Skip to content

M20.L06 — Oligopoly Models: Cournot and Bertrand Competition

Module: Module 20 — Monopoly and Game Theory (Advanced) Lesson: L06 of 06 Duration: ~30 minutes Level: Intermediate Provenance: Principles of Microeconomics (Curtis and Irvine) | University of Utah Intermediate Microeconomics

Learning Objective

Key Diagram

Figure 14: Cournot Duopoly. The Nash equilibrium is at the intersection of reaction functions (Q≈53, P≈47) — between the monopoly (collusion) and competitive outcomes.
Figure 14: Cournot Duopoly. The Nash equilibrium is at the intersection of reaction functions (Q≈53, P≈47) — between the monopoly (collusion) and competitive outcomes.

Compare Cournot and Bertrand equilibrium outcomes using reaction functions.

Cournot Model

Firms simultaneously choose quantities. Market clearing price P(Q) where Q = q₁ + q₂.

Firm 1's problem: max π₁ = P(q₁ + q₂)q₁ - C(q₁)

Australian example: Woolworths (W) and Coles (C) with P = 100 - Q, MC=10:

W's reaction: q_W = (100 - q_C - 10)/2 = 45 - 0.5q_C C's reaction: q_C = 45 - 0.5q_W

NE: q_W = q_C = 30 → P = $40

Bertrand Paradox

With homogeneous goods and MC₁ = MC₂ = c, P₁ = P₂ = c in equilibrium (competitive outcome).

Australian example: Petrol stations in Sydney undercut until P=MC ($1.50/L).

Worked Example

[Australian context]

Two Australian airlines (Qantas, Virgin) compete:

Case 1: Cournot with P=200-Q, MC=80 Case 2: Bertrand with differentiated products: q_Q = 200 - 2p_Q + p_V q_V = 200 - 2p_V + p_Q MC=80

Find both equilibria.

Solution: 1. Cournot: q* = (200-80)/3 = 40 each, P=120 2. Bertrand: Solve reaction functions p_Q = (200 + p_V + 160)/4 etc → p_Q=p_V=120

Common Misconception

"More competitors always reduce prices"

With capacity constraints or product differentiation, prices may remain above MC even with many firms.

Key Takeaways

  • Cournot firms compete on quantities
  • Bertrand firms compete on prices
  • Product differentiation softens price competition
  • Hotelling model explains spatial differentiation

Practice

  1. Solve Cournot duopoly with P=80-Q, MC₁=10, MC₂=20
  2. Explain why Bertrand with capacity constraints resembles Cournot
  3. Find Hotelling equilibrium with transport cost t=2

Further Resources

Provenance: Curtis and Irvine | Utah Economics