b3-bertrand

Bertrand Oligopoly

Definition

  • A market structure with two firms selling homogeneous products.

  • Prices are set by firms while quantity sold is determined by market demand.

Characteristics

  • Homogeneous Products: The product offered by both firms is identical, leading to price competition.

  • Lowest Price Rule: The firm with the lowest price captures all sales.

  • Price Equality: If both firms set the same price, sales are shared equally.

Demand and Cost Functions

  • Inverse Demand Function: P = a - bQ

  • Total Cost Function: TC(q) = F + c * q

    • Constant Returns to Scale: F = 0

    • Increasing Returns to Scale: F > 0

    • Decreasing Returns to Scale: TC(q) = z * q^2 (to be considered later)

Best Response and Equilibrium

Principles

  • Focused on increasing or constant returns to scale.

  • Let pr1(p2) denote Firm 1's best response to Firm 2's price.

Conditions for Best Response

  1. Price above Monopoly Price: If p2 > Monopoly Price, then pr1(p2) = pM.

  2. Price under Marginal Cost: If p2 < mc1, then pr1(p2) > p2, hence use pr1(p2) = mc1.

  3. At Equal Prices: If p2 = mc1, then pr1(p2) must satisfy pr1(p2) ≥ p2.

  4. Price Relations: mc1 < p2 ≤ PM leads to pr1(p2) = p2 - ǫ.

Analysis of Equilibrium Positions

  • Prices Above mc: Firms will undercut each other until prices fall.

  • Prices Below mc: Leads to losses as every sale results in negative profits.

  • Equilibrium Condition: p1 = p2 = mc; results in zero profits if constant returns to scale (CRTS) are assumed.

  • Increasing Returns to Scale (IRTS): Losses equal to fixed costs.

Bertrand Paradox

Setup of Entry Game

  1. Firm 1 sets a pre-entry price.

  2. Firm 2 decides to enter if it sees non-negative profits.

  3. After entry, firms set prices simultaneously.

Outcomes of Entry

  • If entry occurs, both firms face losses of -F.

  • Monopoly Scenario: If F > 0 implies a permanent monopoly.

  • Perfect Competition: If F = 0 leads to a perfect competition environment.

Vebco - AMMXCO Case Study

Background

  • Considerations of homogeneous goods and differential marginal costs.

  • Vebco's marginal cost = cH and AMMXCO's marginal cost = cL, where cL < cH.

Strategic Pricing Analysis

  • Each firm focuses on its own marginal cost; Vebco will not price below cH.

  • AMMXCO may offer a slightly lower price at pv = cH to increase sales.

Theory of Contestable Markets

Core Principles

  • No strategic foreclosure; monopoly is only based on cost (or quality) advantage.

  • Assumes constant returns to scale with negligible sunk costs.

  • Every monopoly faces potential threats from 'hit and run' entrants.

Implications

  • Pricing behavior is similar to that of firms with homogeneous goods.

  • Dynamics suggest that incumbents cannot charge above the marginal costs of potential new entrants.

AMR (American Airlines) Case Study

Overview of Predatory Pricing

  • Incumbent firms may lower prices after entry, aiming to eliminate potential competition.

  • Questions arise about market conditions and pricing below average costs (AC).

AMR's Hub and Spoke System

  • AMR's pricing strategies during market segmentation with major and low-cost carriers (LCCs).

  • The firm's economic advantages through larger, more efficient aircraft and operational structures.

Legal Outcome

  • Court rulings favor AMR, justifying prices set above marginal costs but below average costs, reinforcing predatory pricing debates.