Entry, Accommodation and Exit. Why do supernormal profits persist in industries? Why doesn t entry of new firms wipe out such profits?

Transcription

1 Entry, Accommodation and Exit. Why do supernormal profits persist in industries? Why doesn t entry of new firms wipe out such profits?

2 Harvard school of IO economists (Joe Bain): barriers to entry. Bain: a barrier to entry is anything that allows incumbents to enjoy strictly positive economic profits without threat of entry. These may include government regulation-permits, licenses, patents etc. - but we shall abstract from these.

3 Bain argued there are four major types of entry barriers: 1. Economies of Scale (fixed cost): If minimum efficient scale is large relative to market demand, there can only be few firms in the market (e.g., natural monopoly) & they may earn strictly positive profit without inviting entry.

4 2. Absolute Cost Advantages: of incumbents (superior technology, previous capital accumulation, firm specific learningetc.)

5 3. Product Differentiation Advantages: Incumbents may have patented product innovations & cornered important niches in the product space, dynamic investment in forming consumer loyalty...

6 4. Capital requirement: imperfect capital market, entrants may find it more difficult or costly to raise capital.

7 The Chicago school led by George Stigler approached entry barriers as simply being cost asymmetries between incumbent firms and outsiders (incumbents could charge price above average cost because outside firms had higher average cost curves).

8 Traditional model of entry barrier by incumbent firms: Limit pricing model by Sylos-Labini, Modigliani etc.: Incumbent prices low enough so that outside firms cannot enter.

9 This theory suffers from a credibility problem. Why would potential entrants believe that incumbents would hold on to those low prices if entry occurred? Not subgame perfect.

10 Modern version: Spence (1977) - Dixit (1979,1980) Model: Capacity choice used as a credible precommitment to flooding market & low prices.

11 Milgrom - Roberts (1982): asymmetric information between incumbents and potential entrants, - low prices signal private information about low profitability of potential entrants after entry.

12 Scale Economies as Entry Barrier: Contestability. The idea that scale economies act as entry barriers is best exemplified by the case of increasing returns to scale leading to a natural monopoly. If the average cost continually declines with output, no more than one firm can produce profitably in the industry (in a homogenous good market, if two firms sell output q 1,q 2 > 0 at price p that allows them to earn nonnegative profit, then one of the two firms can sell q 1 + q 2 at a price slightly lower than p and since average cost will be significantly lowered, earn higher profit).

13 Even if the AC curve is U-shaped and the minimum efficient scale is large, the number of firms that can produce profitably in the industry is small (natural oligopoly).

14 Baumol, Panzar and Willig (1982) argued that even though scale economies create entry barriers, - the threat of being replaced by potential entrants may act as a disciplining device on current incumbents and restrict the degree of market power. They developed the concept of contestable markets to capture this idea.

15 Consider a homogenous good industry with n symmetric firms each with cost function C(q),C(0) = 0. Note that this allows for fixed cost (that is not sunk) as long as lim q 0 C(q) > 0. Of these n firms, i =1,...m are incumbents and i = m +1,..., n are potential entrants, n>m. Market demand is given by D(p).

16 A sustainable industry configuration is a set of output {q 1,..., q m } and a price p charged by all firms such that: (i) market clears (demand = supply) (ii) incumbent firms make non-negative profits (iii) there does not exist any price p c p and output q c D(p c ) such that p c q c >C(q c ) (i.e., it is not possible for a potential entrant to make strictly positive profit by charging a lower price and selling some quantity).

17 A perfectly contestable market is one where every "equilibrium" generates a sustainable industry configuration.

18 Consider the case of natural monopoly with increasing returns to scale: C(q) = cq + f,c > 0,f >0 for q>0 = 0, for q =0.

19 Let π m =max q [(P (q) c)q] denote the gross monopoly profit and assume π m >f.

20 One can check that there is a unique sustainable industry configuration here where m =1and the incumbent charges the price ep = P (eq) where ep = c + f eq. This is identical to the solution obtained by average cost pricing regulation and is the constrained socially optimal solution when subsidies are not allowed. It is remarkable that this solution can emerge through market forces and threat of entry. Thus, regulation of industries with high scale economies may not be warranted.

21 The trouble is that for other demand and cost functions, theremaynotbeasustainableindustryconfiguration in a natural monopoly so that a constrained efficient industry structure may not be sustainable against entry. For example: U-shaped average cost curve where the demand curve intersects the AC curve slightly to the right of minimum efficient scale.

22 How to think of the strategic foundation of the contestable outcome? Easy to see that the outcome in the natural monopoly case requires that incumbent does not alter price after he learns about the output decision of potential entrant.

23 One game: firms choose prices first and then choose output/entry.

24 Problem: Prices usually adjust faster than output or entry decisions.

25 Sunk Cost/Capacity as Barrier to Entry: Spence-Dixit Model. Stackelberg- Firms enter market at different points of time - some enter early because of technological leadership - and can be thought of as incumbents. Others enter later. Early incumbents accumulate capacity and other forms of capital (including knowledge) over time that is "sunk" at any point of time. This allows firms to compete aggressively (for example, because marginal costs are low or production capacity is bigger).

26 So, when capacity or capital accumulation is observed by potential entrants, the latter take this into account in their calculation of post-entry profitability. Early entrants can prevent entry by using their first mover advantage and engaging in significant capital accumulation.

27 Model: Homogenous good market with demand D(p) =1 p. Production cost =0. 2 firms. Firm 1: Incumbent Firm 2: (Potential ) entrant. Entrant incurs fixed entry cost f > 0 if it enters the market. For the incumbent, the entry cost is sunk, does not affect the calculations and hence assumed to be zero.

28 Two stage game: Stage 1: Firm 1 sets its capacity K 1. Stage 2: Firm 2 (after observing firm 1 s choice) sets its own capacity K 2 (no entry equivalent to K 2 =0) After this both firms set a price that clears the market when they produce at full capacity viz., p =1 K 1 K 2 (p =0, if K 1 + K 2 1).

29 Profits: π 1 (K 1,K 2 ) = K 1 (1 K 1 K 2 ), if K 1 + K 2 1 = 0, if K 1 + K 2 1 π 2 (K 1,K 2 ) = K 2 (1 K 1 K 2 ) f, if K 2 > 0 and K 1 + = f, if K 2 > 0 and K 1 + K 2 1 = 0, if K 2 =0.

30 Definition: Entry is said to be blockaded if the entrant does not enter even though the incumbent s action is identical to what would be optimal (for the incumbent) if there was no threat of entry. Entry is said to be deterred if the entrant does not enter even because the incumbent chooses an action that would be suboptimal (for the incumbent) if there was no threat of entry. Entry is said to be accommodated if entry occurs and the incumbent adjusts his behavior reconciling to entry.

31 Blockaded entry: If there was no threat of entry, incumbent would choose K 1 at the monopoly output level i.e., solving which yields K m 1 = 1 2. max K 1 K 1 (1 K 1 )

32 Given this capacity of firm 1, the maximum profit that firm 2 can make by entering is given by: max K 2 = 1 16 f. K 2 ( 1 2 K 2) f Thus: entry is blockaded if f 1 16.

33 Entry Deterrence: If f< 16 1, entry will occur if the incumbent ignores the possibility of entry and sticks to monopoly capacity level. However, if it sets capacity at a sufficiently higher level, the entrant will find it unprofitable to enter.

34 What is the critical level of incumbent s capacity K b 1 such that entrant is indifferent between entering and not entering: max K 2 and this implies: K 2 (1 K b 1 K 2)=f K b 1 =1 2 qf. Note f< 1 16 implies Kb 1 =1 2 f> Obviously, K b 1 < 1.

35 Consider stage 2 subgame for f< If the capacity set in stage 1 is K 1 K1 b, then no entry occurs (i.e., K 2 =0). If, on the other hand, K 1 <K1 b, then entry occurs and firm 2 sets K 2 so as to: max K 2 (1 K 1 K 2 ) f K 2 which yields reaction function: K 2 (K 1 )= 1 K 1 2 which yields the following profit for firm 1: K 1 ( 1 K 1 ). 2

36 Now, consider the reduced form game in stage 1. Firm 1 s reduced form payoff: π 1 (K 1 ) = K 1 ( 1 K 1 ),K 1 <K1 b 2 = K 1 (1 K 1 ),K 1 K1 b. Observe that firm 1 will never set K 1 > K b 1 because K b 1 > 1 2. and π 1 K K1 >K b =1 2K 1 <

37 Therefore, the optimal capacity choice for firm 1 on [K1 b, 1] is K1 b yielding profit: K1 b q (1 Kb 1 qf(1 )=2 2 f) (1) This is the profit from deterring entry.

38 On [0,K1 b ), the profit maximizing capacity of firm 1 is given by setting: which yields: π 1 K K1 <K b =0 1 1 K 1 = 1 2 and profit: 1 8. (2) This is the profit from accommodating entry.

39 Entry deterring profit in (1) entry accommodating profit in(2)iff q q 2 f(1 2 f) 1 8. Let f be defined by q q 2 f(1 2 f) = 1 8. It can be checked that f (0, ).

40 Thus: for f f, entry is accommodated. For f (f, ), entry is deterred (and the incumbent holds large capacity equal to 1 2 f).

41 Note that when entry is deterred, the market appears to be a monopoly but market power is lower than in a monopoly. Potential entry restrains the exercise of market power.

42 Also, verify that when entry is accommodated, the subgame perfect equilibrium is K 1 = 1 2,K 2 = 1 4 leading to profits π 1 = 1 8,π2 = 16 1 f. Even if f =0,firm1 has a first mover s advantage. The version of the above sequential game where f =0 is called the Stackelberg game.

43 Stackelberg- Spence-Dixit sequential capacity choice by incumbent-entrant. Original Stackelberg game: sequential choice of quantities. Interpretation of payoff function? Why incumbent s first mover advantage in quantity? Why quantity has commitment value?

44 Spence-Dixit: interpret quantity as capacity. -the profit function after both choose capacity interpreted as reduced form payoff from short run product market competition (for example, price competition) given capacity levels - first mover advantage may arise as one firm (jncumbent) has earlier access to technology or quicker to act - capacities are sunk, difficult to change in the short run, and hence have commitment value.

45 The actual models of Spence and Dixit - short run competition after capacity choice is simultaneous quantity competition. This last stage may itself be interpreted as the reduced form of a two stage game where firms first set "selling capacities" (given production capacities) and then compete in prices. Also, they allow firms to add (but not reduce!) capacity in the product market competition stage.

46 Dixit (1980): Stage 1: Firm 1 sets capacity K 1 0 Stage 2: Firms 1 and 2 set capacities f K 1 K 1,K 2 0 as well outputs q 1 [0, f K 1 ],q 2 [0,K 2 ] simultaneously. Cost of acquiring each unit of capacity: c 0 Unit cost of production: c For the time being, ignore fixed cost of entry for firm 2.

47 Consider stage 2. Firm 2 sets equal capacity and output (K 2 = q 2 ) - his decision problem is equivalent to that of determining quantity of output at constant marginal cost c 0 + c. His reaction function (on the quantity space) is the standard Cournot reaction function of a firm that produces at marginal cost c 0 + c.

48 Firm 1 s problem in stage 2 is different. Ignoring previous sunk cost of acquiring capacity, he can produce any output up to K 1 at marginal cost c and output greater than K 1 at effective marginal cost c 0 + c. His reaction function is the Cournot reaction function of a firm that produces at unit cost c as long as that reaction output is below K 1 and then it jumps below to the reaction function of a firm that produces at unit cost c 0 + c. A jump discontinuity at K 1. Firm 1 much more aggressive than firm 2 (higher reaction function) till K 1.

49 If K 1 =0, the second stage game is just a simultaneous move game with a symmetric Nash equilibrium. By setting a high K 1 in stage 1, firm 1 pushes up his own reaction function in the second stage (by reducing current marginal cost) for a whole range of output so that the new Nash equilibrium is more favorable to firm 1. With fixed cost of entry, can be deterred.

50 One feature of the equilibrium in a linear demand model: no excess capacity - all capacity is used. This is generally true as long as demand is concave (downward sloping reaction functions in the quantity space). But if demand is convex and reaction functions are upward sloping - there may be excess capacity. Maskin (1986): uncertainty about demand or cost can lead to incumbent acquiring too much of capacity to deter entry and thus lead to excess capacity in certain states of nature.

51 Remark: Welfare analysis of entry deterrence is ambiguous. Incumbent s increase in capacity and output to deter entry - is welfare improving (as long as all capacity is used). If entry occurs (not deterred) after observing incumbent s capacity, then entrant s output and capacity is welfare improving. Fixed costs complicate.

52 Multiple incumbents: Public good problem in entry deterrence? If one incumbent deters entry by making a large investment, other incumbents benefit. Incentive to free ride underinvestment in the aggregate. Gilbert and Vives (1986) - contributing to entry deterrence is not quite like contributing to a pure public good. The benefit from entry deterrence also depends on each firm s own "contribution". Profit of an incumbent firm from entry deterrence depends on its own market share after entry is deterred which, in turn, creates competitive pressure to increase investment in capacity. overinvestment in entry deterrence.

53 Possibility of post-entry merger in bargaining for the buy-out of entrant by incumbent, entrant can certainly get whatever it would make if there was no merger after entry + part of the increase in industry profit associated with merger (monopolization). Thus, prospect of buy-out encourages entry. Of course, it also increases market concentration.

54 Note: entrant may acquire lot of capacity to increase bargaining strength (threat point) in the buyout phase. After buyout, incumbent may not use all of entrant s capacity (hold excess capacity).

55 Other forms of capital accumulation to deter entry: * Cost reduction (Process R&D) makes incumbent more aggressive competitor post entry.

56 *Learningbydoing.

57 * Developing clientele : More imperfect the consumers information and more important the costs of switching suppliers, the greater the clientele effect. Sometimes, overinvestment in clientele may not be an optimal way to prevent entry as the incumbent then has a large captive segment and is therefore less aggressive in price competition making entry more lucrative for entrant.

58 * Network effect among consumers: increases incentive to expand size of installed network base by incumbent firm.

59 * Exclusive franchises with retailers increases distribution costs for entrants

60 * Development of new product - specially when patented.

61 Strategic effect of pre-commitment on rival s actions: overinvestment vs. underinvestment. A simple reduced form three-stage model.

62 Stage 1: Firm 1 (incumbent) commits to a variable K 1 (call it "investment") Observed by firm 2. Stage 2: Firm 2 decides whether or not to enter. Stage 3: Firms in the industry engage in short run product market competition and each firm i in the market decides on variable x i.

63 If entry does not occur, firm 2 receives zero payoff and firm 1 s payoff is π 1m (K 1,x m 1 (K 1)) where x m 1 (K 1) is the monopoly level of variable x 1 (given investment K 1 ) that is set by firm 1 in stage 3.

64 If entry occurs, the profits for any choice of x 1,x 2 in stage 3 are π 1 (K 1,x 1,x 2 ) and π 2 (K 1,x 1,x 2 ) where π 2 is net of entry cost. Assume: π 1 (K 1,x 1,x 2 ),π 2 (K 1,x 1,x 2 ) are differentiable. Let {x 1 (K 1),x 2 (K 1)} be the Nash equilibrium of the stage 3 product market competition game, given K 1. It can be shown that x 1 (K 1),x 2 (K 1) are continuous in K 1. Assume: Given K 1,NE is unique, interior and "stable".

65 If K 1 is chosen such that π 2 (K 1,x 1 (K 1),x 2 (K 1)) 0 then entry does not occur. Indeed, if in equilibrium, firm 1 chooses K 1 so that π 2 (K 1,x 1 (K 1),x 2 (K 1)) < 0, prevention of entry is not a binding constraint of firm 1 s choice of investment entry is blockaded.

66 Entry deterred: π 2 (K 1,x 1 (K 1),x 2 (K 1)) = 0

67 Entry accommodated: π 2 (K 1,x 1 (K 1),x 2 (K 1)) > 0.

68 Assume: π 1m (K 1,x m 1 (K 1)),π 2 (K 1,x 1 (K 1),x 2 (K 1)) are strictly concave in K 1 and that x 1 (K 1),x 2 (K 1) are differentiable.

69 Consider situation of entry deterrence: π 2 (K 1,x 1 (K 1),x 2 (K 1)) = 0 (3) As x 2 (K 1) is the best response of firm2instage3to x 1 (K 1), FOCimplies: π 2 (K 1,x 1 (K 1),x 2 (K 1)) x 2 =0.

70 Taking total derivative with respect to K 1 of we have π 2 (K 1,x 1 (K 1),x 2 (K 1)) dπ 2 = π2 + π2 x 1 + π2 x 2 dk 1 K 1 x 1 K 1 x 2 K 1 = π2 + π2 x 1 K 1 x 1 K 1 = Direct Effect + Strategic Effect Direct Effect : Change in K 1 may directly change rival s profitability by changing demand for the latter s product or its cost of production (through spillovers) etc If K 1 is investment that affects only firm 1 s own cost or technology, then direct effect is zero. Strategic effect: change in K 1 changes firm 1 s ex post behavior and his choice in the product market which in turn affects firm 2 s profit.

71 These effects may run in opposite directions.

72 Taxonomy of business strategies: Top dog: be big or strong to look tough or aggressive Puppy dog: Be weak or small to look soft or inoffensive Lean and hungry look: Be weak or small to look tough or aggressive Fat cat: be big or strong to look soft or inoffensive

73 To deter entry, firm 1 wants to look tough. Investment makes firm 1 TOUGH if dπ2 dk 1 < 0 and in that case firm 1 should overinvest ("top dog" strategy). Investment makes firm1softif dπ2 dk 1 > 0 and in that case firm 1 should underinvest ("stay lean and hungry" strategy).

74 In Spence-Dixit kind of investment games, overinvestment (top dog) strategy to deter entry is optimal. But in investment in forming loyal clientele, underinvestment (stay lean and hungry) may be better to deter entry.

75 If entry deterrence is too costly, it is better for firm 1 to accommodate entry. Under accommodation, the incentive to invest is determined by the effect of K 1 on π 1 (K 1,x 1 (K 1),x 2 (K 1)). Observe: dπ 1 = π1 + π1 dx 1 + π1 dx 2 dk 1 K 1 x 1 dk 1 x 2 dk 1 = π1 + π1 dx 2 K 1 x 2 dk 1 = Direct Effect + Strategic Effect The direct effect exists even if firm 1 s investment is not observed by firm 2. The strategic effect is the effect of observing this investment on firm 2 s behavior in the product market. For the time being, let us focus on the strategic effect.

76 Assume: π1 x 2 and π2 x 1 havethesamesign (product market variables of both firms have the same nature). Now, dx 2 dk 1 = dx 2 dx 1 dx 1 dk 1 = R 0 2 (x 1 ) dx 1 dk 1

77 so that sign of the strategic effect: sign( π1 x 2 dx 2 dk 1 ) = sign( π1 x 2 )sign(r 0 2 (x 1 ) dx 1 dk 1 ) = sign( π2 x 1 )sign(r 0 2 (x 1 ) dx 1 dk 1 ) = sign( π2 x 1 dx 1 dk 1 )sign(r 0 2 ) Note π2 x 1 dx 1 dk 1 = strategic effect under entry deterrence. If R 0 2 > 0 (x 1 and x 2 are strategic complements), whether overinvestment or underinvestment is optimal under entry accommodation (focusing on strategic effect) follows the same prescription as under entry deterrence. If R 0 2 < 0 (x 1 and x 2 are strategic substitutes), overinvestment is optimal under entry accommodation if underinvestment is optimal under entry deterrence and viceversa.

78 π 2 Assume: K =0so that dπ2 1 dk in the entry deterrence 1 case depends only on the strategic effect.

79 Thelatterimpliesthatintheentrydeterrencecasewe only have two kinds of situation: (a) where the strategic effect is such that investment makes firm 1 look tough. (b) where the strategic effect is such that investment makes firm 1 look soft. strategic complements strategic substitutes (a) A : Puppy Dog D : Top Dog A : Top Dog D : Top Dog (b) A : Fat Cat D : Lean and Hungry A : Lean and Hungry D : Lean and Hungry In all cases, firm 1 tries to make firm 2 behave softly.

80 Inducement of Exit: Very similar to entry deterrence. Suppose there are two firms in the market. Fixedcostofstayingoninthemarket. Suppose firm 1 has a first mover advantage Can pre-emptively commit to an investment (a long run variable) K 1 which is observed by firm 2 Then, firm 2 decides whether or not to exit the market. If it does not exit, firms engage in short run product market competition setting x 1,x 2.

81 Exit occurs as long as π 2 (K 1,x 1 (K 1),x 2 (K 1)) 0 The analysis of entry prevention can be easily re-written as exit inducement.

82 Applications of the taxonomy of business strategies for entry deterrence & accommodation. In general, K 1 can be interpreted as any stage 1 (or, long run) variable (whether or not set by a firm) that is observable prior to product market competition between firms in the industry and taken as given, at that stage.

83 * Voluntary limitation of capacity: Puppy dog ploy.. A firm may choose to commit to small capacity in order to reduce price competition in the product market. Price competition : strategic complementarity. For example, entrant may commit to small capacity so as not to trigger aggressive price competition from large capacity incumbent.

84 * Product Differentiation: Puppy Dog ploy. Here, a firm commits to closeness to rival s product type or location, prior to price competition. Closer = more aggressive price competition (think of this as higher capital).

85 *LearningbyDoing: Two periods. One firm in period 1. Investment in capital = higher production in initial time period. Reduces marginal cost in the next period.

86 If second period market competition (if entry occurs) is in quantities (strategic substitutes), overinvestment is optimal i.e., top dog strategy. It reduces firm 2 s market share in period 2 (if it enters). This is independent of whether entry is deterred or accommodated.

87 What if product market competition is in prices? Top dog is still good for entry deterrence. But for accommodation, experience accumulation and lower marginal cost triggers lower price from rival. Makes overinvestment less worthwhile - underinvestment often optimal. Puppy Dog.

88 Spillovers: learning reduces marginal cost of rival too. This effect reduces the appeal of top dog strategy.

89 * Most favored customer clause (price protection). Guarantees current customers that they will be reimbursed any difference between current price and the lowest price upto a date in the future. Helps to commit to not reduce price and sustain current level of price in future. Interesting effect: Reduces price competition in the future and creates price-leadership!

90 Consider a two period differentiated good price duopoly. Demand in each period D i (p i,p j ). For simplicity, set cost =0. Firms set prices simultaneously each period. Upward sloping reaction function. No discounting.

91 If no price protection: Static NE (p 1,p 2 ) each period. outcome in

92 Suppose firm 1 unilaterally introduces price protection in period 1 and sets price ep 1 = p 1 + in period 1. Also, suppose consumers expect firm 1 not to reduce price infuture(sonoonebuysjusttogeta"reimbursement"): this will be self-fulfilling in equilibrium. Quantity sold by firm1inperiod1: eq 1 = D 1 ( ep 1,p 2 ).

93 Consider price competition in period 2. Firm 1 s second period profit at any pair of prices (p 1,p 2 ) charged by the firms in period 2: eπ 1 (p 1,p 2 ) = p 1 D 1 (p 1,p 2 ), if p 1 ep 1 = p 1 D 1 (p 1,p 2 ) eq 1 ( ep 1 p 1 ), if p 1 < ep 1. Observe that price protection has led to a downward shift of firm 1 s profit function - becomes weak to look inoffensive.

94 Indeed, for p 1 < ep 1, eπ 1 (p 1,p 2 )=p 1 (D 1 (p 1,p 2 )+eq 1 ) eq 1 ep 1 and maximizing this is equivalent to maximizing p 1 (D 1 (p 1,p 2 )+eq 1 ) whichisasiffirm 1 faced higher demand curve D 1 (p 1,p 2 )+ eq 1. Higher demand : price reaction higher.

95 So, firm 1 s reaction function in the modified price game in period 2 is the standard static reaction function (when firm 1 s payoff is p 1 D 1 (p 1,p 2 )) as long as his reaction price is ep 1. Let ep 2 be such that ep 1 = R 1 ( ep 2 ). For p 2 < ep 2, firm 1 s reaction jumps outward to the reaction function when this firm faces higher demand given by D 1 (p 1,p 2 )+eq 1. Jump discontinuity. NE: p 1 = ep 1,p 2 = R 2 ( ep 1 ). (As long as ep 1 is not too high relative to p 1 ). Stackelberg price leadership outcome.

96 Both firms charge higher prices than in the static outcome. Firm 1 loses some profit in period 1 as it is not charging its best response to p 2. If ep 1 is close to p 1, the loss in firm 1 s profit is of "second order" (as marginal profit offirm 1 at p 1 is zero). But firm 1 s gain by getting the leadership profitinperiod 2 is of first order. So, firm 1 gains in total profit by unilaterally deviating to price protection in period 1. Puppy dog strategy

97 * Multimarket oligopoly. Two separate markets. Market 1 is a duopoly. Firm1isamonopolistinmarket2. Firm 1 s production cost depends on sum of output sold in both markets. (Diseconomy of scope or decreasing returns to scale...).

98 All quantities determined simultaneously. If demand increases in market 2, firm 1 has incentive to sell more in market 2 - this raises its marginal cost of selling in market 1 - its reaction function in market 1 falls - yields market share to firm 2 in equilibrium. Bulow et al (1985): total profit offirm 1 may fall. Price competition + increasing returns to scale (economies of scope): similar outcome. Strategic disadvantage caused by puppy dog effect of increase in market demand.

99 * Quotas and Tariffs. Changes strategic positions of domestic and foreign firm. Export subsidy: makes domestic firm a top dog if quantity competition in foreign market. Quota, tariff: lowers reaction function of foreign firm in thedomesticmarket.

100 * Vertical contracts. Between manufacturers and retailers influence competition between downstream units.

101 *Tying. Whinston (1987). Two firms and two completely unrelated markets. Market A is monopolized by firm 1. Unit mass of identical consumers with unit demand and valuation v. Unit cost c. Market B: differentiated good price duopoly with firms 1 and 2.

102 Same consumers in both markets. Demand for firm i in market B: D i (p i,p j ) [0, 1]. Unit cost (of both firms) in market B: c 1 Question: Does firm 1 have an incentive to tie (or bundle) products A & B?

103 First, consider the following game: Firms simultaneously decide on their prices and at the same time, firm 1 decides whether to bundle the two products or two sell them separately.

104 Given any p 2, firm 1 can never gain strictly by tying the goods. To see this, suppose firm 1 ties the goods and sells the bundle at some price P 1. For a consumer who buys this bundle, the marginal price paid for good B is P 1 v. So, quantity sold by firm 1 is D 1 (P 1 v, p 2 ).

105 The profit is (P 1 c c 1 )D 1 (P 1 v, p 2 ) If firm 1 sells the good separately and prices good A at v and good B at P 1 v, hisprofit is (v c)+(p 1 v c 1 )D 1 (P 1 v, p 2 ) (v c)d 1 (P 1 v, p 2 )+(P 1 v c 1 )D 1 (P 1 v, p 2 ) = (P 1 c c 1 )D 1 (P 1 v, p 2 ) with strict inequality unless D 1 (P 1 v, p 2 )=1. So, tying hurts firm 1 as it reduces its degrees of freedom in pricing.

106 Under bundling, if we set ep 1 = P 1 v (the effective marginal price of buying good B for consumers), then firm 1 maximizes with respect to ep 1. ( ep 1 (c 1 (v c)))d 1 ( ep 1,p 2 ) When selling separately and setting its price in market B, firm 1 sets price p 1 for good B so as to maximize: (p 1 c 1 )D 1 (p 1,p 2 ) Under bundling the firm is effectively selling good B at lower marginal cost under bundling - a unit of loss of sales in market B costs v c to firm 1 in Market A in terms of lost profit - so its reaction is more aggressive in market B under bundling, then when selling separately.

107 Reaction function of firm 1 more aggressive (like a cost reduction).

108 Next, consider the following two stage game: Firm 1 first decides whether to bundle or sell separately. Then, firms set prices in both markets simultaneously. [If goods are complements, bundling may be equivalent to making firm 1 s product in market A incompatible with firm 2 s product in market B: a technological decision.]

109 Here bundling intensifies price competition in stage 2 and hurts both firms. Better to follow puppy dog strategy of no bundling. But it still may be optimal to bundle for deterring entry.

110 * Systems of Complementary Products and Choice of Compatibility Ex. computer hardware and software; cameras, lenses and films; music systems... Products in each system can be purchased individually but they cannot be consumed as a system ("mix and match") unless they are compatible. A manufacturer that makes its system incompatible with other systems effectively bundles the components in his system.

111 Simple model: Two firms. Each firm produces two complementary products: X and Y. A unit each of X and Y together constitute a system.

112 Product differentiation: Consumers are uniformly located on a unit-square on the x-y space. Firms products are located at the two diametric ends of the square: Firm 1 at (0,0) and Firm 2 at (1,1). A consumer located at (x, y) incurs psychological cost tx + ty when buying both components from firm 1 and t(1 x)+t(1 y) when buying both components from firm 2. If she buys component X from firm 1 and Y from firm 2, her psychological cost is tx + t(1 y) etc...

113 Suppose unit cost is same for both firms and both products.

114 Under incompatibility: each firm offers a bundle of X and Yandtheconsumerlocatedat(x, y) compares with P 1 + tx + ty P 2 + t(1 x)+t(1 y) If both systems are sold and market is fully covered, using the standard indifference condition, we can figure out the demand for each firm s system and the symmetric NE. In this NE, the square is split along the diagonal between the systems sold by the two firms.

115 Under compatibility, components are sold separately at prices (p X 1,pY 1,pX 2,pY 2 ) and consumer can mix and match. There are four potential systems that the consumer can choose from - product variety increases. If she buys system with compenent X from firm 1 and Y from firm 2, her total cost is: p X 1 + py 2 + tx + t(1 y) and so on. Consumer chooses one with minimum total cost. If all four systems are sold and market is fully covered, then from indifference condition, we can get the linear demand function for each component of each firm as function of all four prices.

116 Solve for symmetric NE. In this NE, the square is split into four square quadrants, the southwest quadrant buys both components from firm 1, southeast buys X from firm 2 and Y from firm 1 etc Consumers in the NW and SE quadrants buy systems by using mix-n-match that are closer to their taste than under incompatibility.

117 Compatibility: ** Raises demand - products better suited to taste incentive to charge higher prices.

118 ** Softens price competition (unbundled products). When firm 1 cuts price of component X 1 : - under incompatibility, it increases only the demand for its own bundled system (X 1 Y 1 ) as that is the only system that includes component X 1 - under compatibility, it also increases the demand for the system X 1 Y 2 whose benefit accruestofirm 2. This externality reduces the incentive of firm to cut price. Price competition less aggressive. So both firms gain under compatibility.