Chapter 19 TRADITIONAL MODELS OF IMPERFECT COMPETITION MICROECONOMIC THEORY BASIC PRINCIPLES AND EXTENSIONS EIGHTH EDITION WALTER NICHOLSON Copyright 2002 by South Western a division of Thomson Learning All rights reserved Pricing Under Homogeneous Oligopoly We will assume that the market is perfectly competitive on the demand side there are many buyers each of whom is a price taker We will assume that the good obeys the law of one price this assumption will be relaxed when product differentiation is discussed Pricing Under Homogeneous Oligopoly We will assume that there is a relatively small number of identical firms n we will initially start with n fixed but later allow n to vary through entry and exit in response to firms profitability The output of each firm is qi i 1 n symmetry in costs across firms will usually require that these outputs are equal Pricing Under Homogeneous Oligopoly The inverse demand function for the good shows the price that buyers are willing to pay for any particular level of industry output P f Q f q1 q2 qn Each firm s goal is to maximize profits i f Q qi TCi qi i f q1 q2 qn qi TCi Oligopoly Pricing Models The quasi competitive model assumes price taking behavior by all firms P is treated as fixed The cartel model assumes that firms can collude perfectly in choosing Q and P Oligopoly Pricing Models The Cournot model assumes that firm i treats firm j s output as fixed in its decisions qj qi 0 The conjectural variations model assumes that firm j s output will respond to variations in firm i s output qj qi 0 Quasi Competitive Model Each firm is assumed to be a price taker The first order condition for profitmaximization is i qi P TCi qi 0 P MCi qi i 1 n Along with market demand these n supply equations will ensure that this market ends up at the short run competitive solution Quasi Competitive Model Price If each firm acts as a price taker P MCi so QC output is produced and sold at a price of PC MC PC D MR QC Quantity Cartel Model The assumption of price taking behavior may be inappropriate in oligopolistic industries each firm can recognize that its output decision will affect price An alternative assumption would be that firms act as a group and coordinate their decisions so as to achieve monopoly profits Cartel Model In this case the cartel acts as a multiplant monopoly and chooses qi for each firm so as to maximize total industry profits PQ TC1 q1 TC2 q2 TCn qn f q1 q2 qn q1 q2 qn n TC q i i 1 i Cartel Model The first order conditions for a maximum are that P P q1 q2 qn MC qi 0 qi qi This implies that MR Q MCi qi At the profit maximizing point marginal revenue will be equal to each firm s marginal cost Cartel Model If the firms form a group and act as a monopoly MR MCi so QM output is produced and sold at a price of PM Price PM MC D MR QM Quantity Cartel Model There are three problems with the cartel solution these monopolistic decisions may be illegal it requires that the directors of the cartel know the market demand function and each firm s marginal cost function the solution may be unstable each firm has an incentive to expand output because P MCi Cournot Model Each firm recognizes that its own decisions about qi affect price P qi 0 However each firm believes that its decisions do not affect those of any other firm qj qi 0 for all j i Cournot Model The first order conditions for a profit maximization are i P P qi MCi qi 0 qi qi The firm maximizes profit where MRi MCi the firm assumes that changes in qi affect its total revenue only through their direct effect on market price Cournot Model Each firm s output will exceed the cartel output the firm specific marginal revenue is larger than the market marginal revenue Each firm s output will fall short of the competitive output qi P qi 0 Cournot Model Price will exceed marginal cost but industry profits will be lower than in the cartel model The greater the number of firms in the industry the closer the equilibrium point will be to the competitive result Cournot s Natural Springs Duopoly Assume that there are two owners of natural springs each firm has no production costs each firm has to decide how much water to supply to the market The demand for spring water is given by the linear demand function Q q1 q2 120 P Cournot s Natural Springs Duopoly Because each firm has zero marginal costs the quasi competitive solution will result in a market price of zero total demand will be 120 the division of output between the two firms is indeterminate each firm has zero marginal cost over all output ranges Cournot s Natural Springs Duopoly The cartel solution to this problem can be found by maximizing industry revenue and profits PQ 120Q Q2 The first order condition is Q 120 2Q 0 Cournot s Natural Springs Duopoly The profit maximizing output price and level of profit are Q 60 P 60 3 600 The precise division of output and profits is indeterminate Cournot s Natural Springs Duopoly The two firms revenues and profits are given by 1 Pq1 120 q1 q2 q1 120q1 q12 q1q2 2 Pq2 120 q1 q2 q2 120q2 q22 q1q2 First order conditions for a maximum are 1 120 2q1 q2 0 q1 2 120 2q2 q1 0 q2 Cournot s Natural Springs Duopoly These first order equations are called reaction functions show how each firm reacts to the other s output level In equilibrium each firm must produce what the other firm thinks it will Cournot s Natural Springs Duopoly We can solve the reaction functions simultaneously to find that q1 q2 40 P 120 q1 q2 40 1 2 Pq1 Pq2 1 600 Note that the Cournot equilibrium falls between the quasi competitive model and the cartel model Conjectural Variations Model In markets with only a few firms we can expect there to be strategic interaction among firms One way to build strategic concerns into our model is to consider the assumptions that might be made by one firm about the other firm s behavior Conjectural Variations Model For each firm i we are concerned with the assumed value of qj qi for i j because the value will be speculative models based on various assumptions about its value are termed conjectural variations models they are concerned with firm i s conjectures about firm j s output variations Conjectural Variations Model The first order condition for profit maximization becomes P i P q j P qi MCi qi 0 qi qi j i q j qi The firm must consider how its output decisions will affect price in two ways directly indirectly through their effects on the output decisions of other firms Price Leadership Model Suppose that the market