12. Market Entry and the Emergence of Perfect Competition

1. 12. Market Entry and the Emergence of Perfect Competition 12.1 The Need for Entry-Prevention Strategies monopolist’s profits will attract entrants, which diminishes the former monopolist’s profits. Hence he would like to prevent entry 12.2 Limit Pricing in the Bain, Modigliani, Sylos-Labini Model basic idea: incumbent chooses a quantity high enough such that remaining demand is too low for entry to pay term “limit pricing” might appear a bit inconsistent since the strategic variable is quantity

2. assumptions: • two periods: pre-entry (t=0) and entry (t=1). In period 1 entrant decides whether to enter • one established firm, incumbent, i, and one potential entrant, e • consumers are not loyal, no switching costs • demand does not change over time • in period 0, i will commit to output level xi, which it will maintain in future periods • e believes that if e enters, then i will maintain xiindependent of e’s actions and market price last 2 assumptions are critical and problematic

3. Blockading Market Entry assume linear inverse demand p = a - b(qi+qe) in period 0 qe = 0, so i faces p = a – bqi profit maximum attains for qi= qm (Fig 12.1) e faces residual demand p = (a – bqm) – bqe, demand is shifted down (Fig 12.2) if residual demand is so low (always below average cost) that e cannot recover costs for any output, e will not enter entry is blockaded, i can prevent entry by simply producing monopoly quantity (and hence obtains the best possible outcome) depends of course on assumptions 5 and (in particular) 6

4. Impeding Market Entry if the residual demand after i chooses qm is sufficient for e to make a profit (Fig 12.4), blockading entry by producing monopoly quantity is not possible but i can impede entry by producing a quantity qL>qm that shifts residual demand further down such that it is tangent to e’s average cost curve and hence e cannot make profit (Fig 12.5) hence e will not enter qL is called limit quantity and the associated pLlimit price qL is the smallest quantity and pL the highest price that impede entry

5. 12.3 Criticisms of the Bain, Modigliani, Sylos-Labini Model: Subgame Perfection game: first stage (period 0): i chooses quantity, second stage (period 1): e decides whether to enter; if e enters, third stage (period 1): i decides whether to stick to quantity from period 0 (Fig 12.6) assumptions 5 and 6 say i threatens to stick to qL chosen in period 0 also in period 1; but threat is not credible: assume entrant will choose Cournot-equilibrium quantity if he enters by backward induction the only subgame-perfect equilibrium is: qm in period 0, e enters, and then i changes quantity to Cournot-equilibrium quantity given that entry occurs, i should adapt level to best reply, hence it pays to enter, i maximizes in period 0 how can incumbent commit to a quantity that deters entry?

6. 12.4 Entry Prevention, Overinvestment, and the Dixit-Spence Model Consulting Report 12.2: overinvestiment in capacity makes threat of producing large quantity credible and entry deterrence subgame-perfect strategy model: if firm has installed production capacity K, then marginal cost for quantity <K is v, but for quantity >K, marginal cost is v+s. If a firm has excess capacity, i.e. more capital than needed, then for an additional unit only additional variable inputs are needed, but if there is no excess capacity, then for each unit the capacity has to be extended (Fig 12.8) incumbent has capacity K, hence cost function is Ci(q,K)=vq+F for q<K, Ci(q,K)=vq+s(q-K)+F for q  K the entrant has not build capacity, hence cost function is Ce(q,K)=(v+s)q+F, will enter only if fixed costs F can be covered

7. due to fixed costs, reaction curve of e drops to 0 at an output level of i that drives down prices far enough, call this quantity qL limit quantity (Fig 12.9) the reaction function of the incumbent depends on its capacity lower marginal cost implies a higher best response (because best response is quantity where MR=MC) hence i’s reaction function Ri(0)for marginal cost v+s (K=0) is below Ri(Q(0)) for marginal cost v (K is large enough to satisfy whole demand at price 0) for intermediate capacity K, the reaction function Ri(K) is equal to Ri(Q(0)) for q<K and then drops down to Ri(0) game: period 0: i chooses K, period 1: e decides whether to enter, period 2: quantities are chosen (simultaneously) if K=0, outcome will be Cournot-equilibrium. But if K qL (and v is small enough), e’s best response would be to produce nothing and hence not to enter subgame perfect, because i chooses optimally after entry i builds capacity higher than monopoly quantity for MC= v+s

8. 12.5 Perfect Competition as the Limit of Successful Entry – When Entry Prevention Fails assume incumbent cannot prevent entry and there are eventually n firms output of firm 1= q1, etc,total output is Q = q1+...+ qn inverse demand p(Q) in case of monopoly the price is p = MC/[1- 1/|(Q)|] now for firm i the marginal revenue is MRi=p(Q)+(dp/dQ)qi rewriteMRi=p(Q) [ 1+ (dp/dQ) (Q/p(Q)) (qi/Q) ] denote by qi/Q = si firm i’s market share, then MRi=p(Q) [ 1- si / |(Q)| ] a profit maximizing oligopolist will choose qi such that MRi=MCi, and hence p(Q)= MCi / [ 1- si / |(Q)| ] thus the price markup will be smaller than in monopoly and is decreasing with si and hence in the number of firms; price converges to marginal cost as number of firms goes to 

9. The Characteristics of Perfectly Competitive Markets as number of firm grows, price converges to marginal costs and hence to the welfare-maximizing outcome for a large number of firms, the demand a firm faces is essentially flat (infinitely elastic); it cannot influence the price and only decide how much to produce at a given price firms act as price takers, industry of price-taking firms constitutes a perfectly competitive market, characteristics of perfectly competitive markets : • many firms with insubstantial market shares • free entry, no barriers to entry • homogenous product, i.e. all firms produce the same • perfect factor mobility, can move to and from other industries • perfect information, all participants know price and potential profits

10. Appendix: Incomplete Information and Entry Prevention Milgrom-Roberts Model: there are two possible technologies and hence two different possible marginal costs game: period 0: nature determines the level of marginal cost for incumbent, only i is informed about his marginal cost period 1: incumbent acts as monopolist, selects quantity and earns profit period 2: entrant decides whether to enter (has fixed cost K): if yes, e learns i’s marginal costs; they play Cournot-game assume e would not like to enter if i has low cost, but would like to enter if i has high cost then high cost incumbent would like to pretend to have low cost

11. if e’sexpected payoff against probability distribution of high and low is negative, there is pooling equilibrium: both types of i produce low cost monopoly quantity, e does not enter if e’sexpected payoff against probability distribution of high and low is positive, there is separating equilibrium: low cost type produces high quantity (this may be larger than the low cost monopoly quantity) such that high cost type is better off with high cost monopoly and then entry, e enters if i chooses low quantity (i.e. monopoly quantity of the high cost incumbent) in period 1