Managerial Economics and Business Strategy: Oligopoly Models

Chapter 9 - Basic Oligopoly Models

Learning Objectives

  • Identify the conditions for a contestable market and explain the ramifications for market power and the sustainability of long-run profits.

    • A market is contestable if:

    • All producers have access to the same technology.

    • Consumers respond quickly to price changes.

    • Existing firms cannot respond quickly to entry by lowering price.

    • There are no sunk costs.

    • If these conditions are met, incumbent firms have no market power over consumers, leading to prices equating marginal costs (P = MC) and firms earning zero economic profits.

  • Apply reaction (or best-response) functions to identify optimal decisions and likely competitor responses in oligopoly settings.

  • Identify the conditions under which a firm operates in a Sweezy, Cournot, Stackelberg, or Bertrand oligopoly, and the ramifications of each type of oligopoly for optimal pricing decisions, output decisions, and firm profits.

  • Explain how beliefs and strategic interaction shape optimal decisions in oligopoly environments.

Oligopoly Market Structure

  • An oligopoly is characterized by:

    • A few firms that are large relative to the total industry.

    • The typical number of firms is between 2 and 10.

    • Products can either be identical or differentiated.

    • An oligopoly market composed of two firms is classified as a duopoly.

    • Oligopoly settings are complex because managers must consider the impact of their decisions on other firms' decisions in the market.

Reaction Functions in Oligopoly

  • Strategic interaction means a firm's demand depends on the actions of rivals.

  • Sweezy Oligopoly Characteristics:

    • Few firms serving many consumers.

    • Firms produce differentiated products.

    • Each firm believes rivals will decrease prices in response to a price cut but will not raise prices if a firm raises them.

    • Barriers to entry exist.

  • Cournot Oligopoly Characteristics:

    • Few firms serving many consumers.

    • Firms can produce either differentiated or homogeneous products.

    • Each firm believes rivals will hold their output constant if it changes its output.

    • Barriers to entry exist.

Cournot Oligopoly: Output Decisions

  • In a Cournot duopoly, each firm's output decision is based on the belief that the rival will hold output constant when one firm changes its own output.

  • This interdependence leads to each firm's marginal revenue being influenced by the other firm's output decision.

  • The relationship is described as a best-response or reaction function, denoted as:

    • For firm 1: Q1 = R1(Q_2)

    • For firm 2: Q2 = R2(Q_1)

Example Reaction Functions:

  • Given a linear (inverse) demand function:
    P = a - (Q1 + Q2)

  • Cost functions:
    C1(Q1) = c1 Q1
    C2(Q2) = c2 Q2

  • The reaction functions can be expressed as:

    • Q1 = R1(Q2) = \frac{1}{2}(a - c1 - Q_2)

    • Q2 = R2(Q1) = \frac{1}{2}(a - c2 - Q_1)

Cournot Equilibrium

  • At equilibrium, neither firm has an incentive to change its output given the other firm’s output.

  • Isoprofit Curves:

    • Functions that define combinations of outputs that yield the same profit level for a firm.

    • Points on an isoprofit curve lead to equal profits.

    • Curves further away from the origin correspond to higher profit levels.

    • Isoprofit curves do not intersect.

Stackelberg Oligopoly Characteristics:

  • Composed of few firms serving many consumers with either differentiated or homogeneous products.

  • One firm (the leader) determines output before other firms (the followers) choose their output levels based on the leader's decision.

  • Barriers to entry exist.

    • Leader's Output Function:

    • For example, if the demand function is:

    • P = a - (QL + QF) (where $QL$ is leader quantity and $QF$ is follower quantity)

Stackelberg Equilibrium Output Functions

  • Follower reacts according to its reaction function:

    • QF = RF(QL) = \frac{1}{2}(a - cF - Q_L)

  • Leader's output can be derived from knowing the follower's reaction:

    • The market equilibrium is reached when both firms have maximized their profits given their outputs.

Bertrand Oligopoly Characteristics

  • Few firms in the market serving many consumers with identical products and constant marginal costs.

  • Firms engage in price competition, optimally reacting to competitor prices.

  • Assumption: Consumers have perfect information and no transaction costs exist.

  • Under these conditions, firms will continuously undercut prices until the price equals marginal cost, leading to no economic profit in equilibrium:

    • P = MC

Collusion in Oligopoly

  • Markets with a few dominant firms can lead to collusion to limit output and increase prices at the expense of consumers.

  • While collusion can benefit firms by increasing profits, it is prone to cheating because firms have incentives to undercut each other.

Conclusion

  • Understanding these oligopoly models provides insights into firm behaviors, strategic decision-making, and market outcomes in environments characterized by few large competitors. Each model (Sweezy, Cournot, Stackelberg, and Bertrand) has distinct implications for pricing and output strategies, influencing firm profitability and market efficiency.