Model Answer
0 min readIntroduction
Bertrand competition, a model of oligopoly developed by Joseph Bertrand in 1883, focuses on firms competing on price. Unlike Cournot competition which focuses on quantity, Bertrand assumes firms have identical or differentiated products and compete by setting prices. This model is particularly relevant in understanding markets where consumers are highly price-sensitive and firms can easily switch production. The question asks us to analyze the Bertrand equilibrium in a duopoly with differing marginal costs and contrast it with the outcome under perfect competition, highlighting the nuances of price competition.
Bertrand Equilibrium with Differing Marginal Costs
The Bertrand model assumes firms simultaneously set prices. Consumers purchase from the firm offering the lowest price. If prices are equal, demand is split. In a market with two firms, Firm 1 with marginal cost C₁ and Firm 2 with marginal cost C₂ where C₁ > C₂.
Deriving the Equilibrium
- Firm 1’s Strategy: Firm 1 will never set a price below C₂. If it does, it will incur losses.
- Firm 2’s Strategy: Firm 2 will undercut Firm 1’s price as long as the resulting price is above its own marginal cost, C₂.
- The Outcome: The equilibrium occurs when Firm 1 sets its price equal to C₂ and Firm 2 sets its price equal to C₂. Firm 2 serves the entire market. Firm 1 makes zero profit.
This is because if Firm 1 priced above C₂, Firm 2 would undercut it and capture the entire market. If Firm 1 priced at C₂, Firm 2 would be indifferent between matching the price and capturing half the market or slightly undercutting and capturing the whole market. However, any slight undercutting by Firm 2 would be matched by Firm 1, leading to a price war. The stable outcome is for Firm 1 to accept the market price of C₂.
Competitive Equilibrium
In a perfectly competitive market, numerous firms compete, and no single firm has market power. The equilibrium price is driven down to the marginal cost of the most efficient firm. In this case, the competitive equilibrium price would be C₂.
Comparing Bertrand and Competitive Equilibrium
While both equilibria result in a price of C₂, the *process* by which this price is reached is fundamentally different.
| Feature | Bertrand Equilibrium | Competitive Equilibrium |
|---|---|---|
| Number of Firms | Two (Duopoly) | Many |
| Price | C₂ (lower cost firm’s marginal cost) | C₂ (lower cost firm’s marginal cost) |
| Market Share | Firm 2 captures the entire market; Firm 1 has zero share. | Market share is distributed among many firms. |
| Process | Strategic interaction and potential undercutting. Firm 1 accepts the price of C₂. | Price is determined by market supply and demand, with firms being price takers. |
| Profit | Firm 1 earns zero profit; Firm 2 earns non-negative profit. | Firms earn zero economic profit in the long run. |
The Bertrand model demonstrates that even with only two firms, price competition can drive the price down to the competitive level. However, this outcome relies on the strategic interaction between firms. In perfect competition, the outcome arises from the collective actions of many firms responding to market signals, not from explicit strategic behavior. The Bertrand paradox highlights that price competition can be more intense than quantity competition.
Conclusion
In conclusion, the Bertrand equilibrium with differing marginal costs results in the lower-cost firm capturing the entire market at a price equal to its marginal cost, while the higher-cost firm exits the market or produces nothing. Although the final price is the same as in a perfectly competitive market, the underlying mechanisms are distinct. The Bertrand model emphasizes the power of price competition even with limited market participants, while perfect competition relies on the atomistic behavior of numerous firms. This distinction is crucial for understanding real-world market dynamics and the effectiveness of competition policy.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.