Chapter 11: Horizontal Mergers1 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 12: Vertical and Conglomerate Mergers 11 Introduction General Electric and Honeywell proposed to merge in 2000 –GE supplies jet engines for commercial aircraft –Honeywell produced various electrical and other control systems for jet aircraft Deal was approved in the US But was blocked by the EU Competition Directorate –this was a merger of complementary firms –it is “like” a vertical merger –so can potentially remove inefficiencies in pricing benefiting the merged firms and consumers –so why block the merger?

Chapter 12: Vertical and Conglomerate Mergers 12 Introduction 2 Vertical mergers can be detrimental –if they facilitate market foreclosure by the merged firms refuse to supply non-merged rivals But they can also be beneficial –if they remove market inefficiencies Regulators need to look for the balance these two forces in considering any proposed merger

Chapter 12: Vertical and Conglomerate Mergers 13 Complementary Mergers Consider first a merger between firms that supply complementary products 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 = 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?

Chapter 12: Vertical and Conglomerate Mergers 14 Complementary mergers 2 Supplier 1Supplier 2 price v 1 price v 2 price P Final Producer Consumers

Chapter 12: Vertical and Conglomerate Mergers 15 Complementary producers  Consider the profit of the final producer: this is  f = (P - v 1 - v 2 )Q = (140 - v 1 - v 2 - Q)Q  Maximize this with respect to Q  f /  Q = (v 1 + v 2 ) - 2Q = 0 Solve this for Q  Q = 70 - (v 1 + v 2 )/2  This gives us the demand for each input Q 1 = Q 2 = 70 - (v 1 + v 2 )/2  So the profit of supplier 1 is then:  1 = v 1 Q 1 = v 1 (70 - v 1 /2 - v 2 /2)  Maximize this with respect to v 1

Chapter 12: Vertical and Conglomerate Mergers 16 Complementary producers 2  Maximize this with respect to v 1  1 = v 1 Q 1 = v 1 (70 - v 1 /2 - v 2 /2)  1 /  v 1 = 70 - v 1 - v 2 /2 = 0 Solve this for v 1 v 1 = 70 - v 2 /2  We can do exactly the same for v 2 v 2 = 70 - v 1 /2 The price charged by each supplier is a function of the other supplier’s price We need to solve these two pricing equations v2v2 v1v R1R1 140 R2R2 v 1 = 70 - (70 - v 1 /2)/2 = 35 + v 1 /4 so 3v 1 /4 = 35,i.e., v 1 = $ and v 2 = $

Chapter 12: Vertical and Conglomerate Mergers 17 Complementary products 3  Recall that Q = Q 1 = Q 2 = 70 - (v 1 + v 2 )/2 so Q = Q 1 = Q 2 = units  The final product price is P = Q = $  Profits of the three firms are then: supplier 1 and supplier 2:  1 =  2 = x = $1, final producer:  f = ( ) x = $544.29

Chapter 12: Vertical and Conglomerate Mergers 18 Complementary products 4 Supplier 1Supplier $46.67 each $ each Final Producer Consumers $46.67 each Now suppose that the two suppliers merge

Chapter 12: Vertical and Conglomerate Mergers 19 Complementary mergers 5 Supplier 1Supplier 2 price v price P Final Producer Consumers The merger allows the two firms to coordinate their prices

Chapter 12: Vertical and Conglomerate Mergers 20 Complementary mergers 6  Consider the profit of the final producer: this is  f = (P - v)Q = (140 - v - Q)Q  Maximize this with respect to Q  f /  Q = v- 2Q = 0 Solve this for Q  Q = 70 - v/2  This gives us the demand for each input Q 1 = Q 2 = Q m = 70 - v/2  So the profit of the merged supplier is:  m = vQ m = v(70 - v/2)  Maximize this with respect to v

Chapter 12: Vertical and Conglomerate Mergers 21 Complementary mergers 7  m = vQ m = v(70 - v/2)  Differentiate with respect to v  m /  v = 70 - v = 0 so v = $70 This is the cost of the combined input: the merger has reduced costs to the final producer  Recall that Q m = Q = 70 - v/2 so Q m = Q = 35 units  This gives the final product price P = Q = $105 The merger has reduced the final product price: consumers gain  What about profits? For the merged upstream firm:  m = vQ m = 70 x 35 = $2,480 This is greater than the combined pre-merger profit  For the final producer:  f = ( ) x 35 = $1,225 This is greater than the pre-merger profit

Chapter 12: Vertical and Conglomerate Mergers 22 Complementary mergers 8 A merger of complementary producers has –increased profits of the merged firms –increased profit of the final producer –reduced the price charged to consumers Everybody gains from this merger: a Pareto improvement! Why? This merger corrects a market failure –prior to the merger the upstream suppliers do not take full account of their interdependence –cut in price by one of them reduces downstream costs, increases downstream output and benefits the other upstream firm –but this is an externality and so is ignored Merger internalizes the externality

Chapter 12: Vertical and Conglomerate Mergers 23 Vertical Mergers The same result arises when we consider vertical mergers: mergers of upstream and downstream firms If the merging firms have market power –lack of co-ordination in their independent decisions –double marginalization –merger can lead to a general improvement Illustrate with a simple model –one upstream and one downstream monopolist manufacturer and retailer –upstream firm has marginal costs c –sells product to the retailer at price r per unit –no other retail costs: one unit of input gives one unit of output –retail demand is P = A – BQ

Chapter 12: Vertical and Conglomerate Mergers 24 Vertical merger 2 ManufacturerMarginal costs c wholesale price r Price P Consumer Demand: P = A - BQ

Chapter 12: Vertical and Conglomerate Mergers 25 Vertical merger 3 Consider the retailer’s decision –identify profit-maximizing output –set the profit maximizing price Price Quantity Demand A A/B  mm arginal revenue downstream is MR = A – 2BQ MR A/2B  r r etail marginal cost is r MCr  ee quate MC = MR to give the quantity Q = (A - r)/2B A - r 2B  ii dentify the price from the demand curve: P = A - BQ = (A + r)/2 (A+r)/2  pp rofit to the retailer is (P - r)Q which is  D = (A - r) 2 /4B  pp rofit to the manufacturer is (r-c)Q which is  M = (r - c)(A - r)/2B Retail Profit c Man. Profit

Chapter 12: Vertical and Conglomerate Mergers 26 Vertical merger 4 Price Quantity Demand A A/B MR A/2B MCr  ss uppose the manufacturer sets a different price r 1 r1r1 A - r 2B  tt hen the downstream firm’s output choice changes to the output Q 1 = (A - r 1 )/2B A - r 1 2B  aa nd so on for other input prices  dd emand for the manufacturer’s output is just the downstream marginal revenue curve Upstream demand

Chapter 12: Vertical and Conglomerate Mergers 27 Vertical merger 5 Price Quantity Demand A A/B MR A/2B  tt he manufacturer’s marginal cost is c Upstream demand c MC  uu pstream demand is Q = (A - r)/2B which is r = A – 2BQ  uu pstream marginal revenue is, therefore, MR u = A – 4BQ A/4B  ee quate MR u = MC: A – 4BQ = c  ss o Q*=(A-c)/4B (A-c)/4B the input price is (A+c)/2 (A+c)/2  ww hile the consumer price is (3A+c)/4 (3A+c)/4  tt he manufacturer’s profit is (A-c) 2 /8B  tt he retailer’s profit is (A-c) 2 /16B MR u Manufacturer Profit Retail Profit

Chapter 12: Vertical and Conglomerate Mergers 28 Vertical merger 6 Now suppose that the retailer and manufacturer merge –manufacturer takes over the retail outlet –retailer is now a downstream division of an integrated firm –the integrated firm aims to maximize total profit –Suppose the upstream division sets an internal (transfer) price of r for its product –Suppose that consumer demand is P = P(Q) –Total profit is: upstream division: (r - c)Q downstream division: (P(Q) - r)Q aggregate profit: (P(Q) - c)Q The internal transfer price nets out of the profit calculations Back to the example

Chapter 12: Vertical and Conglomerate Mergers 29 Vertical merger 7 Price Quantity Demand A A/B MR  tt he integrated demand is P(Q) = A - BQ c MC  mm arginal revenue is MR = A – 2BQ  mm arginal cost is c  ss o the profit-maximizing output requires that A – 2BQ = c  ss o Q* = (A – c)/2B (A-c)/2B  ss o the retail price is P = (A + c)/2 (A+c)/2 This merger has benefited consumers  aa ggregate profit of the integrated firm is (A – c) 2 /4B This merger has benefited the two firms Aggregate Profit

Chapter 12: Vertical and Conglomerate Mergers 30 Vertical merger 8 Integration increases profits and consumer surplus Why? –the firms have some degree of market power –so they price above marginal cost –so integration corrects a market failure: double marginalization What if manufacture were competitive? –retailer plays off manufacturers against each other –so obtains input at marginal cost –gets the integrated profit without integration Why worry about vertical integration? –two possible reasons price discrimination vertical foreclosure