Horizontal Mergers Chapter 16 Horizontal Mergers 1

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 aggregate 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 that the profit of each firm is: p. Ci = (A - c)2 The ordering of the firms 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, given by 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: p. Cm p. Cnm M. p. Ci = M. (A - c)2 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 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 a(N) 5 80% M 4 10 81. 5% 9 15 83. 1% 20 84. 5% 25 85. 5% 13 17 22 Chapter 16: Horizontal Mergers 9

The Merger Paradox 2 • Why is this happening? – the 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 – 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 Merger • the non-merged firm has profit 1, 600 - f is likely to be profitable • the merged firm has profit 1, 600 when fixed costs are “high” and – af the merger gives “significant” merger is profitable for the merged firm if: costs savings in fixed – 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: Merger of a 9)/2 > 0 • This simplifies to: 25(7 – 3 b)(15 b – high-cost and low- cost firm is profitable if cost • first term must be positive for firm 3 to havethe high-cost output disadvantage of non-negative pre-merger firm is “great enough” • 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 merged firms cannot make a credible commitment to “high” post-merger output • Can we find a mechanism that gives such a commitment? – suppose that the merged firms become Stackelberg leaders postmerger – can choose their outputs anticipating non-merged firms subsequent reactions • may resolve the paradox • may also create another paradox – one merger may well induce others – “domino effect” characteristic of many markets Chapter 16: Horizontal Mergers 17

A Leadership Game • Suppose that there has been a set of two-firm mergers – – – so the market contains L leader firms and there are F follower firms so there are N = F + L firms in total assume linear demand P = A – B. Q 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 = (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 P 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 firm has greater output than each follower firm • 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 of the 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

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 25

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 26

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 27

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 28

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 29

The spatial model illustrated Assume that firm 1 sets Price What if firm 1 raises price p 1 and firm 2 sets Price its price? price p 2 p’ 1 p 2 p 1 x’m Firm 1 xm All consumers to x moves to the Firm 2 m left of xm buy left: some consumersall consumers from And firm 1 to the switch to firm 2 right buy from firm 2 Chapter 16: Horizontal Mergers 30

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 31

Merger of Differentiated Products now consider a merger between some of these firms a merger of nonneighboring firms has no effect AA merger of firms 22 and 3 does and 4 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 32

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 33

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 34

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 35

Price Discrimination What happens if the firms can price discriminate? This leads to a dramatic change in the price equilibrium Price p 1 i+1 p 2 i p*i(s) t i t s Firm i supplies these consumers 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 i+1 and firm i+1 these consumers Chapter 16: Horizontal Mergers 36

Merger with price discrimination This is much better Start with a no-merger equilibrium for consumers than no price discrimination 1 2 Price equilibrium Profit for each firm pre-mergerby the is given by the bold lines shaded areas 3 Chapter 16: Horizontal Mergers 4 37

Merger with price discrimination This is beneficial for the Now suppose that firms 2 and 3 merged firms but harms Prices the price equilibrium changes They no longer compete in prices soto the captive consumers between 2 and 3 increase Profits to the merged firms increase 1 2 3 Chapter 16: Horizontal Mergers 4 38

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 39

Chapter 16: Horizontal Mergers 40