Model Answer
0 min readIntroduction
In economics, a duopoly represents a market structure dominated by two firms. Collusion, in this context, refers to a tacit or explicit agreement between these firms to limit competition, typically by fixing prices, restricting output, or dividing the market. While collusion can lead to higher profits for both firms compared to a competitive outcome, it is inherently unstable. This instability arises because each firm, acting in its own rational self-interest, faces a strong incentive to ‘cheat’ on the collusive agreement, potentially gaining at the expense of its partner. This answer will explain the underlying economic reasons for this incentive to cheat in a duopoly model of collusion.
Understanding Collusion in a Duopoly
Collusion aims to mimic the outcome of a monopoly. By restricting output and raising prices, firms can collectively earn supernormal profits. However, unlike a monopolist, duopolists are independent decision-makers. The success of collusion hinges on both firms adhering to the agreed-upon terms. This is where the inherent instability arises.
The Incentive to Cheat: A Game Theory Perspective
The incentive to cheat stems from the individual firm’s profit maximization objective. Consider a scenario where two firms, Firm A and Firm B, have colluded to restrict output and charge a higher price. From Firm A’s perspective, it can increase its profits further by secretly increasing its output, even while Firm B adheres to the agreed-upon restriction. This is because:
- Demand Curve Faced by Firm A: When Firm A increases output, it faces a relatively elastic portion of the market demand curve. This means that the increase in quantity sold will not lead to a proportionally large decrease in price.
- Marginal Revenue and Marginal Cost: Firm A will continue to increase output as long as its marginal revenue (MR) exceeds its marginal cost (MC). By cheating, Firm A can sell more units at a price slightly below the collusive price, increasing its overall revenue and profit.
- Firm B’s Response: Firm B, unaware of Firm A’s cheating, continues to restrict its output. This allows Firm A to capture a larger market share and earn higher profits.
This situation mirrors the classic Prisoner’s Dilemma. Each firm, acting rationally, will choose to cheat, even though both would be better off if they both cooperated.
Mathematical Illustration
Let's assume the market demand function is P = 100 - Q, where P is price and Q is total quantity. Let the cost function for both firms be C(q) = 10q, where q is the quantity produced by each firm. If the firms collude and act as a monopolist, they maximize profit by setting marginal revenue equal to marginal cost. The total quantity produced is Q = 45, and each firm produces q = 22.5. The price is P = 55, and each firm earns a profit of (55-10)*22.5 = 1112.5.
Now, suppose Firm A cheats and increases its output to 25. Firm B still produces 22.5. The total quantity is 47.5, and the price falls to P = 52.5. Firm A’s profit becomes (52.5-10)*25 = 1062.5. While Firm A’s profit decreases, if it anticipates Firm B’s unchanged output, it might still cheat, believing the short-term gain outweighs the risk of retaliation.
Factors Affecting Collusion
Several factors can influence the stability of collusion:
- Number of Firms: Collusion is more difficult to sustain with a larger number of firms. The more firms involved, the greater the chance that one firm will cheat.
- Product Homogeneity: Collusion is easier when products are homogeneous, as it simplifies price fixing.
- Market Concentration: Higher market concentration (a few dominant firms) makes collusion more likely.
- Barriers to Entry: High barriers to entry prevent new firms from entering the market and disrupting the collusive agreement.
- Repeated Interactions: If firms interact repeatedly, they may be more likely to cooperate, fearing retaliation from the other firm. This is known as a ‘grim trigger’ strategy.
- Transparency: Lack of transparency regarding costs, output, and sales makes it easier for firms to cheat undetected.
Legal and Regulatory Framework
Most countries have antitrust laws designed to prevent collusion and promote competition. In India, the Competition Act, 2002, prohibits anti-competitive agreements, including cartels and bid-rigging. The Competition Commission of India (CCI) is responsible for enforcing the Act and penalizing firms engaged in collusive practices.
Conclusion
In conclusion, the incentive to cheat is a fundamental flaw in collusive agreements within a duopoly. While collusion offers the potential for higher profits, the rational self-interest of each firm to maximize its own profits creates a powerful temptation to deviate from the agreement. The stability of collusion depends on a complex interplay of factors, including the number of firms, product characteristics, market structure, and the threat of retaliation. Effective antitrust enforcement is crucial to prevent collusion and ensure a competitive market environment.
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.