Managerial Economics & Business StrategyOverviewOligopoly EnvironmentRole of Strategic InteractionAn ExampleSlide 6Slide 7Key InsightSweezy (Kinked-Demand) Model EnvironmentSweezy Demand and Marginal RevenueSweezy Profit-Maximizing DecisionSweezy Oligopoly SummaryCournot Model EnvironmentInverse Demand in a Cournot DuopolyBest-Response FunctionBest-Response Function for a Cournot DuopolyGraph of Firm 1’s Best-Response FunctionCournot EquilibriumGraph of Cournot EquilibriumSummary of Cournot EquilibriumStackelberg Model EnvironmentThe Algebra of the Stackelberg ModelStackelberg SummaryBertrand Model EnvironmentBertrand EquilibriumContestable MarketsConclusionManagerial Economics & Business StrategyChapter 9Basic Oligopoly ModelsMcGraw-Hill/IrwinMichael R. Baye, Managerial Economics and Business StrategyCopyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.OverviewI. Conditions for Oligopoly?II. Role of Strategic InterdependenceIII. Profit Maximization in Four Oligopoly SettingsSweezy (Kinked-Demand) ModelCournot ModelStackelberg Model Bertrand ModelIV. Contestable Markets9-2Oligopoly Environment•Relatively few firms, usually less than 10.Duopoly - two firmsTriopoly - three firms•The products firms offer can be either differentiated or homogeneous.•Firms’ decisions impact one another.•Many different strategic variables are modeled:No single oligopoly model.9-3Role of Strategic Interaction•Your actions affect the profits of your rivals.•Your rivals’ actions affect your profits.•How will rivals respond to your actions?9-4An Example•You and another firm sell differentiated products.•How does the quantity demanded for your product change when you change your price?9-5PQD1 (Rival holds itsprice constant)P0PLD2 (Rival matches your price change)PHQ0QL2QL1QH1QH29-6PQD1P0Q0D2 (Rival matches your price change)(Rival holds itsprice constant)DDemand if Rivals Match Price Reductions but not Price Increases9-7Key Insight•The effect of a price reduction on the quantity demanded of your product depends upon whether your rivals respond by cutting their prices too!•The effect of a price increase on the quantity demanded of your product depends upon whether your rivals respond by raising their prices too!•Strategic interdependence: You aren’t in complete control of your own destiny!9-8Sweezy (Kinked-Demand) Model Environment•Few firms in the market serving many consumers.•Firms produce differentiated products.•Barriers to entry.•Each firm believes rivals will match (or follow) price reductions, but won’t match (or follow) price increases.•Key feature of Sweezy ModelPrice-Rigidit y.9-9Sweezy Demand and Marginal RevenuePQP0Q0D1(Rival holds itsprice constant)MR1D2 (Rival matches your price change)MR2DS: Sweezy DemandMRS: Sweezy MR9-10Sweezy Profit-Maximizing DecisionPQP0Q0DS: Sweezy DemandMRSMC1MC2MC3D2 (Rival matches your price change)D1 (Rival holds price constant)9-11Sweezy Oligopoly Summary•Firms believe rivals match price cuts, but not price increases.•Firms operating in a Sweezy oligopoly maximize profit by producing where MRS = MC.The kinked-shaped marginal revenue curve implies that there exists a range over which changes in MC will not impact the profit-maximizing level of output.Therefore, the firm may have no incentive to change price provided that marginal cost remains in a given range.9-12Cournot Model Environment•A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated).•Firms’ control variable is output in contrast to price.•Each firm believes their rivals will hold output constant if it changes its own output (The output of rivals is viewed as given or “fixed”).•Barriers to entry exist.9-13Inverse Demand in a Cournot Duopoly•Market demand in a homogeneous-product Cournot duopoly is•Thus, each firm’s marginal revenue depends on the output produced by the other firm. More formally, 2122bQbQaMR 1212bQbQaMR  21QQbaP 9-14Best-Response Function•Since a firm’s marginal revenue in a homogeneous Cournot oligopoly depends on both its output and its rivals, each firm needs a way to “respond” to rival’s output decisions.•Firm 1’s best-response (or reaction) function is a schedule summarizing the amount of Q1 firm 1 should produce in order to maximize its profits for each quantity of Q2 produced by firm 2.•Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.9-15Best-Response Function for a Cournot Duopoly•To find a firm’s best-response function, equate its marginal revenue to marginal cost and solve for its output as a function of its rival’s output.•Firm 1’s best-response function is (c1 is firm 1’s MC)•Firm 2’s best-response function is (c2 is firm 2’s MC) 21211212QbcaQrQ  12122212QbcaQrQ 9-16Graph of Firm 1’s Best-Response FunctionQ2Q1(Firm 1’s Reaction Function)Q1MQ2Q1r1(a-c1)/bQ1 = r1(Q2) = (a-c1)/2b - 0.5Q29-17Cournot Equilibrium•Situation where each firm produces the output that maximizes its profits, given the the output of rival firms.•No firm can gain by unilaterally changing its own output to improve its profit.A point where the two firm’s best-response functions intersect.9-18Graph of Cournot EquilibriumQ2*Q1*Q2Q1Q1Mr1r2Q2MCournot Equilibrium(a-c1)/b(a-c2)/b9-19Summary of Cournot Equilibrium•The output Q1* maximizes firm 1’s profits, given that firm 2 produces Q2*.•The output Q2* maximizes firm 2’s profits, given that firm 1 produces Q1*.•Neither firm has an incentive to change its output, given the output of the rival.•Beliefs are consistent: In equilibrium, each firm “thinks” rivals will stick to their current output – and they do!9-20Stackelberg Model Environment•Few firms serving many consumers.•Firms produce differentiated or homogeneous products.•Barriers to entry.•Firm one is the leader.The leader commits to an output before all other firms.•Remaining firms are followers.They choose their outputs so as to maximize profits, given the leader’s output.9-21The Algebra of the Stackelberg Model•Since the follower reacts to the leader’s output, the follower’s output is determined by its reaction function•The Stackelberg leader uses this reaction function to