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Section 2: Mergers

Section 2: Mergers. Introduction. Merger mania is everywhere each week brings new announcements of mega-mergers AOL/Time-Warner Pfizer/Warner-Lambert Vodafone/Mannesman each year seems to break the record of the year before Reasons for merger are many need to become “global”

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Section 2: Mergers

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  1. Section 2: Mergers EC 171: Topics in Industrial Organization

  2. Introduction • Merger mania is everywhere • each week brings new announcements of mega-mergers • AOL/Time-Warner • Pfizer/Warner-Lambert • Vodafone/Mannesman • each year seems to break the record of the year before • Reasons for merger are many • need to become “global” • response to other mergers • search for synergies in operations • to achieve significant cost savings EC 171: Topics in Industrial Organization

  3. Questions • Why do mergers occur? • many reasons have been suggested relating to costs and market power • Are mergers beneficial or is there a need for regulation? • the US government is particularly concerned with these questions • anti-trust website • mergers might not be beneficial: they operate like legal cartels • Are all mergers the same or are there different types? • distinguish mergers that are • horizontal • complementary • vertical EC 171: Topics in Industrial Organization

  4. 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 EC 171: Topics in Industrial Organization

  5. An Example Assume 3 identical firms; market demand P = 140 - Q; each firm with marginal costs of $20. The firms act as Cournot competitors. Applying the Cournot equations we know that: each firm produces output q(3) = (140 - 20)/(3 + 1) = 30 units the product price is P(3) = 140 - 3x30 = $50 profit of each firm is p(3) = (50 - 20)x30 = $900 Now suppose that two of these firms merge then there are two independent firms so output of each changes to: q(2) = (140 - 20)/3 = 40 units; price is P(2) = 140 - 2x40 = $60 profit of each firm is p(2) = (60 - 20)x40 = $1,600 But prior to the merger the two firms had aggregate profit of $1,800 This merger is unprofitable and should not occur EC 171: Topics in Industrial Organization

  6. Example (cont.) Now suppose that all three firms merge. This creates a monopoly so that we have: output = (140 - 20)/2 = 60 units price = (140 - 60) = $80 profit = p(1) = (80 - 20)x60 = $3,600 Prior to this merger aggregate profit was 3x$900 = $2,700 Merger to monopoly is always profitable EC 171: Topics in Industrial Organization

  7. 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: (A - c)2 The ordering of the firms does not matter pCi = 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. EC 171: Topics in Industrial Organization

  8. Generalization (cont.) 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 + …. + qN 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 EC 171: Topics in Industrial Organization

  9. Generalization (cont.) The profit of each of the merged and non-merged firms is then: Profit of each surviving firm increases with M (A - c)2 pCm = pCnm = B(N - M + 2)2 The aggregate profit of the merging firms pre-merger is: M.(A - c)2 M.pCi = B(N + 1)2 So for the merger to be profitable we need: (A - c)2 M.(A - c)2 > this simplifies to: B(N - M + 2)2 B(N + 1)2 (N + 1)2> M(N - M + 2)2 M > 0.8N for this inequality to be satisfied EC 171: Topics in Industrial Organization

  10. The Merger Paradox • 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 • product differentiation • Bertrand competition • give the merged firms some additional market power • perhaps they can exercise market leadership EC 171: Topics in Industrial Organization

  11. Horizontal Merger and Leadership • Suppose that when two firms merge they become Stackelberg leaders • how does this affect merger profitability? • what is the impact on consumers? EC 171: Topics in Industrial Organization

  12. Merger and leadership: an example Suppose that there are N identical Cournot firms in the market Market demand is P = 140 - Q and marginal cost is $20 Prior to the merger the Cournot equilibrium has: output of each firm: 120/(N + 1); price: PC = (140 + 20N)/(N + 1) profit of each firm: pC = 14,400/(N + 1)2 Now suppose that 2 firms merge and become market leaders Since a merger is a legal cartel we can use the Selten analysis of the previous chapter to get the effect of this merger The merged firm will produce the Stackelberg output: QL = (140 - 20)/2 = 60 units EC 171: Topics in Industrial Organization

  13. The leadership example (cont.) There are N - 2 non-merged firms that act as followers. So they each produce output: 140 - 20 60 qF = = 2(N - 1) (N - 1) 60(N - 2) 60(2N - 3) Total output is: QT = 60 + = (N - 1) (N - 1) 40 + 20N Price is: PL = 140 - QT = (N - 1) 60 and the price-cost margin is PL - 20 = (N - 1) EC 171: Topics in Industrial Organization

  14. The leadership example (cont.) Profit of the merged (lead) firm is: pL = (PL - 20)QL = 3,600/(N - 1) Profit of each non-merged (follower) firm is: pF = (PL - 20)qF = 3,600/(N - 1)2 The merged firm is always more profitable than each non-merged firm Is the merger profitable for the merged firms? Profit pre-merger was: 2pC = 28,800/(N + 1)2 3,600 28,800 so pL> 2pC requires: > which requires: (N - 1) (N + 1)2 (N + 1)2> 8(N - 1) This is always true for N > 3 EC 171: Topics in Industrial Organization

  15. The leadership example (cont.) What about the effect of the merger on the non-merged firms and on consumers? Profit pre-merger was: pC = 14,400/(N + 1)2 3,600 14,400 so pF>pC requires: > which requires: (N - 1)2 (N + 1)2 (N + 1)2> 4(N - 1)2 This is only true for N < 3 The pre-merger price-cost margin is: PC - 20 = 120/(N + 1) The post-merger price-cost margin is: PL - 20 = 60/(N - 1) 60 120 the merger reduces price if: < or 60N + 60 > 120N - 120 N - 1 N + 1 This is true if N > 3 EC 171: Topics in Industrial Organization

  16. Mergers and Market Leadership • A two-firm merger that creates a market leader is profitable for the merged firms if there are three or more firms in the market • Moreover, such a merger • increases the market share of the merged firms • reduces profit and market share for each non-merged firm • benefits consumers by reducing price • So why worry about mergers? • What might the non-merged firms do? • Will they also seek merger partners? • If so, what then happens to price and consumer welfare? EC 171: Topics in Industrial Organization

  17. Mergers and leadership (cont.) • The “leadership” merger reduces profits of the non-merged firms • Won’t these firms also seek merger partners? • certainly consistent with casual evidence • So, consider more than one two-firm merger • creates a series of merged firms • and a series of non-merged firms • How does “leadership” work here? • (Daughety) merged firms compete against each other • but as a group act as leaders relative to the non-merged firms • another variant on the Cournot model EC 171: Topics in Industrial Organization

  18. Mergers and leadership (cont.) • Need to distinguish output decisions of the group of leaders (L) and the group of followers (F) • stage game • stage 1: leaders each choose their output levels in competition with the other lead firms • stage 2: followers see output decisions of the lead firms then choose their outputs with respect to residual demand in competition with other follower (non-merged) firms • Stick with the Cournot model we have used • market demand P = 140 - Q; marginal cost $20; N firms • the firms are in two groups • L leaders or merged firms • N - L followers or non-merged firms • solve this game “backwards” EC 171: Topics in Industrial Organization

  19. Mergers and leadership (cont.) Suppose that the aggregate output of the lead firms is QL Residual demand for the non-merged firms is then: P = 140 - QL - QF where Q = QL + QF and QF is output of the non-merged firms QF can be written qf + QF-f where QF-f denotes output of the non-merged firms other than firm f So the profit of non-merged firm f can be written: pf = (140 - QL - QF-f - qf - 20)qf = (120 - QL - QF-f - qf)qf Differentiate this with respect to qf to give the condition: pf/ qf = 120 - QL - QF-f - 2qf = 0 Solve this for qf EC 171: Topics in Industrial Organization

  20. An example of leadership (cont.) We have the best response functionfor firm f: qf = 60 - QL/2 - QF-f/2 as a response to both the output of the leaders andthe other followers But all the followers are identical so in equilibrium they produce the same outputs: so Q*F-f = (N - L - 1)q*f so q*f = 60 - QL/2 - (N - L - 1)q*f/2 so (N - L + 1)q*f/2 = 60 - QL/2 120 - QL q*f = N - L + 1 Aggregate output of the non-merged firms is then: (N - L)(120 - QL) Q*F = N - L + 1 EC 171: Topics in Industrial Organization

  21. (N - L)(120 - QL) Q*F = N - L + 1 An example of leadership (cont.) What about a lead (merged) firm in stage 1? The same technique can be used. Residual demand for a lead firm is: P = 140 - QF - QL = 140 - QF - Q-l - ql where Q-l is output of all the lead firms other than firm l The difference between the merged firms and the non-merged firms is that each merged firm knows what QF is going to be. The typical lead firm correctly anticipates the actions of the non-merged firms and so can use this information Recall that and substitute this into the residual demand equation EC 171: Topics in Industrial Organization

  22. An example of leadership (cont.) This gives the residual demand equation For the moment we treat the merged firms as a group (N - L)(120 - QL) P = 140 - - QL N - L + 1 140 + 20(N - L) (N - L)QL = + - QL N - L + 1 N - L + 1 140 + 20(N - L) QL = - N - L + 1 N - L + 1 This can now be rewritten: 140 + 20(N - L) - Q-l ql P = - N - L + 1 N - L + 1 EC 171: Topics in Industrial Organization

  23. An example of leadership (cont.) Profit of a typical merged firm is: pl = (P - 20)ql But we know what P is so we have 140 + 20(N - L) - Q-l ql P - 20 = - - 20 N - L + 1 N - L + 1 140 - 20 - Q-l ql = - N - L + 1 N - L + 1 So profit of a typical merged firm becomes: (120 - Q-l - ql) pl = ql (N - L + 1) Differentiate this with respect to ql to give the profit maximizing condition. EC 171: Topics in Industrial Organization

  24. (120 - Q-l - ql) pl = ql (N - L + 1) An example of leadership (cont.) We have: Differentiating gives the condition: 120 - Q-l - 2ql pl/ ql = = 0 N - L + 1 So we have the condition: Q*-l + 2q*l = 120 In solving this we can again use a symmetry argument: Since Q-l contains L - 1 firms in equilibrium all the lead firms will have the same output so Q*-l = (L - 1)q*l which gives: (L + 1)q*l = 120 so q*l = 120/(L + 1) Aggregate output of the merged firms is then: Q*L = 120L/(L + 1) EC 171: Topics in Industrial Organization

  25. (N - L)120 120 Q*F = q*F = (N - L + 1)(L + 1) (N - L + 1)(L + 1) (N - L)(120 - QL) Q*F = N - L + 1 An example of leadership (cont.) Recall that • Now substitute for Q*L = 120L/(L + 1). This gives: and • This has been a lot of work!!! But now we can see the effect of a group of mergers. • We can easily compare outputs of the different types of firms. The leader (merged) firms are larger than the follower (non-merged) firms: as we would expect EC 171: Topics in Industrial Organization

  26. An example of leadership (cont.) • What about profits? Is the profit of a leader firm more than twice that of the profit it would make as a follower? • To make this comparison we need the equilibrium price. • Aggregate output is: Q*F + Q*L (N - L)120 120L 120(N + NL - L2) so Q*T = + = (N - L + 1)(L + 1) (L + 1) (N - L + 1)(L + 1) • This looks nasty but check that it is greater than the Cournot output • Stackelberg leaders produce more than Cournot firms. This reduces output of the followers but not by an offsetting amount. • Followers are under pressure: lower output and lower prices. • Increases the likelihood that followers will merge. EC 171: Topics in Industrial Organization

  27. An example of leadership (cont.) • Check the profitability of an additional merger. To do so,we need profits of followers and leaders. • This requires that we calculate the price-cost margin. 120(N + NL - L2) Price is PL = 140 - Q*T = 140 - (N - L + 1)(L + 1) and the price-cost margin is PL - 20 which gives: 120 PL - 20 = (N - L + 1)(L + 1) • This then gives us the profit equations for each type of firm EC 171: Topics in Industrial Organization

  28. An example of leadership (cont.) • Profit of a typical follower is: 14,400 pf(N, L) = (N - L + 1)2(L + 1)2 • Profit of a typical leader is: 14,400 pl(N, L) = (N - L + 1)(L + 1)2 • Each leader is more profitable than each follower but this is not the appropriate comparison • Compare profits of two followers before they merge with their profits after they merge. EC 171: Topics in Industrial Organization

  29. An example of leadership (cont.) • Starting from any configuration of leaders and followers a further two firms will always wish to merge. • Is such a group of two-firm mergers desirable for consumers? • firms that join the leader group increase output • but there are fewer firms in the market • So will a further two-firm merger increase or decrease output? • for this to happen we must have L < N/3 - 1 For price to fall as a result of a merger the leader group should contain no more than one-third of the total number of firms in the market EC 171: Topics in Industrial Organization

  30. Product Differentiation and Merger • The discussion so far has assumed that products are identical • It can be extended to differentiated products: • suppose demand is of the form: • q1 = A - Bp1 + C(p2 + p3 +…+ pn) • and similarly for the other products • Now a merger allows coordination of the outputs of the different products • but the merger does not lead to one of the products being eliminated EC 171: Topics in Industrial Organization

  31. An Example of Product Differentiation QC = 63.42 - 3.98PC + 2.25PP MCC = $4.96 QP = 49.52 - 5.48PP + 1.40PC MCP = $3.96 This example can be generalized to more than two products EC 171: Topics in Industrial Organization

  32. Product differentiation • Take a different approach • spatial model of product differentiation • The idea is simple • suppose firms are offering different varieties of a product • the analogy is that these products have different “locations” • then merger between some of these firms avoids some of the problems of the merger paradox • don’t have to close down particular locations • but can coordinate prices and, perhaps, locations • Many mergers “look like” this • join product lines that compete but do not perfectly overlap EC 171: Topics in Industrial Organization

  33. 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 EC 171: Topics in Industrial Organization

  34. The spatial model illustrated Assume that firm 1 sets price p1 and firm 2 sets price p2 What if firm 1 raises its price? Price Price p’1 p2 p1 xm x’m Firm 1 All consumers to the left of xm buy from firm 1 xm moves to the left: some consumers switch to firm 2 Firm 2 And all consumers to the right buy from firm 2 EC 171: Topics in Industrial Organization

  35. The Spatial Model • Suppose that there are five firms evenly distributed 1  these firms will split the market r12 r51  we can then calculate the Nash equilibrium prices each firm will charge 2 5  each firm will charge a price of p* = tL/5 r45 r23  profit of each firm is then tL2/25 - F 4 3 r34 EC 171: Topics in Industrial Organization

  36. Merger of Differentiated Products A merger of firms 2 and 4 does nothing  now consider a merger between some of these firms A merger of firms 2 and 3 does something Price  a merger of non-neighboring firms has no effect  but a merger of neighboring firms changes the equilibrium r51 1 r12 2 r23 3 r34 4 r45 5 r51 Main Circle (flattened) EC 171: Topics in Industrial Organization

  37. 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? r51 1 r12 2 r23 3 r34 4 r45 5 r51 Main Circle (flattened) EC 171: Topics in Industrial Organization

  38. Spatial Merger (cont.) The impact of the merger on prices and profits is as follows Pre-Merger Post-Merger Price Profit Price Profit tL/5 tL2/25 1 1 14tL/60 49tL2/900 tL/5 tL2/25 2 2 19tL/60 361tL2/7200 3 3 19tL/60 361tL2/7200 tL/5 tL2/25 4 4 14tL/60 49tL2/900 tL/5 tL2/25 5 tL/5 tL2/25 5 13tL/60 169tL2/3600 EC 171: Topics in Industrial Organization

  39. 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 EC 171: Topics in Industrial Organization

  40. Price Discrimination What happens if the firms can price discriminate? This leads to a dramatic change in the price equilibrium Price p1i take two neighboring firms p1i+1 consider a consumer located at s p2i suppose firm i sets price p1i p*i(s) i+1 can undercut with price p1i+1 i can undercut with price p2i and so on i wins this competition by “just” undercutting i+1’s cost of supplying s t t the same thing happens at every consumer location i s i+1 Firm i supplies these consumers and firm i+1 these consumers equilibrium prices are illustrated by the bold lines EC 171: Topics in Industrial Organization

  41. This is much better for consumers than no price discrimination Merger with price discrimination Price equilibrium pre-merger is given by the bold lines Profit for each firm is given by the shaded areas Start with a no-merger equilibrium 1 2 3 4 EC 171: Topics in Industrial Organization

  42. 1 2 3 4 This is beneficial for the merged firms but harms consumers Merger with price discrimination Now suppose that firms 2 and 3 merge Prices to the captive consumers between 2 and 3 increase They no longer compete in prices so the price equilibrium changes Profits to the merged firms increase EC 171: Topics in Industrial Organization

  43. Vertical Mergers • Now consider very different types of mergers • between firms at different stages in the production chain • also applies to suppliers of complementary products • These mergers turn out, in general, to be beneficial for everyone. EC 171: Topics in Industrial Organization

  44. Complementary Mergers • Take a simple example: • final production requires two inputs in fixed proportions • one unit of each input is needed to make one unit of output • input producers are monopolists • final product producer is a monopolist • demand for the final product is P = 140 - Q • marginal costs of upstream producers and final producer (other than for the two inputs) normalized to zero. • What is the effect of merger between the two upstream producers? EC 171: Topics in Industrial Organization

  45. Complementary mergers (cont.) Supplier 1 Supplier 2 price v2 price v1 Final Producer price P Consumers EC 171: Topics in Industrial Organization

  46. Complementary producers Consider the profit of the final producer: this is pf = (P - v1 - v2)Q = (140 - v1 - v2 - Q)Q Solve this for Q Maximize this with respect to Q - (v1 + v2) pf/Q = 140 - 2Q = 0  Q = 70 - (v1 + v2)/2 This gives us the demand for each input Q1 = Q2 = 70 - (v1 + v2)/2 So the profit of supplier 1 is then: p1 = v1Q1 = v1(70 - v1/2 - v2/2) Maximize this with respect to v1 EC 171: Topics in Industrial Organization

  47. Complementary producers (cont.) The price charged by each supplier is a function of the other supplier’s price p1 = v1Q1 = v1(70 - v1/2 - v2/2) We need to solve these two pricing equations Solve this for v1 Maximize this with respect to v1 p1/v1 = 70 - v1 - v2/2 = 0 v1 = 70 - v2/2 v2 We can do exactly the same for v2 140 R1 v2 = 70 - v1/2 v1 = 70 - (70 - v1/2)/2 = 35 + v1/4 70 so 3v1/4 = 35 so v1 = $46.67 46.67 R2 and v2 = $46.67 v1 70 140 46.67 EC 171: Topics in Industrial Organization

  48. Complementary products (cont.) Recall that Q = Q1 = Q2 = 70 - (v1 + v2)/2 so Q = Q1 = Q2 = 23.33 units The final product price is P = 140 - Q = $116.67 Profits of the three firms are then: supplier 1 and supplier 2: p1 = p2 = 46.67 x 23.33 = $1,088.81 final producer: pf = (116.67 - 46.67 - 46.67) x 23.33 = $544.29 EC 171: Topics in Industrial Organization

  49. Complementary products (cont) Now suppose that the two suppliers merge Supplier 1 Supplier 2 23.33 units @ $46.67 each 23.33 units @ $46.67 each Final Producer 23.33 units @ $116.67 each Consumers EC 171: Topics in Industrial Organization

  50. Complementary mergers (cont.) Supplier 1 Supplier 2 price v The merger allows the two firms to coordinate their prices Final Producer price P Consumers EC 171: Topics in Industrial Organization

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