Chapter 11: Horizontal Mergers1 Horizontal Mergers

Chapter 11: Horizontal Mergers2 Introduction Merger mania of 1990s disappeared after 9/11/2001 But now appears to be returning –Oracle/PeopleSoft –AT&T/Cingular –Bank of America/Fleet Reasons for merger –cost savings –search for synergies in operations –more efficient pricing and/or improved service to customers

Chapter 11: Horizontal Mergers3 Questions Are mergers beneficial or is there a need for regulation? –cost reduction is potentially beneficial –but mergers can “look like” legal cartels and so may be detrimental US government is particularly concerned with these questions –Antitrust Division Merger Guidelines seek to balance harm to competition with avoiding unnecessary interference Explore these issues in next two chapters –distinguish mergers that are horizontal: Bank of America/Fleet vertical: Disney/ABC conglomerate: Gillette/Duracell; Quaker Oats/Snapple

Chapter 11: Horizontal Mergers4 Horizontal mergers Merger between firms that compete in the same product market –some bank mergers –hospitals –oil companies Begin with a surprising result: the merger paradox –take the standard Cournot model –merger that is not merger to monopoly is unlikely to be profitable unless “sufficiently many” of the firms merge with linear demand and costs, at least 80% of the firms but this type of merger is unlikely to be allowed

Chapter 11: Horizontal Mergers5 An Example  Assume 3 identical firms; market demand P = Q; each firm with marginal costs of $30. The firms act as Cournot competitors.  Applying the Cournot equations we know that: each firm produces output q(3) = ( )/(3 + 1) = 30 units the product price is P(3) = x30 = $60 profit of each firm is  (3) = ( )x30 = $900  Now suppose that two of these firms merge, then there are two independent firms so output of each changes to: q(2) = ( )/3 = 40 units;price is P(2) = x40 = $70 profit of each firm is  (2) = ( )x40 = $1,600  But prior to the merger the two firms had total profit of $1,800 This merger is unprofitable and should not occur

Chapter 11: Horizontal Mergers6 A Generalization  Take a Cournot market with N identical firms.  Suppose that market demand is P = A - B.Q and that marginal costs of each firm are c.  From standard Cournot analysis we know the profit of each firm is:  C i = (A - c) 2 B(N + 1) 2  Now suppose that firms 1, 2,… M merge. This gives a market in which there are now N - M + 1 independent firms. The ordering of the firms does not matter

Chapter 11: Horizontal Mergers7 Generalization 2  Each non-merged firm chooses output q i to maximize profit:  i (q i, Q -i ) = q i (A - B(q i + Q -i ) - c) where Q -i = is the aggregate output of the N - M firms excluding firm i plus the output of the merged firm q m  The newly merged firm chooses output q m to maximize profit:  m (q m, Q -m ) = q m (A - B(q m + Q -m ) - c) where Q -m = q m+1 + q m+2 + …. + q N is the aggregate output of the N - M firms that have not merged  Comparing the profit equations then tells us: the merged firm becomes just like any other firm in the market all of the N - M + 1 post-merger firms are identical and so must produce the same output and make the same profits

Chapter 11: Horizontal Mergers8 Generalization 3  The profit of each of the merged and non-merged firms is then:  C m =  C nm = (A - c) 2 B(N - M + 2) 2  The aggregate profit of the merging firms pre-merger is: Profit of each surviving firm increases with M  C i = M(A - c) 2 B(N + 1) 2  So for the merger to be profitable we need: (A - c) 2 B(N - M + 2) 2 > M(A - c) 2 B(N + 1) 2 this simplifies to: (N + 1) 2 > M(N - M + 2) 2

Chapter 11: Horizontal Mergers9 The Merger Paradox  Substitute M = aN to give the equation (N + 1) 2 > aN(N – aN + 2) 2 Solving this for a > a(N) tells us that a merger is profitable for the merged firms if and only if: a > a(N) = Typical examples of a(N) are: N a(N)80%81.5%83.1%84.5%85.5% M

Chapter 11: Horizontal Mergers10 The Merger Paradox 2 Why is this happening? –merged firm cannot commit to its potentially greater size the merged firm is just like any other firm in the market thus the merger causes the merged firm to lose market share the merger effectively closes down part of the merged firm’s operations –this appears somewhat unreasonable Can this be resolved? –need to alter the model somehow asymmetric costs timing: perhaps the merged firms act like market leaders product differentiation

Chapter 11: Horizontal Mergers11 Merger and Cost Synergies Suppose that firms in the market –may have different variable costs –incur fixed costs Merger might be profitable if it creates cost savings An example –three Cournot firms with market demand P = 150 – Q –two firms have marginal costs of 30 and fixed costs of f –total costs are: –C(q 1 ) = f + 30q 1 ; C(q 2 ) = f + 30q 2 –third firms has potentially higher marginal costs –C(q 3 ) = f + 30bq 3, where b > 1

Chapter 11: Horizontal Mergers12 Case A: Merger Reduces Fixed Costs Suppose that b = 1 –all firms have the same marginal costs of 30 –but the merged firms has fixed costs af with 1 < a < 2 We know from the previous example that: –pre-merger profit of each firm are 900 – f –post-merger the non-merged firm has profit 1,600 - f the merged firm has profit 1,600 – af The merger is profitable for the merged firm if: –1,600 – af > 1,800 – 2f –which requires that a < 2 – 200/f Merger is likely to be profitable when fixed costs are “high” and the merger gives “significant” savings in fixed costs

Chapter 11: Horizontal Mergers13 Case A: 2 Also, the non-merged firm always gains –and gains more than the merged firms So the merger paradox remains in one form –why merge? –why not wait for other firms to merge?

Chapter 11: Horizontal Mergers14 Case B: Merger Reduces Variable Costs Suppose that merger reduces variable costs –assume that b > 1 and that f = 0 –firms 2 and 3 merge –so production is rationalized by shutting down high-cost operations –pre-merger: –outputs are: –profits are: –post-merger profits are $1,600 for both the merged and non- merged firms

Chapter 11: Horizontal Mergers15 Case B: 2 Is this a profitable merger? For the merged firm’s profit to increase requires: This simplifies to: 25(7 – 3b)(15b – 9)/2 > 0 first term must be positive for firm 3 to have non-negative output pre-merger so the merger is profitable if the second term is positive which requires b > 19/15 Merger of a high-cost and low- cost firm is profitable if cost disadvantage of the high-cost firm is “great enough”

Chapter 11: Horizontal Mergers16 Summary Mergers can be profitable if cost savings are great enough –but there is no guarantee that consumers gain –in both our examples consumers lose from the merger Farrell and Shapiro (1990) –cost savings necessary to benefit consumers are much greater than cost savings that make a merger profitable –so should be skeptical of “cost savings” justifications of mergers –and the paradox remains non-merged firms benefit more from merger than merged firms

Chapter 11: Horizontal Mergers17 The Merger Paradox Again The merger paradox arises because despite merging, merged firms are symmetric with non- merged firms? What kind of asymmetries might arise? –merged firms become Stackelberg leaders post-merger –By committing to merger, merged firms may induce others to merge –Can these alterations remedy the merger paradox?

Chapter 11: Horizontal Mergers18 A Leadership Game Suppose that there has been a set of two-firm mergers –market has L leaders and F followers = N = F+L total –assume linear demand P = A – BQ –each firm has constant marginal cost of c –two-stage game: stage 1: each leader firm chooses its output q l independently gives aggregate output Q L stage 2: each follower firm chooses its output q f independently, but in response to the aggregate output of the leader firms gives aggregate follower output Q F clearly, leader firms correctly anticipate Q F

Chapter 11: Horizontal Mergers19 Leadership Game 2 Recall that –if the inverse demand function is P = a – bQ –there are n identical Cournot firms –and all firms have marginal costs c –then each firm’s Cournot equilibrium output is: In our example –if the leaders produce Q L then inverse demand for the followers is P = (A – BQ L ) – bQ F –there are N - L identical Cournot follower firms –so that a = (A – BQ L ), b = B and n = N – L

Chapter 11: Horizontal Mergers20 Leadership Game 3 So the Cournot equilibrium output of each follower firm is: Aggregate output of the follower firms is then: Substituting this into the market inverse demand gives the inverse demand for the leader firms: in this case a = (A + (N – L)c/(N – L + 1); b = B/(N – L +1) and n = L

Chapter 11: Horizontal Mergers21 Leadership Game 4 So the Cournot equilibrium output of each leader firm is: Note that when L = 1 this is just the standard Stackelberg output for the lead firm. Substitute into the follower firm’s equilibrium and simplifying gives the output of each follower firm: Clearly, each leader has greater output than each follower merger to join the leader group has an advantage

Chapter 11: Horizontal Mergers22 Leadership Game 5 Substituting the equilibrium outputs into the inverse demand gives the equilibrium price-cost margin and profits for each type of firm: The leaders are more profitable than the non-merged followers Is one more merger profitable for the merging firms? Such a merger leads to there being L + 1 leaders, F – 2 followers and N – 1 firms in all

Chapter 11: Horizontal Mergers23 Leadership Game 6 So for an additional merger to be profitable for the merging firms we need  L (N – 1, L + 1) > 2  F (N, L) This requires that (L + 1) 2 (N – L + 1) 2 – 2(L + 2) 2 (N – L – 1) > 0 Note that this does not depend on any demand parameters A, B or c It is possible to show that this condition is always satisfied No matter how many leaders and followers there are an additional two follower firms will always want to merge –this squeezes profits of the non-merged firms –so resolves the merger paradox

Chapter 11: Horizontal Mergers24 Leadership Game 7 What about consumers? For an additional merger to benefit consumers N – 3(L + 1) > 0 An additional merger benefits consumers only if the current group of leaders contains fewer than one-third of the total number of firms in the market. Admittedly this model is stylized –how to attain leadership? –distinction between leaders and followers not necessarily sharp But it is suggestive of actual events and so qualitatively useful

Chapter 11: Horizontal Mergers25 Sequential Mergers It is possible to think of the merger paradox as a coordination problem. What does this mean? It may be the case that if enough firms complete mergers each merger will be profitable but that for small group to merge by itself is not profitable Consider a market with potential merger pairs: –Merger Pair 1 (Firm A and Firm B) –Merger Pair 2 (Firm A’ and B’) The game may have two Nash Equilibria, one where both pairs merge and one where neither merges

Chapter 11: Horizontal Mergers26 Sequential Mergers 2 Merger Pair 2 Don’t Merge Merge ($772, $772)($1063, $752) ($752, $1063)($1100, $1100) This is a Nash Equilibrium in simultaneous play This is a Nash Equilibrium in simultaneous play ($1100, $1100) ($772, $772) Merger Pair 1 This is also a Nash Equilibrium in simultaneous play This is also a Nash Equilibrium in simultaneous play Ideally, the merger pairs would like to coordinate their decisions and arrive at the Both Merge equilibrium. However, with simultaneous play, it is not clear how such coordination will happen.

Chapter 11: Horizontal Mergers27 Sequential Mergers 3 Merger Pair 2 Don’t Merge Merge ($772, $772)($1063, $752) ($752, $1063)($1100, $1100) Merger Pair 1 This is a Nash Equilibrium in sequential play This is a Nash Equilibrium in sequential play Sequential play with Merger Pair 1 going first solves the coordination problem. Merger Pair 2 will realize that if they merge, Merger Pair 2 will do the same This will make Merger Pair 1’s merger profitable

Chapter 11: Horizontal Mergers28 Sequential Mergers 4 The sequential merger analysis may solve the merger paradox if the source of that paradox is a coordination problem The analysis has an advantage over the Stackelberg leader model because it is explicitly sequential, i.e., mergers happen in chronological sequence. In the leader model, every firm wants to become a leader simultaneously Cost breakthroughs or changes in transportation and trade barriers can create the setting for the sequential merger analysis Such events can therefore lead to merger waves

Chapter 11: Horizontal Mergers29 Horizontal Mergers and Product Differentiation Assumption thus far is that firms offer identical products But we clearly observe considerable product differentiation Does this affect the profitability of merger? –affects commitment need not remove products post-merger –affects the nature of competition quantities are strategic substitutes –passive move by merged firms met by aggressive response of non- merged firms prices are strategic complements –passive move by merged firms induces passive response by non-merged firms

Chapter 11: Horizontal Mergers30 Merger with Price Competition Mergers with price competition and product differentiation are profitable Why? –prices are strategic complements –merged firms can strategically commit to producing a range of products –with homogeneous products there is no such ability to commit unless the merged firms can somehow become market leaders

Chapter 11: Horizontal Mergers31 Merger with Price Competition 2 Suppose there are N firms with linear demand With zero marginal cost, each firm’s first order condition is Using symmetry we get If firms 1,…M merge, it will have a new first order condition:

Chapter 11: Horizontal Mergers32 Merger with Price Competition Because of symmetry, the prices on all the products of the merged firms will be the same and the prices and only the nonmerged firms will bill be the same. For a not merged firm and a merged firm we have Using

Chapter 11: Horizontal Mergers33 Merger with Price Competition Gives first order conditions for the nonmerged firms And for the merged firm Which gives prices

Chapter 11: Horizontal Mergers34 Merger with Price Competition The merged firm set higher prices –Since prices are strategic complements, nonmerging firms also have higher prices The merger is profitable for the merging firms, but even more profitable for the nonmerging firms The greater the number of merging firms, the more profitable it is

Chapter 11: Horizontal Mergers35 A Spatial Approach Consider a different approach to product differentiation –spatial model of Hotelling –products are differentiated by “location” or characteristics –merger allows coordination of prices –but merged firms can continue to offer the pre-merger product range –is merger profitable?

Chapter 11: Horizontal Mergers36 The Spatial Model The model is as follows –a market called Main Circle of length L –consumers uniformly distributed over this market –supplied by firms located along the street –the firms are competitors: fixed costs F, zero marginal cost –each consumer buys exactly one unit of the good provided that its full price is less than V –consumers incur transport costs of t per unit distance in travelling to a firm –a consumer buys from the firm offering the lowest full price What prices will the firms charge? To see what is happening consider two representative firms

Chapter 11: Horizontal Mergers37 The spatial model illustrated Firm 1Firm 2 Assume that firm 1 sets price p 1 and firm 2 sets price p 2 Price p1p1 p2p2 xmxm All consumers to the left of x m buy from firm 1 And all consumers to the right buy from firm 2 What if firm 1 raises its price? p’ 1 x’ m x m moves to the left: some consumers switch to firm 2

Chapter 11: Horizontal Mergers38 The Spatial Model Suppose that there are five firms evenly distributed  these firms will split the market r 12 r 23 r 34 r 45 r 51  we can then calculate the Nash equilibrium prices each firm will charge  each firm will charge a price of p* = tL/5  profit of each firm is then tL 2 /25 - F

Chapter 11: Horizontal Mergers39 Merger of Differentiated Products Price Main Circle (flattened) r 51 r 12 r 23 r 34 r 45 r 51  now consider a merger between some of these firms  a merger of non- neighboring firms has no effect A merger of firms 2 and 4 does nothing  but a merger of neighboring firms changes the equilibrium A merger of firms 2 and 3 does something

Chapter 11: Horizontal Mergers40 Merger of Differentiated Products Price Main Circle (flattened) r 51 r 12 r 23 r 34 r 45 r 51  merger of 2 and 3 induces them to raise their prices  so the other firms also increase their prices  the merged firms lose some market share  what happens to profits?

Chapter 11: Horizontal Mergers41 Spatial Merger (cont.)  The impact of the merger on prices and profits is as follows Pre-MergerPost-Merger PriceProfitPriceProfit tL/5 tL 2 / tL/60 49tL 2 /900 19tL/60 361tL 2 / tL/60 49tL 2 /900 13tL/60 169tL 2 /3600

Chapter 11: Horizontal Mergers42 Spatial Merger (cont.) This merger is profitable for the merged firms And it is not the best that they can do –change the locations of the merged firms expect them to move “outwards”, retaining captive consumers –perhaps change the number of firms: or products on offer expect some increase in variety But consumers lose out from this type of merger –all prices have increased For consumers to derive any benefits either –increased product variety so that consumers are “closer” –there are cost synergies not available to the non-merged firms e.g. if there are economies of scope Profitability comes from credible commitment

Chapter 11: Horizontal Mergers43 Price Discrimination  What happens if the firms can price discriminate?  This leads to a dramatic change in the price equilibrium tt i i+1  tt ake two neighboring firms s  cc onsider a consumer located at s Price p1ip1i  ss uppose firm i sets price p 1 i  ii +1 can undercut with price p 1 i+1 p 1 i+1  ii can undercut with price p 2 i p2ip2i  aa nd so on  ii wins this competition by “just” undercutting i+1’s cost of supplying s p* i (s)  tt he same thing happens at every consumer location  ee quilibrium prices are illustrated by the bold lines Firm i supplies these consumers and firm i+1 these consumers

Chapter 11: Horizontal Mergers44 Merger with price discrimination  Start with a no-merger equilibrium 1234 Price equilibrium pre-merger is given by the bold lines Profit for each firm is given by the shaded areas This is much better for consumers than no price discrimination

Chapter 11: Horizontal Mergers45 Merger with price discrimination  Now suppose that firms 2 and 3 merge 1234  They no longer compete in prices so the price equilibrium changes Prices to the captive consumers between 2 and 3 increase Profits to the merged firms increase This is beneficial for the merged firms but harms consumers

Chapter 11: Horizontal Mergers46 Public Policy and Horizontal Mergers Antitrust authorities consider the unilateral effects discussed above and coordinate effects –A merger may make collusion easier Consider –Number of firms –Cost structures across firms –Entry barriers

Chapter 11: Horizontal Mergers47 Public Policy and Surplus Focus is generally on Consumer surplus –Ignores profits to merging firms –And to their competitors Most economic theory favors a measure of total surplus, but.. –Distributional concerns favor consumer surplus –Firms may exaggerate cost savings, and consumers are not represented at proceedings Also, firms may have a choice among mergers –Having a criteria of consumer surplus will push them towards ones with higher total surplus since they favor ones with higher producer surplus

Chapter 11: Horizontal Mergers48 Empirical Application: Merger Simulation Antitrust evaluation of a proposed merger requires some prediction of prices and outputs in the post-merger market One way to make such a prediction is to build a mathematical model of the post-merger market and to simulate its workings on a computer Merger simulation is a combination of economic modeling and econometric estimation –Economic modeling reflects standard maximizing behavior in the context of strategic interaction to characterize the post-merger equilibrium –Econometric estimation is required to obtain realistic values for the key parameters of the economic model

Chapter 11: Horizontal Mergers49 Merger Simulation 2 Consider a product-differentiated market before any First-order condition for each firm i is: Note: Market share and price are observable and relatively easy to measure. Cost is difficult to know. But if we have an estimate of the elasticity, then cost can be inferred from the above relationship. Here  ii the (negative of the) elasticity of the firm’s demand with respect to its own price. Defining the price-cost margin as  ii and the firm’s market share as s ii this may be rewritten as

Chapter 11: Horizontal Mergers50 Merger Simulation 3 If two firms, say firms 1 and 2, merge and if they continue to market both products, they will now coordinate the pricing of each good to maximize the combined profits The two first order conditions now are: Assuming market shares do not change “too much”, it is easy to see how the knowledge of the relevant own- and cross-price elasticities, along with the estimates of marginal cost from the pre-merger data can be used to work out the price-cost margins and therefore the prices in the post-merger world What is key is getting estimates of all the relevant elasticities

Chapter 11: Horizontal Mergers51 Merger Simulation 4 Estimating all the relevant elasticities though is a tall order –Need to specify a demand system –Need to link demand parameters to elasticities Usual to specify an almost ideal demand system (AIDS). If there are four pre-merger firms this system is: It is easy to show how the b ij coefficients may be translated into corresponding  ij elasticities. Still it is clear that even ignoring the a ij intercept term, estimating the relevant elasticities for an n firm market requires obtaining estimates for n 2 parameters.

Chapter 11: Horizontal Mergers52 Merger Simulation 4 Estimating n 2 parameters with precision is difficult So, the typical estimation procedure usually imposes additional structure on the market model. For example, Proportionally Calibrated AIDS assumes that the sales loss by a firm when it raises its price is translated to rivals in proportion to their market shares. This removes the need to estimate the cross-elasticities However, such structural restrictions are not without consequences. Depending on the precise demand specification and cross- elasticity restrictions, Slade (2008) find differences in post- merger predictions as high as 40 percent MORAL: Merger simulation is as much art as science and requires great care in implementation & interpretation

Chapter 11: Horizontal Mergers53 Merger Simulation 5 Even if agreement can be reached on simulation technique, different techniques are available for estimating the needed elasticities and these two can lead to great variation in post-merger outcomes Staples-Office Depot Merger is a good example –Are the relevant competitors to a retail office supply store all the other suppliers in a standard metropolitan area, or; –Does the strength of competition decline as the rival firm is located farther from the store under consideration? Producing clear, statistical evidence that non-economists and the courts can easily assess is very difficult