Horizontal Mergers Chapter 16 Horizontal Mergers 1 Introduction

Horizontal Mergers Chapter 16: Horizontal Mergers 1

Introduction • Merger mania of 1990 s disappeared after 9/11/2001 • But now appears to be returning – Oracle/People. Soft – 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 16: Horizontal Mergers 2

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 – Anti. Trust 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 16: Horizontal Mergers 3

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 costs, at least 80% of the firms • but this type of merger is unlikely to be allowed Chapter 16: Horizontal Mergers 4

An Example Assume 3 identical firms; market demand P = 150 - 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) = (150 - 30)/(3 + 1) = 30 units the product price is P(3) = 150 - 3 x 30 = $60 profit of each firm is p(3) = (60 - 30)x 30 = $900 Now suppose that two of these firms merge, then there are two independent firms so output of each changes to: q(2) = (150 - 30)/3 = 40 units; price is P(2) = 150 - 2 x 40 = $70 profit of each firm is p(2) = (70 - 30)x 40 = $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 16: Horizontal Mergers 5

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: (A - c)2 The ordering of the firms C p i= does not matter 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. Chapter 16: Horizontal Mergers 6

Generalization 2 The newly merged firm chooses output qm to maximize profit: pm(qm, Q-m) = qm(A - B(qm + Q-m) - c) where Q-m = qm+1 + qm+2 + …. + q. N is the aggregate output of the N - M firms that have not merged Each non-merged firm chooses output qi to maximize profit: pi(qi, Q-i) = qi(A - B(qi + 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 qm 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 16: Horizontal Mergers 7

Generalization 3 The profit of each of the merged and non-merged firms is then: (A - c)2 Profit of each surviving firm = = increases with M B(N - M + 2)2 The aggregate profit of the merging firms pre-merger is: M(A - c)2 C Mp i = B(N + 1)2 So for the merger to be profitable we need: (A - c)2 M(A - c)2 > this simplifies to: 2 2 B(N - M + 2) B(N + 1)2 > M(N - M + 2)2 p. Cm p. Cnm Chapter 16: Horizontal Mergers 8

The Merger Paradox Substitute M = a. N to give the equation (N + 1)2 > a. N(N – a. N + 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 5 10 15 20 25 a(N) 80% 81. 5% 83. 1% 84. 5% 85. 5% M 4 9 13 17 22 Chapter 16: Horizontal Mergers 9

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 16: Horizontal Mergers 10

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 + 30 q 1; C(q 2) = f + 30 q 2 – third firms has potentially higher marginal costs – C(q 3) = f + 30 bq 3, where b > 1 Chapter 16: Horizontal Mergers 11

Case A: Merger Reduces Fixed Costs • Suppose that b = 1 – all firms have the same marginal costs of 30 is likely to be profitable Merger – but the merged firms has fixed costs af with 1 < costs a < 2 are “high” and when fixed the merger gives “significant” • We know from the previous example that: savings in fixed costs – 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 – 2 f – which requires that a < 2 – 200/f Chapter 16: Horizontal Mergers 12

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 16: Horizontal Mergers 13

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 nonmerged firms Chapter 16: Horizontal Mergers 14

Case B: 2 • Is this a profitable merger? • For the merged firm’s profit to increase requires: • This simplifies to: 25(7 – 3 b)(15 b – Merger of a high-cost and lowcost firm is profitable if cost disadvantage of the high-cost 9)/2 >firm 0 is “great enough” • 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 Chapter 16: Horizontal Mergers 15

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 16: Horizontal Mergers 16

The Merger Paradox Again • The merger paradox arises because despite merging, merged firms are symmetric with nonmerged 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 16: Horizontal Mergers 17

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 ql independently • gives aggregate output QL • stage 2: each follower firm chooses its output qf independently, but in response to the aggregate output of the leader firms • gives aggregate follower output QF • clearly, leader firms correctly anticipate QF Chapter 16: Horizontal Mergers 18

Leadership Game 2 • Recall that – – if the inverse demand function is P = a – b. Q 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 QL then inverse demand for the followers is P = (A – BQL) – b. QF – there are N - L identical Cournot follower firms – so that a = (A – BQL), b = B and n = N – L Chapter 16: Horizontal Mergers 19

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 16: Horizontal Mergers 20

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 16: Horizontal Mergers 21

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 16: Horizontal Mergers 22

Leadership Game 6 • So for an additional merger to be profitable for the merging firms we need p. L(N – 1, L + 1) > 2 p. 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 an additional two follower firms will always want to merge – this squeezes profits of the non-merged firms – so resolves the merger paradox Chapter 16: Horizontal Mergers 23

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 16: Horizontal Mergers 24

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 16: Horizontal Mergers 25

Sequential Mergers 2 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. This is also a Nash This is a Nash Merger Pair 2 Equilibrium in simultaneous play Don’t Merge ($772, $772) ($772, ($1063, $752) Merger Pair 1 Merge ($752, $1063) ($1100, $1100) Chapter 16: Horizontal Mergers 26

Sequential Mergers 3 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 This is a Nash Equilibrium in sequential play Merger Pair 2 Don’t Merge ($772, $772) Merge ($1063, $752) Merger Pair 1 Merge ($752, $1063) ($1100, $1100) Chapter 16: Horizontal Mergers 27

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 16: Horizontal Mergers 28

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 nonmerged firms • prices are strategic complements – passive move by merged firms induces passive response by non-merged firms Chapter 16: Horizontal Mergers 29

Product Differentiation 1 • Extend the linear demand system – suppose that there are three firms with inverse demands: • s lies between 0 and B and is an inverse measure of product differentiation • • s = 0: totally differentiated; s = B the products are identical Each firm has constant marginal costs of c Chapter 16: Horizontal Mergers 30

Product Differentiation 2 • When the firms act as Bertrand competitors profit of each firm is: • Now suppose that firms 1 and 2 merge but: • continue to offer both products, coordinating their prices • merged and non-merged firms continue to act as Bertrand competitors • Then the profits of the merged and non-merged firms are: • The merger is profitable for merged and non-merged firms • Consumers lose from the merger in higher prices • More generally, with N firms any merger is profitable Chapter 16: Horizontal Mergers 31

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 16: Horizontal Mergers 32

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 16: Horizontal Mergers 33

The spatial model illustrated Price Assume that firm 1 sets What if firm 1 raises Price p 1 and firm 2 sets its price? price p 2 p’ 1 p 2 p 1 x’m Firm 1 xm All consumers to xthemoves to the Firm 2 m left of xm buy left: fromsome consumers And all consumers firm 1 to 2 the right buy from switch to firm 2 Chapter 16: Horizontal Mergers 34

The Spatial Model • Suppose that there are five firms evenly distributed 1 r 51 2 5 r 45 r 23 4 3 these firms will split the market we can then calculate the Nash equilibrium prices each firm will charge r 12 each firm will charge a price of p* = t. L/5 profit of each firm is then t. L 2/25 - F r 34 Chapter 16: Horizontal Mergers 35

Merger of Differentiated Products now consider a merger between some of these firms a merger of nonneighboring firms has no effect AAmergerofoffirms 22 and 43 does nothing something Price but a merger of neighboring firms changes the equilibrium r 51 1 r 12 2 r 23 3 r 34 4 r 45 5 r 51 Main Circle (flattened) Chapter 16: Horizontal Mergers 36

Merger of Differentiated Products merger of 2 and 3 induces them to raise their prices Price so the other firms also increase their prices the merged firms lose some market share what happens to profits? r 51 1 r 12 2 r 23 3 r 34 4 r 45 5 r 51 Main Circle (flattened) Chapter 16: Horizontal Mergers 37

Spatial Merger (cont. ) The impact of the merger on prices and profits is as follows Pre-Merger Price Profit 1 t. L/5 t. L 2/25 2 t. L/5 3 Post-Merger Price Profit 1 14 t. L/60 49 t. L 2/900 t. L 2/25 2 19 t. L/60 361 t. L 2/7200 t. L/5 t. L 2/25 3 19 t. L/60 361 t. L 2/7200 4 t. L/5 t. L 2/25 4 14 t. L/60 5 t. L/5 t. L 2/25 5 13 t. L/60 169 t. L 2/3600 Chapter 16: Horizontal Mergers 49 t. L 2/900 38

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 16: Horizontal Mergers 39

Price Discrimination What happens if the firms can price discriminate? This leads to a dramatic change in the price equilibrium Price p 1 i p 1 i+1 p 2 i p*i(s) t i s take two neighboring firms consider a consumer located at s suppose firm i sets price p 1 i i+1 can undercut with price p 1 i+1 i can undercut with price p 2 i and so on i wins this competition by “just” undercutting i+1’s cost of supplying s the same thing happens at every consumer location equilibrium prices are illustrated by the bold lines t Firm i supplies and firm i+1 these consumethese rs consumers i+1 Chapter 16: Horizontal Mergers 40

Merger with price discrimination This is much better Start with a no-merger equilibrium for consumers than no price discrimination 1 2 Price for equilibrium Profit each firm pre-merger is the given is given by byshaded the bold lines areas 3 Chapter 16: Horizontal Mergers 4 41

Merger with price discrimination This is beneficial for the Now suppose that firms 2 and 3 merged firms but harms Prices theprice captive They no longer compete in prices sotothe equilibrium consumerschanges consumers between 2 and 3 increase Profits to the merged firms increase 1 2 3 Chapter 16: Horizontal Mergers 4 42

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 16: Horizontal Mergers 43

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 paramters of the economic model Chapter 16: Horizontal Mergers 44

Merger Simulation 2 • Consider a product-differentiated market before any • First-order condition for each firm i is: • 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 sii this may be rewritten as • 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. Chapter 16: Horizontal Mergers 45

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 16: Horizontal Mergers 46

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 the bij coefficients may be translated into corresponding ij elasticities. Still it is clear that even ignoring the aij intercept term, estimating the relevant elasticities for an n firm market requires obtaining estimates for n 2 parameters. Chapter 16: Horizontal Mergers 47

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 crosselasticity restrictrions, Slade (2008) find differences in postmerger predictions as high as 40 percent • MORAL: Merger simulation is as much art as science and requires great care in implementation & interpretation Chapter 16: Horizontal Mergers 48

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 Chapter 16: Horizontal Mergers 49