Chapter 17: Vertical and Conglomerate Mergers

Transcription

1 Chapter 17: Vertical and Conglomerate Mergers Learning Objectives: Students should learn to: 1. Apply the complementary goods model to the analysis of vertical mergers.. Demonstrate the idea of double marginalization and its impact prices, profits, and consumer elfare. 3. Analyze a model here vertical integration allos or enhances price discrimination. 4. Analyze a model here vertical merger facilitates market foreclosure. Because the integrated firm has a loer acquisition cost from its on upstream supplier and because it has a higher margin on donstream sales to its on affiliate, the integrated firm ill not buy from the other upstream suppliers and ill not sell to other donstream firms. 5. Solve problems involving oligopolistic vertical mergers. 6. Relate scale and scope, transactions costs, proprietary information, and agency problems to incentives for conglomerate mergers. 7. Recognize that vertical integration can eliminate asteful double-marginalization, intensify competition, and yield loer prices for consumers. Understand recent regression analysis shoing this result in the ready-mixed concrete industry. Suggested Lecture Outline: Spend to fifty-minute long lectures on this chapter. Lecture 1: 1. Models ith complementary goods. Price discrimination 3. Market foreclosure 4. Gains from vertical integration 5. Evidence from ready-mixed concrete. Lecture : 1. Oligopolistic vertical mergers. Conglomerate mergers 3. Mergers and the theory of firms Suggestions for the Instructor: 1. Assign a problem set on complementary goods a eek or so before these lectures ould be useful.. Motivate vertical and horizontal mergers ith examples. 3. What if you ere in this position questions about vertical foreclosure are useful in motivating the section on this topic. 4. It is helpful to discuss the ideas of coordination, transactions costs, asset specificity, and hold-up problems in the context of incomplete contracts. Students easily relate to apartment rental contracts. 117

2 Solutions to End of the Chapter Problems: Problem 1 1. Norman International has a monopoly in the manufacture of hatsits. Each hatsit requires exactly one richet as an input and incurs other variable costs of $5 per unit. Richets are made by PepRich Inc., hich is also a monopoly. The variable costs of manufacturing richets are $5 per unit. Assume that the inverse demand for hatsits is p 50 q here p is the price of hatsits in dollars per unit and q is the quantity of hatsits offered for sale by Norman International. (a) Write don the profit function for Norman International assuming that the to monopolists act as independent profit-maximizing companies, ith Norman International setting a price p for hatsits and PepRich setting a price p r for richets. Hence, derive the profit-maximizing price for hatsits as a function of the price of richets, and use this function to obtain the derived demand for richets. Profits for Norman International are given by revenue minus the cost of richets and other variable costs. If a richet costs p r per unit e obtain Taking the derivative ith respect to q and solving for the optimal level of output (q ) ill yield The price of hatsits is then We can then rite the price of richets in inverse demand or price dependent form (b) Use your anser in a to rite don the profit function for PepRich. Hence, derive the profitmaximizing price of richets. Use this to derive the profit-maximizing price of hatsits. Calculate the sales of hatsits (and so of richets) and calculate the profits of the to firms. The profits of PepRich are given by revenue from the sales of richets minus their cost. 118

3 Revenue is given by Profits are given by If e take the derivative of profit ith respect to q r and set equal to zero e obtain The price of richets is then given by The price of hatsits is given by p r r 45 q Sales of hatsits are Profits of Norman International are given by revenue minus the cost of the richets minus the other variable costs or Profits of PepRich are given by Problem (a) No assume that these to firms merge to form NPR International. Write don the profit function for NPR given that it sets a price p for hatsits. Hence, calculate the postmerger profit-maximizing price for hatsits, sales of hatsits, and the profits of NPR. Profits for NPR are given by revenue minus the cost of richets (5) and other variable costs. Profits are 119

4 Taking the derivative ith respect to q and solving for the optimal level of output (q ) ill yield the optimal sales of hatsits. The price of hatsits is then Profits for the combined firm are given by p 50 q (b) Confirm that this merger has increased the joint profits of the to firms hile reducing the price charged to consumers. By ho much has consumer surplus been increased by the merger in the market for hatsits? The joint profits are 400. The profits of NI alone ere 100 and the profits of PepRich alone ere 00 for a total of 300. Thus, the profits as a merged firm are larger. The price to consumers of 30 is loer than in the case of separate firms hen the price of hatsits as 40. We can compute consumer surplus most easily by finding the area of the rectangle bounded by the to prices and the original quantity and then adding the area of the triangle ith height equal to the change in price and base equal to the change in quantity. If e let (p 1, q 1 ) be the initial price quantity pair for hatsits and (p, q ) be the subsequent pair e obtain Thus consumers are better off ith the merger. (c) Assume that the to firms expect to last forever and that the discount factor R is 0.9. What is the largest sum that PepRich ould be illing to pay the oners of Norman International to take over Norman International? What is the loest sum that the oners of Norman International ould be illing to accept? (Hint: Calculate the present value of the profit streams of the to firms before and after the merger, and notice that neither firm ill ant to be orse off ith the takeover than ithout it.) 10

5 We can compute the net present value of the merged firm as a perpetuity here e divide the 1 constant annual profit level by the interest rate. If the discount factor is given by R 1 + r 1 R 0.1 then the interest rate r is given by r The net present values of the R 0.9 firms are as follos For example, PepRich could offer NI 1,500 and still have a net present value of,100. NI in this case ould have a net present value of 1,500 and both ould be better off than as independent firms. Therefore, PepRich ould pay up to 1,800 for Norman International hile Norman International ould be thrilled ith an amount over 900. Problem 3 No assume that PepRich gets the opportunity to sell to an overseas market for hatsits, controlled by a monopolist FC Hu Inc., hich has the same operating costs in making hatsits as Norman International. PepRich knos that it ill have to pay transport costs of $ per richet to supply the overseas market. Inverse demand for hatsits in this market is (a) Repeat your calculations for problem 1a. Profits for FC Hu Inc. are given by revenue minus the cost of richets and other variable costs. If a richet costs p r per unit e obtain Taking the derivative ith respect to q and solving for the optimal level of output (q ) ill yield The price of hatsits is then 11

6 We can also rite the price of richets in inverse demand or price dependent form p 35 r q While not asked for, it might be interesting to consider the optimal production level for PepRich if they only sell richets to FC Hu. First find the maximum profit for PepRich, assuming they sell to FC Hu. If e take the derivative of profit ith respect to q r and set equal to zero e obtain Profits of PepRich are given by as compared to 00 in the case of selling to Norman International. FC Hu ould have profits of The authorities in the overseas market are contemplating taking an antidumping action, accusing PepRich of dumping richets into its market. They calculate that by doing so, they ill induce PepRich to offer to take over FC Hu. Assume that PepRich has limited access to funds, so that it can take over only one of Norman International and FC Hu. (b) Are the overseas authorities correct in their calculations? (Hint: Compare the maximum amounts that PepRich ould be illing to pay for Norman International and FC Hu). Profits for the ne merged firm (SPR) are given by revenue minus the cost of richets (5) minus the cost of transport (assuming they continue ith overseas production) and other variable costs. Profits are Taking the derivative ith respect to q and solving for the optimal level of output (q ) ill yield the optimal sales of hatsits. 1

7 Profits for the combined firm are given by The net present value of buying FC Hu as compared to Norman International is found from computing the folloing net present values here + indicates merger and the / indicates a buyer/seller relationship. Assuming the manufacturers of hatsits sell at their reservation value, PepRich is better off merging ith Norman International. Problem 4 Go back to the conditions of question 8, so that PepRich is supplying only Norman International. But no assume that the manufacture of each hatsit requires exactly one richet and one zabit. Zabits are made by ZabCorp., another monopolist, hose variable costs are $.50 per zabit. (a) Assume that the three firms act independently to maximize profit. Calculate the resulting prices of richets, zabits, and hatsits and the profits of the three firms. Remember that p 50 q No let p z denote the price of zabits and p r the price of richets. Profit for Norman International is given by 13

8 Taking the derivative ith respect to q and solving for the optimal output ill yield The price of hatsits is then p 50 q 45 pr p 50 z 55 + pr + p We can also rite the price of richets and zabits in inverse demand or price dependent form p 45 p q r p 45 p q Revenue for the to supply firms (PepRich and Zabcorp.) is given by z z r z Setting marginal revenue equal to marginal cost ill give Since q q r q z e can rite Plugging this into the equation for the optimal q ill give q ( 40 4q ) ( q ) 45 pr pz q q 6. 5 p The market clearing quantities of p r and p z are then Computing profits ill give the folloing 14

9 (b) Assume an infinite life for all three firms and a discount factor R 0.9. PepRich and ZabCorp. are each contemplating a takeover of Norman International. Which of these to companies ould in the bidding for Norman International? What ill be the effect of the inning takeover on consumer surplus in the market for hatsits? We no need to consider the profits of each of the merged firms versus the individual profits computed in a. First consider the PepRich and Norman International merger denoted NPR. The profits of the merged firm are given by Taking the derivative ith respect to q and solving for the optimal output ill yield The price of hatsits is then We can rite the price of zabits in inverse demand or price dependent form We can no compute revenue for Zabcorp. and set marginal revenue equal to marginal cost as follos Since q q z e can rite 15

10 We can then find p from Profits for the combined firm (NPR) are The net present value of this is The net present value of PepRich from a as Therefore PepRich could afford to pay ( ) $ for Norman International. Profits in this ne market for Zabcorp. are No consider the merger of Zabcorp. and Norman International denoted ZN. Proceeding as before e rite the profit for the merged firm, choose the optimal quantity of q, and then find the price of richets. The profits of the merged firm are given by Taking the derivative ith respect to q and solving for the optimal output ill yield The price of hatsits is then We can rite the price of richets in inverse demand or price dependent form We can no compute revenue for PepRich and set marginal revenue equal to marginal cost as follos 16

11 Since q q z e can rite We can then find p from Profits for the combined firm (ZN) are The net present value of this is The net present value of Zabcorp. from (a) as Hence Zabcorp can afford to pay ( ) $ for Norman International. Both firms can afford the same amount and so it is not clear ho ill in the bidding. Hoever, since the price of hatsits is $40.65, hich is less than the price of $43.75 in the original monopoly problem a, consumers are better off. Quantity demanded also increases from 6.15 to Consumers surplus is most easily computed finding the area of the rectangle bounded by the to prices and the original quantity and then adding the area of the triangle ith height equal to the change in price and base equal to the change in quantity. If e let (p 1, q 1 ) be the initial price quantity pair for hatsits and (p, q ) be the subsequent pair e obtain Thus consumers are better off ith either merger. What is obvious is that Norman International ill not accept either offer of $ since the present value of its profit stream before merger is Problem 5 17

12 As an alternative to buying Norman International, the oners of PepRich and ZabCorp. contemplate merging to form PRZ, hich ill control the manufacture of both richets and zabits. (a) Calculate the impact of this merger on (1) the prices of richets, zabits, and hatsits, () the profits of these firms, and (3) consumer surplus in the hatsit market. We no have one firm controlling the production of Richets and Zabits. The profits for Norman International are Taking the derivative ith respect to q and solving for the optimal output ill yield as before. The price of Whatsits is then 45 pr p z 55 + pr + p z p 50 q 50 Since the combined firm of PepRich and Zabcorp. knos that their product is demanded in fixed proportions, they realize that only the total price is relevant to Norman International. Therefore they face an inverse demand curve of Revenue for the merged supply firm is given by here the subscript rz denotes the quantity of Richets or Zabits and RZ denotes the merged firm. The marginal cost of producing a Richet and a Zabit is 7.5. Setting marginal revenue equal to marginal cost ill give Since q q rz e can rite Plugging this into the equation for the optimal q ill give Computing profits ill give the folloing Comparing consumer surplus in this situation versus 18

13 the situation in a e obtain just as before since the prices and quantities in the Whatsit market are the same ith any of the mergers. (b) Which merger ill be preferred (1) by consumers of hatsits? Any of the mergers give the same surplus to consumers so they ould like a merger. () by the oners of PepRich and ZabCorp.? These firms are better off if the other one merges ith Norman International. (3) by the oners of Norman International? If the oners of Norman International are involved in a merger they must share profits, hich are less in total than the total of hat they, and the merging firm got before merger so they ould not like to merge. The best for them is for the supply firms to merge. Problem 6 (Harder) Ginvir and Sipep are Bertrand competitors in the market for carbonated drinks. Consumers consider their products to be differentiated ith the demands for the products of the to firms given by the inverse demand functions P G 5 - q G - q S / for Ginvir and P S 5 - q S - q G / for Sipep Both companies need syrup to make their drinks that is supplied by to competing companies, NorSyr and BenRup. These companies incur costs of $5 per unit in making the syrup. Both Ginvir and Sipep can use the syrup of either supplier. (a) Confirm that competition beteen NorSyr and BenRup leads to the syrup being priced at $5 per unit. NorSyr and BenRup produce identical goods hich are nondifferentiated in that they are perfect substitutes for Ginvir and Sipep. Consequently, Ginvir and Sipep buy from the producer ho charges the loest price. If NorSyr and BenRup charge the same price, e assume that each firm faces a demand schedule equal to half of the market demand at the common price. The market demand for syrup is Q D() here is the price of syrup. Since producing syrup costs $5 per unit, the profit of each firm is 19

14 here the demand for the output of firm i, denoted D i, is given by for NorSyr and for BenRup Combining the profit and demand expressions e obtain The aggregate profit, as usual, cannot exceed the monopoly profit. Each firm can guarantee itself a nonnegative profit by charging a price above marginal cost so e are looking for prices beteen marginal cost ($5) and the monopoly price. A Bertrand equilibrium is a pair of prices ( N, B ) such that each firm s price maximizes that firm s profit given the other firm s price, that is We can sho that the firms ill each charge the same price and that it ill be equal to marginal cost ($5) as follos. Consider, for example, the case here NorSyr charges a price Then NorSyr has no demand, and its profit is zero. On the other hand, if NorSyr charges * N B * (here ε is positive and small ), it obtains the entire market demand, D ( B ε ), and has a positive profit margin of ε Therefore, NorSyr cannot be acting in its on best interest if it charges * N. No suppose that The profit of firm NorSyr is 130

15 If NorSyr reduces its price slightly to * N ε, its profit becomes hich is greater for small ε. The market share of the firm increases in a discontinuous manner. Because no firm ill charge less than the unit cost c (doing so ould make negative profit), e are left ith one or to firms charging exactly c. To sho that both firms charge c, suppose that Then BenRup, hich makes no profit, could raise its price slightly, still supply all the demand, and make a positive profit a contradiction. (b) What are the resulting equilibrium prices for Ginrip and Sipep and hat are their profits? Profit for Ginrip is given by price minus marginal cost multiplied by the quantity sold or Similarly for Sipep e obtain We are given the inverse demand system for the to firms. Because the firms are Bertrand competitors, the optimal prices are determined by taking the derivatives of the to profit expressions ith respect to price and then solving the system for P G and P S. To rite the profit system in terms of prices, e need to solve the inverse demand system for quantity as a function of price. First rerite each inverse demand function as follos. Then substitute for q S in the last expression as follos 131

16 We find q S by substitution as follos We can no rite the to profit equations in the folloing form We obtain P G by substitution: P G )11.66) 0 13

17 .66P G P G Quantities may also be obtained by substitution. Profits are straightforard to compute. Total profits for the to firms, ho are able to buy the syrup at marginal cost of $5 per unit, are Problem 7 No suppose that Ginvir and NorSyr merge and that in doing so NorSyr no longer competes for Sipep s business. (a) What price ill BenRup no charge Sipep for the syrup? Benrup is no longer in Bertrand competition ith a homogeneous product as before, but is a monopolist in the supply of the input to Sipep. The profit maximization problem for Benrup is a follos. It takes one unit of syrup to make one unit of carbonated drink and the quantity of syrup supplied is no variable depending on the price of syrup (hich is no longer fixed at $5.00 by competition). Differentiating profits ith respect to B, e obtain 133

18 134

19 Quantities are also obtained by substitution. First for Ginvir. Then for Sipep. Notice at this point that the prices and quantities for both firms ill be the same if B 5 as in part b. As B rises the price charged by Sipep ill rise and the quantity sold ill fall. We solve for B by using the profit maximization condition for Benrup and substituting as appropriate. Before substituting in this expression note that No substitute in the first order condition (b) What are the resulting profits to the three post-merger companies? First e need to compute the equilibrium prices and quantities for each firm. First the prices. 135

20 Then the quantities are follos Profits are given by substitution. Total profits for the three firms are $ Profits for the combined Benrup/Sipep firm are $ (c). Do BenRup and Sipep have an incentive also to merge? If BenRup and Sipep merge, they ill then be able to compete in a duopoly ith Ginvir as in part b, ith a cost of syrup of $5. This ill lead to profits of $59.593, hich are higher than if they do not merge. So they ill also merge. Given that Ginvir can anticipate this move, they ill also not merge and so nothing ill take place in the industry. Problem 8 Profits ith no vertical integration are: U D ( A c c ) ( ) U D U U D D 4 A c c π 1 π for the upstream firms and π 1 π for the 7B 81B U D 10( A c c ) donstream firms. Total profit for each upstream-donstream pair is:

21 If both firms vertically integrate, they compete as Cournot duopolists, each ith a constant marginal cost of c U + c D. Hence, each merged firm s output is: U D D D A c c q1 q 3B U D U D ( A c c ) A + ( c + c ) Total output is Q and the retail price is P 3B 3 U D ( A c c ) is π. Profit to each firm π 1. This is clearly less than the combined profit earned by an 9B unintegrated pair of upstream and donstream firms. Problem 9 (a) Assume that marginal cost is zero. Since demand is: P 100 Q, monopolization of the industry ould mean a firm facing a marginal revenue described by: MR 100 Q. Equating marginal revenue ith marginal cost (c 0) implies Q 50 P, so that profit is $500. (b) If both firms reject the offer, each earns zero profit. If both accept the offer, the $150 becomes a sunk cost. They ill compete as Cournot duopolists ith a marginal cost of zero. Normally, this ould yield an output of for each. Hoever, since they are constrained by their allotment of 5 units each, they ill simply sell out their entire stock. All fifty units ill be sold and the market price ill be $50. Each ill earn 5 x $50 $150 in operating profit. This ill just cover the charge by the monopoly supplier so that the net profit for each ill again be zero. If only one donstream firms accepts the offer, she becomes a retail monopolist ith a capacity of 5 units. She ill sell all 5 (she ould like to sell more) at a market-clearing price of $75 each for a total revenue of $1875 more than enough to cover the charge of $150 from the upstream supplier. So, the payoff hen only one firms accepts the offer is $ $150 $65. The payoff matrix is then: Donstream Firm Reject Accept Donstream Firm 1 Reject (0,0) (0,$65) Accept ($65,0) (0,0) Accept is a eakly dominant strategy (a slight reduction in the fee from $150 to $149 can make it strictly dominant). Therefore, the Nash Equilibrium is for both to accept the offer. Problem 10 (a) In a sequential setting, if one firm accepts the offer the monopolist can subsequently make the offer to the latter firm and drive all donstream profit to zero. Whichever donstream firm goes first, can prevent this from happening and raise its profit by holding out for a better deal. The fact that a particular firm goes first means that the upstream supplier cannot sell to anyone else until it settles ith the first retailer. This fact gives the firs donstream firm some bargaining poer. (b) Vertical integration eliminates all double marginalization. By foreclosing the alternative retailer, the integrated firm is in exactly the same position as the monopolist in 9a. Therefore, it can exactly duplicate that outcome of P $50; Q 50; and Profit $