L20 Price-Setting Oligopolists

Microeconomics ECA002

Topic 5: Price-Setting Oligopolists

• Lecturer: Luke Garrod

Aims of this Lecture

• Overview: Focus on price-setting behavior of oligopolists.

• Previous Lecture Recap: Discussed how oligopolists influence each other's strategies through quantity-based competition (Cournot model).

• Current Lecture Focus: Analyze Bertrand's criticism of the Cournot model where firms commit to price rather than quantity.

• Historical Context: Bertrand's work predates modern game theory by approximately 70 years, resembling Nash equilibrium.

• Objectives: Understand production levels and pricing in a price-setting oligopoly and contrasts with other competitive models.

Lecture Outline

1. Bertrand’s model of oligopoly (assumptions)

2. Finding the Bertrand-Nash equilibrium

3. Comparison with monopoly and perfect competition

4. The Bertrand paradox

• Readings:

  • Core: Lipsey & Chrystal, Chapter 8

  • Extra: Perloff, Chapter 13.5

Bertrand’s Model of Oligopoly (Assumptions)

A(1): Duopoly Structure

• Two firms in the market (A & B).

• Firms compete on prices and make simultaneous pricing decisions.

A(2): Market Entry

• Complete blockage of further market entry ensuring focus on existing firms only.

A(3): Cost Structure

• Homogeneous costs: Firms have same constant marginal costs with no fixed costs.

• Example: Firm A’s cost structure:

  • Total Costs: C

  • Marginal Costs: MC

  • Average Costs: AC

A(4): Product Characteristics

• Firms produce homogeneous (identical) products that are not differentiated.

• Purchase behavior: Buyers buy from the lowest priced seller.

  • Scenario: If Firm A prices below Firm B, it captures the entire market, while Firm B sells nothing.

  • Equal Pricing: If both firms price equally, the market is split.

A(5): Market Demand

• The market demand is influenced by the lowest prices set by firms:

  • If Firm A's price is lower, all demand shifts to Firm A and vice versa.

Finding the Bertrand-Nash Equilibrium

• Behavior of firms under given assumptions leads to Nash equilibrium:

  • Definition: A situation where no firm wants to change price while considering competitor's price.

  • Nash Equilibrium in Prices: Two prices (pA and pB) satisfy conditions of maximum profit under given competitor's pricing.

Firm-Specific Demand Curve

• Demand for Firm A based on Firm B’s pricing as a function of competition.

• Higher pricing than rival results in zero sales. Pricing equal results in shared demand.

Best Response Functions

• Constructing Firm A's best response based on rivalry pricing utilizes marginal output principles, leading back to monopolistic comparisons.

• Illustrative Steps:

  • If Firm B sets a price above marginal cost, Firm A's optimal response can reflect monopoly conditions.

  • Formulate patterns through visualization of prices set by Firm B and corresponding profits for Firm A.

Bertrand-Nash Equilibrium

• Identified at the intersection of the best response functions of both firms (pB at pA).

Comparison with Monopoly and Perfect Competition

• Monopoly: Duopolists typically charge prices lower than monopolistic pricing leading to higher production levels compared to monopoly scenarios.

• Perfect Competition: Duopolists mirror market prices equivalent to perfect competition.

  • Outcome: No deadweight loss; total welfare is maximized through consistent consumer surplus.

The Bertrand Paradox

• Definition: Observation where the introduction of an identical product leads to perfect competition outcomes.

• Implications: Market transition from monopoly to extreme competition through a mere addition of one competitor leading to price equalization.

Breaking the Bertrand Paradox

• Mechanisms:

1. Product Differentiation

2. Capacity Constraints

3. Incomplete Information & Search Costs

4. Repeated Interaction between firms

Summary of Lecture

• Key Insights:

  • Price-setting behaviors mean firms respond strategically to competitor pricing.

  • Markets characterized by few large sellers with high barriers lead to outcomes akin to perfect competition:

    • Produced amount and pricing align with perfect competition outcomes rather than monopoly.

Post-Lecture Objectives

Following this lecture, students should be able to:

1. State Bertrand’s model assumptions.

2. Explain upward sloping best response functions.

3. Derive the Bertrand-Nash equilibrium.

4. Compare outcomes of Bertrand model with monopoly and Cournot models.