = 2q i (w)(1 2q i (w)) = 2 (1 w)(1 + 2w) 9 Maximize the above function in w by taking the first-order condition: 2/9( (1 + 2w) + 2(1 w) = 0 w = 1/4 Plug this into the manufacturer s profit function: We also know that T is given by π U = = 1 4 T = (1 w)2 9 = 1 16 Conclusion: in equilibrium, the manufacturer offers contract (w = 1/4, T = 1/16). Manufacturer earns π U = 1/4, whereas retailers make 0 profit. Nicolas Schutz Vertical Relations 43 / 71

47 The Single Monopoly Profit Criticism The manufacturer is choosing his tariff as follows: Set w > 0 to make sure that retailers internalize competitive externalities. i.e., set w so as to maximize industry profit. Set T to extract retailers profits. Now, I claim that the manufacturer cannot do better than this. To see this, assume that the manufacturer merges with the two retailers. The profit of the merged entity is given by: π = (1 q 1 q 2 )q 1 + (1 q 1 q 2 )q 2 = (1 q 1 q 2 )(q 1 + q 2 ) = (1 Q)Q Notice that the way total quantity is split b/w retailers is immaterial here: the only thing that matters is Q. This is because retailers are identical (no product differentiation, same costs) and have linear downstream costs. The merged firm will just set Q so as to maximize (1 Q)Q. Solving for this maximization problem, we get Q = 1/2 and π = 1/4. This is the monopoly profit of the industry. Nicolas Schutz Vertical Relations 44 / 71

48 The Single Monopoly Profit Criticism This tells us that, when the industry is non-integrated, the manufacturer is already able to earn the full monopoly profit by carefully designing its twopart tariff contract. Now, do you see why it was without loss of generality to assume that the manufacturer sets a (w, T) which enables both retailers to be active? Nicolas Schutz Vertical Relations 45 / 71

49 The Single Monopoly Profit Criticism This tells us that, when the industry is non-integrated, the manufacturer is already able to earn the full monopoly profit by carefully designing its twopart tariff contract. Now, do you see why it was without loss of generality to assume that the manufacturer sets a (w, T) which enables both retailers to be active? The reason is that, even with this constraint, the manufacturer can extract the whole industry monopoly profit. Notice that, if the manufacturer offered contract (w = 0, T = 1/4), then, only one retailer would accept this contract (there is no way that one retailer can make more than 1/4 if he faces competition from another retailer). In this case, one retailer would be excluded, and the manufacturer would still earn 1/4. But clearly, firm U cannot be better than this, since 1/4 is the industry monopoly profit. Nicolas Schutz Vertical Relations 45 / 71

50 The Single Monopoly Profit Criticism Now, think about the impact of one vertical merger, say, between firms U and D1, in this model. Firm UD1 would then do the following: Set w = T = to exclude retailer D2. Set the monopoly quantity q 1 = 1/2 to earn the monopoly profit: π = 1/4. Conclusion: After the vertical merger, firm D2 is completely foreclosed. But this vertical merger has no anticompetitive effects: downstream price and total quantity are not affected. And the manufacturer has no incentives to merge in the first place, since he can already earn the monopoly profit in the disintegrated industry. Nicolas Schutz Vertical Relations 46 / 71

51 The Single Monopoly Profit Criticism This is the single monopoly profit theory emphasized by Chicago School economists: There is a single monopoly profit, and an upstream bottleneck owner can extract it without merging vertically. An upstream monopolist has no incentives to merge to foreclose a retailer and raise final prices. If we observe a vertical merger in this framework, it has to be for other reasons than anticompetitive motives (say, the elimination of double markups, or upstream-downstream synergies). These other reasons are pro-competitive and welfare-improving. If this point is taken seriously, which many people have, then competition authorities should not worry about vertical mergers. Nicolas Schutz Vertical Relations 47 / 71

52 The Single Monopoly Profit Criticism As emphasized by the Post-Chicago approach, the single monopoly profit theory makes an important (and implicit) assumption: Upstream offers are public (i.e., downstream firms observe the offers made to their rivals), and cannot be renegotiated. We will see that, when upstream contracts are private and / or can be renegotiated, an upstream bottleneck owner may not be able to fully exert its monopoly power. In this case, vertical integration may be a means for the upstream firm to restore its monopoly power. This is important, because, in the majority of vertically related industries, contracts are private and a lot of renegotiation takes place. Nicolas Schutz Vertical Relations 48 / 71

53 The Single Monopoly Profit Criticism To make this point, let me make the following assumption: Between stages 2 and 3, after retailers have decided whether to accept their contracts, firms U and D1 can secretely make another two-part offer ( w, T) to D1. Now, let us see whether the subgame-perfect equilibrium (SPE) we calculated before survives to this possibility of renegotiation. Assume that: Firm U offered the SPE contract w = 1/4, T = 1/16. Firms D1 and D2 have made the SPE acceptance decision, i.e., both of them have accepted the contract. Renegotiation b/w U and D1 is secrete, i.e., firm D2 believes that it does not take place. So D2 still sets the SPE quantity q 2 = 1/4 in stage 3. After renegotiation took place (between periods 2 and 3), firm D1 can change its quantity in period 3. Are there incentives to renegotiate? Nicolas Schutz Vertical Relations 49 / 71

54 The Single Monopoly Profit Criticism If renegotiation takes place, then, firm D1 s profit becomes: π 1 = (P(q 1 + q 2 ) w)q 1 T But, since D2 is not aware of the renegotiation, he still sets q 2 = 1/4. Firm 1 s profit is therefore: π 1 = (1 1/4 q 1 w)q 1 T = (3/4 w q 1 )q 1 T, which firm 1 maximizes in q 1. First-order condition: This yields: 3/4 w 2q 1 = 0 q 1 ( w) = 3/4 w 2 π 1 ( w) = (P(1/4 + q 1 ( w)) w)q 1 ( w) T = (3/4 w)2 4 T Nicolas Schutz Vertical Relations 50 / 71

55 The Single Monopoly Profit Criticism Now, look at firm U s profit under renegotiation. Remember that firm 2 is still paying tariff (1/4, 1/16) and setting quantity q 2 = 1/4. π U ( w, T) = ( w q 1 ( w) + T ) ( ) = ( w q 1 ( w) + T ) Importantly, the profit firm U makes by selling to D2 (1/8) depends neither on w nor on T. As before, the manufacturer should then maximize π U subject to the constraint π 1 ( w, T) = (P(1/4 + q 1 ( w)) w)q 1 ( w) T 0 Again, firm U should choose T so as to saturate this constraint. Plugging the corresponding value of T into the manufacturer s profit function, we get: π U ( w) = P(1/4 + q 1 ( w))q 1 ( w) + 1/8 Since 1/8 is a constant, firm U will set w so as to maximize its joint profit (P(1/4 + q 1 ( w))q 1 ( w)) with retailer D1. Nicolas Schutz Vertical Relations 51 / 71

56 The Single Monopoly Profit Criticism Using the value of q 1 ( w) that we calculated before, we can rewrite π U ( w) as follows: π U ( w) = (3/4 3/4 w 3/4 w ) + 1 (3/4 + w)(3/4 w) = Notice that the first term in the right-hand side is just 9/16 w 2, which is clearly maximized at w = 0. What is the intuition for this? Nicolas Schutz Vertical Relations 52 / 71

57 The Single Monopoly Profit Criticism Using the value of q 1 ( w) that we calculated before, we can rewrite π U ( w) as follows: π U ( w) = (3/4 3/4 w 3/4 w ) + 1 (3/4 + w)(3/4 w) = Notice that the first term in the right-hand side is just 9/16 w 2, which is clearly maximized at w = 0. What is the intuition for this? As usual, the upstream firm uses the variable part of the tariff to solve the double markup problem and to control for competition externalities between retailers. But here, retailer D2 is setting q 2 = 1/4 anyway, and the manufacturer receives profit 1/8 from this retailers anyway: there are no competition externalities here. Therefore, only the double marginalization problem determines w, which leads the manufacturer to charge w = 0. Plugging w = 0 into π U ( w), we get: π U = = > 1 4 Nicolas Schutz Vertical Relations 52 / 71

58 The Single Monopoly Profit Criticism Therefore, renegotiation is strictly profitable for the manufacturer. Remember that T is set so that π 1 ( w, T) = 0. But retailer D1 also made no profits before renegotiating. To break down indifference, the manufacturer could just offer ε profits to D1. We can conclude that renegotiation is profitable both for the manufacturer and for retailer D1. Therefore, it should take place. What about retailer D2? Notice that firm D1 s quantity jumps from q 1 = 1/4 to q 1 = q 1 (0) = 3/8. Clearly, this hurts firm D2. In particular, D2 s profit after U and D1 have renegotiated is: π 2 = ( ) = 1 32, i.e., D2 is making losses because of the renegotiation. Nicolas Schutz Vertical Relations 53 / 71

59 The Single Monopoly Profit Criticism Conclusion: Renegotiation b/w firms U and D1 is profitable, because it increases their joint profits. Since U makes take-it-or-leave-it upstream offers, he can capture all this increase in joint profits. Renegotiation is harmful to firm D2, who makes ex post losses. The fact that firm U s profit increases from 1/4 to 17/64 is all at the expense of firm D2, who loses 1/32. But of course, retailer D2 is not stupid: he should anticipate that, since renegotiation is profitable, it will take place. Therefore, D2 should not accept the (w = 1/4, T = 1/16) contract in the first place. For instance, he should not accept a contract with such a high fixed fee, anticipating that the manufacturer will behave opportunistically b/w periods 2 and 3. Nicolas Schutz Vertical Relations 54 / 71

60 The Single Monopoly Profit Criticism Now, what if firm U can secretely renegotiate with firms D1 and D2 between periods 2 and 3? Which outcome will emerge in equilibrium? Nicolas Schutz Vertical Relations 55 / 71

61 The Single Monopoly Profit Criticism Now, what if firm U can secretely renegotiate with firms D1 and D2 between periods 2 and 3? Which outcome will emerge in equilibrium? Now, things get even worse: neither of the retailers will accept the (w = 1/4, T = 1/16) contract, since they know that the manufacturer has incentives to offer secrete sweetheart deals to their rivals. It can be shown that, if renegotiation with both retailers is possible, then, in equilibrium, both retailers will eventually sign an upstream contract (w = 0, T = π C /2), where π C denotes the Cournot duopoly profit of the industry. This is known as the opportunism problem faced by an upstream bottleneck owner. Compared to the Chicago School situation, in which renegotiation was not allowed, it has the following implications: The manufacturer s profit decreases from 1/4 to 2/9. Total quantity increases from 1/2 to 2/3 / Downstream price decreases from 1/2 to 1/3. Nicolas Schutz Vertical Relations 55 / 71

62 The Single Monopoly Profit Criticism Notice the strong analogy with the durable goods monopoly problem: A durable goods monopoly cannot commit not to cut prices tomorrow. This erodes its monopoly power today. An upstream monopolist cannot commit not to renegotiate. Because of this, he cannot fully exert its monopoly power. Both the durable goods monopoly and the upstream bottleneck owner are creating their own competition, because of their lack of ability to commit. Things can only get worse as the number of retailers increase: in this case, the upstream firm earns the N-firm Cournot profit, which we know is decreasing in N, and goes to zero as N goes to the infinity. The opportunism problem has a lot of relevance in industries in which franchising is common (again, fast-food and restaurant industry, hotel industry, etc.) Franchisees are usually reluctant to accept high franchise fees / royalties, because they anticipate that, ex post, the franchisor will have incentives to flood the market with new licenses. Nicolas Schutz Vertical Relations 56 / 71

63 The Single Monopoly Profit Criticism Now, a vertical merger becomes very useful for the upstream bottleneck. If firms U and D1 merge, then, in equilibrium, Firm UD1 completely forecloses retailer D2, sells the monopoly quantity, and earns the monopoly profit. Of course, integrated firm UD1 has no incentives to offer a sweetheart deal to D2, since this would reduce his profits. The single monopoly profit theory does not apply when upstream contracts can be renegotiated: A vertical merger is profitable, as it enables the upstream bottleneck owner to solve the opportunism problem and to fully exert its monopoly power. This vertical merger involves foreclosure of the other retailer. It is anticompetive, since the downstream price increases from the Cournot price to the monopoly price. Nicolas Schutz Vertical Relations 57 / 71

64 The Upstream Competition Criticism The second part of the Chicago School criticism was that, even when integrated firms have incentives to raise their rivals costs, this does not kill the competitive pressure on the upstream market. To make this point we need to build a model with At least two upstream firms (otherwise, there is no upstream competition). And at least two downstream firms (otherwise, a vertical merger could not have a foreclosure effect anyway). Nicolas Schutz Vertical Relations 58 / 71

65 The Upstream Competition Criticism U1 D1 U2 D2 Upstream market: Price competition w/ homogenous products. Downstream market: Cournot competition w/ inverse demand P(Q) = 1 Q. All costs are normalized to zero. Timing: Final consumers 1 Merger: D1 can bid to acquire U1. 2 Upstream competition: Firms U1 and U2 set their (linear) prices w 1 and w 2 simultaneously. Each downstream firm elects at most one input supplier. 3 Downstream competition: Firms D1 and D2 set their quantities simultaneously. Look for subgame-perfect equilibria and solve by backward induction. Nicolas Schutz Vertical Relations 59 / 71

66 The Upstream Competition Criticism Assume that no merger has taken place, and that firms U1 and U2 have set w1 and w2 respectively. Assume firm D1 has accepted Ui s offer, so that its marginal cost is c 1 = w i. Assume also that D2 has accepted Uj s offer (were j may or may not be equal to i) and denote its marginal cost by c 2 = w j. Firms D1 and D2 compete à la Cournot with profit functions π k = (1 q 1 q 2 c k )q k. As usual, solve for the best-response functions, and look for the Nash equilibrium of this quantity-setting game. You should get: q k = 1 2c k + c k 3 and π k = (1 2c k + c k ) 2 9 Notice that π k c k = 4 9 (1 2c k + c k ) = 4 3 q k < 0 In words, when firm Dk s marginal cost increases, its profit decreases. Is this surprising? Nicolas Schutz Vertical Relations 60 / 71

67 The Upstream Competition Criticism The fact that π k / c k < 0 implies that downstream firms will always go for the cheapest upstream offer. In particular, if w i < w j, then, both downstream firms will choose firm Ui s contract. On the other hand, if w i = w j, firms are indifferent between the two contracts. Let s assume that each downstream firm chooses firm Ui s offer w/ probability 1/2 when this is the case. Now, go back to the upstream competition stage. Both upstream firms anticipate that downstream firms will elect their upstream suppliers rationally. Consider firm Ui: If w i < w j, then, both retailers choose Ui, and c 1 = c 2 = w i. Firm Ui s total input demand is therefore 2q k = 2(1 w i )/3. Its profit is π Ui = 2w i (1 w i )/3. If w i > w j, then, nobody chooses Ui s offer. Ui makes zero profit. If w i = w j = w, then, c 1 = c 2 = w. On average, firm Ui supplies one retailer. Its expected profit is π Ui = w(1 w)/3. Nicolas Schutz Vertical Relations 61 / 71

68 The Upstream Competition Criticism Upstream firms are just playing a Bertrand competition game with homogenous products. We have proven several times that marginal cost pricing will emerge in equilibrium. Conclusion: When no merger has taken place, The input is priced at marginal cost: w 1 = w 2 = 0. Upstream firms make no profits: π U1 = π U2 = 0. Each downstream firm sets q i = 1/3 earns π Di = 1/9. Nicolas Schutz Vertical Relations 62 / 71

69 The Upstream Competition Criticism Now, assume that firms U1 and D1 have merged. Then, firm U1D1 produces the input for its downstream division. This firm may also sell the input to retailer D2. Assume first that U2 supplies D2 at price w2. Firms U1D1 and D2 set their quantities simultaneously. Their payoff functions are given by: First-order conditions are: This yields equilibrium quantities π U1D1 = (1 q 1 q 2 )q 1 π D2 = (1 q 1 q 2 w 2 )q 2 0 = 1 2q 1 q 2 0 = 1 q 1 2q 2 w 2 and profits: q 1 = 1 + w 2 3 π U1D1 = (1 + w 2) 2 9 and q 2 = 1 2w 2 3 and π D2 = (1 2w 2) 2 9 Nicolas Schutz Vertical Relations 63 / 71

70 The Upstream Competition Criticism Conversely, assume that firm U2 purchases the input from firm U1D1 at price w 1. Payoff functions in the downstream competition subgame are: π U1D1 = (1 q 1 q 2 )q 1 + w 2 q 2 π D2 = (1 q 1 q 2 w 1 )q 2 So, players payoff functions are different, but, as it turns out, first-order conditions are the same as when U2 was the upstream supplier: 0 = 1 2q 1 q 2 0 = 1 q 1 2q 2 w 1 Therefore, equilibrium quantities are the same: q 1 = 1 + w 1 3 and q 2 = 1 2w 1 3 Firm D2 earns π D2 = (1 2w 1) 2 9 (same as before), and firm U1D1 earns π U1D1 = (1+w 1 ) 2 1 2w 9 + w (same downstream profits as before + upstream profits). Nicolas Schutz Vertical Relations 64 / 71

71 The Upstream Competition Criticism Notice that, as in the zero-merger case, π D2 w i = 4 3 q 2 < 0 This implies that firm D2 will always go for the cheapest offer. Assume D2 chooses U1D1 (resp. U2) w/ probability 1/2 when w 1 = w 2. Now, go back to the upstream price competition subgame: Firm U2 s profit is: 1 2w w if w 2 < w 1 w π U2 = 2 1 2w if w 2 = w 1 0 if w 2 > w 1 This implies that U2 will always undercut U1D1, as long as w 1 is above marginal cost. Put differently, U2 s best response is to set w 1 ε as long as w 1 > 0. Nicolas Schutz Vertical Relations 65 / 71

72 The Upstream Competition Criticism Now, look at U1D1 s profit. Assume U2 sets w 2 > 0. If U1D1 sets w 1 > w 2, then, his profit is π U1D1 = (1+w 2) 2 9. If U1D1 sets w 1 = w 2, then, he supplies the upstream market with probability 1/2. His profit becomes π U1D1 = (1+w 2) w 2 1 2w If he sets w 1 = w 2 ε, with ε 0, then, he supplies the upstream market, and his profit is π U1D1 = (1+w 2) 2 1 2w 9 + w Clearly, the last alternative is the most profitable. This implies that U1D1 will undercut as long as the input price is above marginal cost. As a result, the only Nash equilibrium of the upstream price competition subgame is marginal cost pricing. In equilibrium, w 1 = w 2 = 0 and q 1 = w 2 = 1/3. π U1D1 = π D2 = 1/9 and π U2 = 0. Nicolas Schutz Vertical Relations 66 / 71

73 The Upstream Competition Criticism Conclusion: The vertical merger b/w U1 and D1 is not (strictly profitable). U1 and D1 s joint profits remain equal to 1/9. This merger has no foreclosure effect: the input remains priced at marginal cost. Final consumers are not affected either: total downstream quantity stays at 2/3. The merger has no anticompetitive effect. This is the upstream competition criticism: U1D1 would like to raise D2 s cost, so as to earn π U1D1 = (1+w 2) 2 9 > 1/9, or even π U1D1 = (1+w 2) 2 1 2w 9 + w > 1/ but such an outcome cannot arise in equilibrium, because firms are still competing on the upstream market. Nicolas Schutz Vertical Relations 67 / 71

74 The Upstream Competition Criticism Post-Chicago approach: What if firm U1D1 can commit to exit the upstream market after the vertical merger? How do you acquire such a commitment? The answer is not obvious. U1D1 could, for instance, make its input incompatible w/ firm D2 s product. The credibility of U1D1 s commitment would then depend on whether the decision to make the input incompatible is irreversible. Would U1D1 choose to use this commitment power? Assume U1D1 exits the upstream market. Then, U2 becomes a monopoly on the input market. The upstream firm sets w 2 so as to maximize π U2 = w 2 q 2 = w 2 1 2w 2 3 The first-order condition writes as 1 4w 2 = 0, i.e., w 2 = 1/4. Nicolas Schutz Vertical Relations 68 / 71

75 The Upstream Competition Criticism In this case, firm U1D1 s profit is (1 + w 2 ) 2 /9 = 25/144 > 1/9. Therefore, firm U1D1 will use his commitment to exit the upstream market. The intuition is simple: If U1D1 does not use the commitment, Bertrand competition drives the input price down to marginal cost. At the end of the day, U1D1 faces an equally efficient downstream competitor, and makes no upstream profits. If he uses the commitment, U1D1 still makes no upstream profits, but U2 uses his monopoly power, and D2 ends up being partially foreclosed. As a result, in equilibrium, U1 and D1 merge, and U1D1 exits the upstream market. Nicolas Schutz Vertical Relations 69 / 71

76 The Upstream Competition Criticism What are the consequences of this (equilibrium) vertical merger? After the merger, U1D1 sets q 1 = (1 + w 2 )/3 = 5/12 and D2 sets q 2 = (1 2w 2 )/3 = 1/6. i.e., the total quantity decreases from 2/3 to 7/12. Downstream price increases from 1/3 to 5/12. The merger is anticompetitive. U2 s profit increases from 0 to 1/48, thanks to his monopoly position on the upstream market. D2 is partially foreclosed, and his profit decreases from 1/9 to 1/36. Conclusion: If a vertically integrated firm can credibly commit to exit the upstream market, then the Chicago School criticism does not necessarily apply. A vertical merger can (partially) foreclose the remaining unintegrated downstream firms and raise final prices. Nicolas Schutz Vertical Relations 70 / 71