Oligopoly Notes

Oligopoly

• Oligopoly: A market with a small number of large firms and significant barriers to entry.
• Key characteristic: Firms have market power but are interdependent.
• Duopoly: A special case of oligopoly with only two firms.

Market Structures

• Markets differ based on:
  • Number of firms.
  • Ease of entry and exit.
  • Product differentiation.
• Oligopoly:
  • Few firms.
  • Limited entry.
  • Long-run profit $\geq 0$.
  • Price setter, P > MC.
  • Strategy dependent on rival firms.
  • Products may be differentiated.

Cartels

• Cartel: Firms collude to coordinate activities and produce at monopoly output levels.
• Objective: Increase profits by restricting output and raising prices.
• Why cartels fail:
  • Lack of market control.
  • Cheating among members.
• Laws: Sherman Antitrust Act and Federal Trade Commission Act prohibit actions that reduce competition.

Oligopoly Dilemma

• Firms must decide to compete or cooperate.
• Cooperation (cartel): Higher profits for all if output is restricted.
• Temptation to cheat: Individual firms can gain extra profit by increasing output, but if all cheat, prices fall.

Game Theory and Oligopoly

• Game theory explains why cartels fail.
• Firms make strategic decisions that affect each other.
• Cooperation: Restrict output, set high prices.
• Temptation: Cheat to gain profit.
• Outcome if both cheat: Supply increases, prices fall, profits decrease.

Cournot Duopoly

• Duopoly: Oligopoly with two firms.
• Models:
  • Cournot: Firms choose quantities simultaneously.
  • Stackelberg: Leader firm chooses quantity first.
  • Bertrand: Firms choose prices simultaneously.
• Assumptions for Cournot model:
  • Identical firms with same cost functions.
  • Market lasts for one period.

Nash-Cournot Equilibrium

• Firms independently set output levels.
• Equilibrium: No firm can gain by changing output, given the output of competitors.

Airlines Market Example

• Market demand: $Q = 339 - p$
• Marginal cost: MC = $147
• American Airlines' inverse residual demand: $p = (339 - q<em>U) - q</em>A$
• American Airlines' marginal revenue: $MR = (339 - q<em>U) - 2q</em>A$
• Best response function (BRF) for American Airlines: $q<em>A = 96 - (1/2)q</em>U$
• Cournot equilibrium: $q<em>A = q</em>U = 64$, P = $211

Key Takeaways

• Monopoly (Cartel): Higher price ($243$), lower output (96).
• Duopoly (Nash-Cournot): Lower price ($211$), higher output (128).
• Duopoly leads to lower prices and profits compared to a monopoly due to diluted market power.