Model Answer
0 min readIntroduction
Bertrand competition, developed by Joseph Bertrand in 1883 as a critique of Cournot’s model of oligopoly, is a model of price competition where firms produce homogeneous products. Unlike Cournot competition which focuses on quantity competition, Bertrand assumes firms compete by setting prices. This model is particularly relevant in industries where consumers primarily base their purchasing decisions on price, such as commodity markets or retail sectors with easily comparable products. Understanding the dynamics of Bertrand competition is crucial for analyzing market structures and predicting firm behavior, especially in scenarios with limited product differentiation. This answer will demonstrate how the equilibrium price is arrived at under Bertrand competition with homogeneous products.
Understanding Bertrand Price Competition
Bertrand competition operates under several key assumptions:
- Homogeneous Products: Products offered by all firms are identical.
- Perfect Information: Consumers have complete information about prices offered by all firms.
- Sufficient Capacity: Firms have the capacity to meet market demand at any price.
- No Collusion: Firms act independently and do not collude.
- Constant Marginal Cost: Each firm has a constant marginal cost of production.
The Logic of Price Undercutting
The core of Bertrand competition lies in the strategic interaction of firms attempting to capture market share through price adjustments. Let's consider a duopoly (two firms) for simplicity, but the logic extends to oligopolies with more firms.
- Initial Price Setting: Suppose Firm 1 sets a price P1.
- Firm 2's Response: Firm 2 has two options:
- Match the Price: If Firm 2 matches P1, the firms split the market.
- Undercut the Price: If Firm 2 sets a price P2 slightly below P1 (P2 < P1), it captures the entire market demand.
- The Race to the Bottom: This logic continues iteratively. If Firm 2 undercuts P1, Firm 1 will then undercut P2, and so on. This process leads to a continuous reduction in prices.
Equilibrium Price Determination
The price undercutting continues until price equals marginal cost (P = MC). Here's why:
If a firm sets a price above its marginal cost (P > MC), a competitor can always undercut it by setting a price slightly below P but still above MC. This competitor will capture the entire market. Therefore, no firm has an incentive to set a price above MC.
If a firm sets a price equal to its marginal cost (P = MC), it earns zero economic profit. However, it can maintain its market share as long as other firms also price at MC. Any attempt to price below MC would result in losses.
Therefore, the Nash Equilibrium in Bertrand competition with homogeneous products is for both firms to set their price equal to their marginal cost. This results in a perfectly competitive outcome, even in an oligopolistic market structure.
Mathematical Representation
Let:
- n = number of firms
- MC = marginal cost (assumed to be the same for all firms)
- Pi = price set by firm i
The equilibrium condition is:
Pi = MC for all i = 1, 2, ..., n
Real-World Considerations and Limitations
While the Bertrand model provides a powerful theoretical framework, it has limitations in the real world:
- Product Differentiation: In reality, products are rarely perfectly homogeneous. Even slight differentiation allows firms to exercise some price control.
- Capacity Constraints: Firms may not have the capacity to meet the entire market demand if they undercut their competitors significantly.
- Switching Costs: Consumers may face switching costs, reducing their willingness to switch to a slightly cheaper product.
- Repeated Interactions: The model assumes one-shot interactions. In reality, firms interact repeatedly, allowing for tacit collusion or price leadership.
Conclusion
In conclusion, Bertrand price competition with homogeneous products leads to an equilibrium price equal to the marginal cost of production. This outcome arises from the relentless undercutting of prices by firms seeking to capture the entire market. While the model provides a valuable theoretical insight, its assumptions are often relaxed in real-world scenarios, leading to prices above marginal cost due to product differentiation, capacity constraints, and other factors. Understanding the core principles of Bertrand competition remains crucial for analyzing competitive dynamics in various industries.
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.