Perfect competitionSearch markets:IntroductionCaltechEc106(Caltech) Search Feb 2010 1 / 16Why are prices for the same item so different across stores?(see evidence)A puzzle considering basic economic theory: review this.Consider the benchmark of perfect competition(Caltech) Search Feb 2010 2 / 16Perfect competitionReview: perfect competitionThe perfectly competitive firm is a price taker: it cannot influence theprice that is paid for its product.This arises due to consumers’ indifference between the products ofcompeting firms =⇒ for example, buy from store with lowest price.Consumers’ indifference arises from:Product homogeneityNo transactions costMany firmsConsumers have perfect information (relax this later)PC firm faces horizontal demand curve at market price p(Caltech) Search Feb 2010 3 / 16Perfect competitionPC firm’s profit maximization problemmaxqπ(p) = pq − C (q)First-order condition: p = C′(q) = MC (q)Second-order condition: C′′(q) > 0, satisfied if MC(q) is anincreasing functionIf p ↑, production rises along MC(q) curve: MC(q) is the “supplycurve” of the firm.(Caltech) Search Feb 2010 4 / 16Perfect competitionThe perfectly-competitive industry: Short runIn the short run:Number of firms fixedIndustry supply curve: sum of individual firms’ supply curves. Zerosupply at prices below shutdown point. Graph.Industry demand curve: downward sloping. Graph.Price determined by intersection of industry demand and supplycurves. Graph.In short-run equilibrium: p osit ive profits for each firm as long asp > AC(q).(Caltech) Search Feb 2010 5 / 16Perfect competitionThe perfectly competitive industry: Long-runNumber of firms can varyFree entry and exit:Any short-run profits soaked up by new firms in long-run =⇒ Price isdriven down to the minimum of the AC curveLong-run industry supply curve: horizontal at minimum of theaverage cost curve(Caltech) Search Feb 2010 6 / 16Perfect competitionLeaving the PC worldOne important implicit assumption of PC paradigm is that consumers areaware of prices at all stores. This implies an i nfinitel y elastic demand curvefacing firms. (ie. if one firm raises prices slightly, he will lose all demand).Obviously, this assumption is not realistic. Here we consider whathappens, if we relax just this assumption, but maintain other assumptionsof PC paradigm: l arge #firms, perfect substitutes, etc.(Caltech) Search Feb 2010 7 / 16Perfect competitionSearch modelEach consumer demands one unit;Starts out at one store, incurs cost c > 0 to search at any other store.Consumer only knows prices at stores that she has been to, and buysfrom the canvassed store with the lowest price. “free recall”Utility u from purchasing product: demand function ispurchase if p ≤ udon’t purchase otherwise(1)What is equilibrium in this market?(Caltech) Search Feb 2010 8 / 16Perfect competitionDiamond paradoxClaim: a nonzero search cost c > 0 leads to equilibrium price equal tou (“monopoly price”)Assume that marginal cost=0, so that under PC, p = 0n firms, with n large. Consumers equally distributed initially amongall firms.Start out with all firms at PC outcome. What happens if one firmdeviates, and charges some p1such that 0 < p1< c?◮Consumers at this store?◮Consumers at other stores?◮How will other stores respond?◮By iterating this reasoning ....(Caltech) Search Feb 2010 9 / 16Perfect competitionNow start at “monopoly outc ome”, where all firms are charging u.What are consumers’ purchase rules?Do firms want to undercut? Given consumer behavior, what do theygain?Role for advertising?P. Diamond (1971), “A Theory of Price Adjustment”, Journal ofEconomic Theory(Caltech) Search Feb 2010 10 / 16Perfect competitionRemarksDiamond result quite astounding, since it suggests PC result is“knife-edge” case.But still doesn’t explain price dispersionAssume consumers differ in search costsTwo types of consumers: “natives” are perfectly informed aboutprices, but “tourists” are not.(Caltech) Search Feb 2010 11 / 16Perfect competitionTourist-natives modelTourists and natives, in proportions 1 − α and α. L total consumers(so αL natives, and (1 − α)L tourists).Tourists buy one unit as long as p ≤ u, but natives always shop at thecheapest store.Each of n identical firms has U-shaped AC curveEach firm gets equal number of tourists(1−α)Ln; natives always goto cheapest store.Consider world in which all firms start by setting pc= minqAC (q).Note that deviant store always wants to price higher. Demand curvefor a deviant firm is kinked (graph). Deviant firm sells exclusively totourists.(Caltech) Search Feb 2010 12 / 16Perfect competitionDeviant firm will always charge u. Only tourists shop at this store. Ifcharge above u, no demand. If below u, then profits increase by charing u.First case: many informed consumers (α large)Number qu≡(1−α)Lnof tourists at each store so small thatu < AC(qu).In free-entry equilibrium, then, all firms charge pc, and produce thesame quantity L/n.If enough informed consumers, competitive equilibrium can obtain(not surprising)(Caltech) Search Feb 2010 13 / 16Perfect competitionSecond case: few informed consumers (α small)Assume enough tourists so that u > AC(qu).But now: hi-price firms making positive profits, while lo-price firmsmaking (at most) zero profits. Not stable.In order to have equilibrium: ensure that given a set of high-pricefirms (charing u) and low-price firms (charging pc), no individual firmwants to deviate. Free entry ensures this.Let β denote proportion of lo-price firms.Each high-price firm charges u and sells an amountqu=(1 − α)L(1 − β)n(1 − β)=(1 − α)Ln(2)Each low-price firm charges pcand sellsqc=αL + (1 − α)Lβnβ(3)(Caltech) Search Feb 2010 14 / 16Perfect competitionIn equilibrium, enough firms of each type enter such that each firmmakes zero profits. Define quantities qa, qAsuch that (graph):AC (qa) = u; AC (qc) = pc.(Quantities at which both hi- and lo-price firms make zero profits.)With free entry, n and β must satisfyqa= qu=(1 − α)LnAC (qc); qA= qcαL + (1 − α)Lβnβ(4)Solving the two equations for n and β yieldsn =(1 − α)Lqa; β =αqa(1 − α)(qA− qa)(5)N.B: arbitrary which firms become high or low price. Doesn’t specifyprocess whereby price dispersion develops.As α → 0, then β → 0 (Diamond result)(Caltech) Search Feb 2010 15 / 16Perfect competitionSummaryPrice dispersion for homogeneous good a puzzleBenchmark: perfectly