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##### Limit Pricing and Entry Deterrence

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**Introduction**• A firm that can restrict output to raise market price has market power • Microsoft (95% of operating systems) and Campbell’s (70% of tinned soup market) are giants in their industries • Have maintained their dominant position for many years • Why can’t existing rivals compete away the position of such firms? • Why aren’t new rivals lured by the profits? • Answer: firms with monopoly power may • eliminate existing rivals • prevent entry of new firms • These actions are predatory conduct if they are profitable only if rivals, in fact, exit • e.g., R&D to reduce costs is not predatory**Evolution of market structure**• Evolution of markets depends on many factors • one is relationship between firm size and growth • Gibrat’s Law • begin with equal sized firms • each grows in each period by a rate drawn from a random distribution • this distribution has constant mean and variance over time • result is that firm size distribution approaches a log-normal distribution • Very mechanistic • no strategy for growth • Including strategic decision making affects distribution but not conclusion that firm sizes are unequal • What about the facts in the market place?**Monopoly power and market entry**• Several stylized facts about entry • entry is common • entry is generally small-scale • so small-scale entry is relatively easy • survival rate is low: >60% exit within 5 years • entry is highly correlated with exit • not consistent with entry being caused by excess profits • “revolving door” • reflects repeated attempts to penetrate markets dominated by large firms • Not always easy to prove that this reflects predatory conduct • But we need to understand predation it if we are to find it**Predatory conduct and limit pricing**• Predatory actions come in two broad forms • Limit pricing: prices so low that entry is deterred • Predatory pricing: prices so low that existing firms are driven out • Outcome of either action is the same—the monopolist retains control of the market • Legal action focuses on predatory pricing because this case has an identifiable victim • a firm that was in the market but that has left • Consider first a model of limit pricing • Stackelberg leader chooses output first • entrant believes that the leader is committed to this output choice • entrant has decreasing costs over some initial level of output**By committing to output**Qd the incumbent deters entry. Market price Pd is the limit price A limit pricing model Then the entrant’s residual demand is R1 = D(P) - Q1 These are the cost curves for the potential entrant With the residual demand R1, the entrant can operate profitably.Entry is not deterred by the incumbent choosing Q1. $/unit Then the entrant’s marginal revenue is MRe R1 At price Pe entry is unprofitable The entrant’s residual demand is Re = D(P) - Qd The entrant equates marginal revenue with marginal cost MCe Pd Assume instead that the incumbent commits to output Qd ACe Assume that the incumbent commits to output Q1 Pe D(P) = Market Demand Re MRe Quantity qe Qd Q1 Qd**Limit pricing**• Committing to output Qd may be aimed either at eliminating an existing rival or driving out a potential entrant. • Either way, several questions arise: • Is limit pricing more profitable than other strategies? • Is the output commitment credible? • If output is costly to adjust then commitment is possible • why should this property hold? • could be claimed to be ad hoc to support the theory • even if it holds, is monopoly at output Qd better than Cournot? • may not be if the entrant’s costs are low enough • Credibility may relate output to capacity**Capacity expansion and entry deterrence**• For predation to be successful and rational • the incumbent must convince the entrant that the market after the entrant comes in will not be profitable one • How can the incumbent credibly make this threat? • One possible mechanism • install capacity in advance of production • installed capacity is a commitment to a minimum level of output • the lead firm can manipulate entrants through capacity choice • the lead firm may be able to deter entry through its capacity choice • but is this credible? • capacity must be costly to install and should be irreversible**The Dixit model**• Consider a two-stage game • incumbent in period 1 installs capacity • capacity K1 costs r.K1 to install • in second period incumbent can produce up to K1 at unit cost w • capacity can be expanded in period 2 at additional cost r per unit • capacity cannot be reduced in period 2 • potential entrant in period 2 observes incumbent’s capacity choice • to enter and produce entrant needs capacity K2 which costs r.K2 • unit cost of production is w • note: entrant will never install unused capacity • if entry takes place firms play a Cournot game in the second period • Market demand: P = A – B(q1 + q2)**The Dixit model 2**• Costs for the incumbent are: • C1 = F1 + w.q1 + r.K1 for q1<K1; marginal cost w • C1 = F1 + (w + r)q1 for q1 > K1; marginal cost w + r • Costs for the entrant are: • C2 = F2 + (w + r)q2 ; marginal cost w + r • Standard Cournot analysis gives the best response functions: • q*1 = (A – w)/2B – q2/2 when q1<K1 • q*1 = (A – w – r)/2B – q2/2 when q1 > K1 • q*2 = (A – w – r)/2B – q1/2 provided that q*2 > 0 • for the entrant to enter it must expect to cover the sunk costs F2 • this implies a lower limit on the output that the entrant must make**The Dixit model 3**q2 • The incumbent’s best response function has a break in it at K1 L’ • The entrant’s best response function has a break where sunk costs are not covered N’ R’ R • Equilibrium depends upon these two breaks N L q1 K1**q2**L’ N’ R’ R N q1 L The Dixit model 4 • Consider the possibilities • Suppose that firm 2 enters • Equilibrium must lie between T and V • Where depends upon location of the break in R’R • Firm 1’s output is greater than T1 and smaller than V1 T T2 V • So capacity choice lies between T1 and V1 V2 T1 V1**q2**L’ N’ R’ T T2 V V2 R N q1 T1 V1 L The Dixit model 5 • Now suppose that firm 2 does not enter • Must be that it cannot break even at output less than T2 • Then firm 1 would want to choose capacity M1 • this is the monopoly output with MC = w + r • M1 is actually the Stackelberg output level for firm 1 • firm 1 as market leader will never choose output and capacity less than M1 S M2 M1**q2**BS L’ BL N’ R’ T T2 S M2 V BL V2 R N q1 T1 M1 V1 L The Dixit model 6 • Suppose that the break in the entrant’s best response function lies at BL in R’T • Incumbent chooses capacity M1 and entry is deterred • Suppose that the break in the entrant’s best response function lies at BS in TS • Incumbent chooses capacity M1 and entry is deterred • Suppose that the break in the entrant’s best response function lies at BL in VR • Incumbent chooses capacity M1 and entry is accommodated**q2**L’ N’ R’ T T2 S M2 B* V V2 R N q1 T1 M1 V1 L The Dixit model 7 • Now suppose that the break in the entrant’s best response function lies at B* in SV • Incumbent can choose to install capacity M! and share the market • Or install capacity B! and maintain monopoly in the market • Choice depends upon relative profitability B1 • If B* is “close to” S then use capacity to deter entry • If B* is “close to” V then accommodate entry as Stackelberg leader**Capacity expansion and entry deterrence 2**• An example: • P = 120 - Q = 120 - (q1 + q2) • marginal cost of production $60 for incumbent and entrant • cost of each unit of capacity is $30 • firms also have fixed costs of F • incumbent chooses capacity K1 in stage 1 • NOTE: incumbent will always produce at least K1 in production stage—otherwise it throws away revenue that could help cover the cost of installed capacity • entrant chooses capacity and output in stage 2 • firms compete in quantities in stage 2.**Entry deterrence**• Entry may not occur • entrant’s costs are too high • blockaded entry • not predatory • Entry may be accommodated • entrant’s costs are low • incumbent takes advantage of its being first in the market • but does not deter • Entry may be strategically deterred • strategic deterrence profitable for the incumbent • installs excess capacity as an entry-deterring strategy • uses a credible commitment**Preemption and the persistence of monopoly**• A distinct but related issue is an incumbent investing early to prevent new entry • market may be a natural monopoly at current size • but expected to grow and attract entry • Now we have an issue of timing • It may be in the interests of an incumbent to preempt by • building new plants prior to a rival’s entry • adding new products prior to a rival’s entry • Related to another issue • entrant may race to innovate to preempt entry • A simple model:**Preemption and the persistence of monopoly 2**• A market with an incumbent • current profit pM • market is expected to double in the next period and stay at the new size in perpetuity • to meet the new demand requires additional capacity at cost of F • the new capacity can be added: • In first period or in second period • By incumbent or by new entrant • With no threat of entry • incumbent installs new capacity at beginning of second period • profit is 2M minus cost of capacity • With threat of entry may need to install capacity early**Preemption and the persistence of monopoly 3**• Consider the entrant choosing in period 1 • suppose that competition is Cournot if entry occurs • entry in period 1 gives the entrant e1 = C + 2C/(1 – R) - F • R is the discount factor = 1/(1+r) where r is the discount rate • entry in period 2 gives the entrant e2 = 2C/(1 – R) – RF in present value terms • suppose e1 < e2 which implies (1 + r)C < rF • entrant will enter in the second period**Preemption and the persistence of monopoly 4**• What about the incumbent? • do nothing in period 1 • entry takes place in period 2 • earns 2C/(1 – R) • install additional capacity in period 1 • entry deterred • earns 2M/(1 – R) – F • install capacity early provided that 2(M - C)/(1 – R) > F • provided that present value of additional profit from protecting monopoly is greater than the fixed cost • Incumbent wants to maintain monopoly; entrant only shares in non-cooperative profits**Market preemption**• Why does the incumbent have a stronger incentive to invest “early”? • the incumbent is protecting a valuable monopoly • the entrant is seeking a share of the market • so the incumbent’s incentive is stronger • willing to incur initial losses to maintain market control**Evidence on predatory expansion**• Some anecdotal evidence • Alcoa • evidence that consistently expanded capacity in advance of demand • Safeway in Edmonton • evidence that it aggressively expanded store locations in response to potential entry • DuPont in titanium oxide • rapidly expanded capacity in response to to changes in rivals’ costs • market share grew from 34% to 46%