Model Answer
0 min readIntroduction
The Cournot model, developed by Antoine Augustin Cournot in 1838, is a model of imperfect competition where firms compete on the quantity of output they produce, assuming the other firm’s output is fixed. It’s a foundational concept in industrial economics. Initially conceived for homogenous products, the model has been extended to analyze duopolies with differentiated products, reflecting the reality of many markets where products aren’t perfect substitutes. Understanding the nuances of the Cournot model under these differing product conditions is crucial for analyzing firm behavior and market outcomes. This answer will delineate the differences between the Cournot model with similar and differentiated products.
Cournot Model with Similar Products (Homogenous Oligopoly)
In the classic Cournot model with similar products, firms produce identical goods. The key assumptions are:
- Two firms (Duopoly): The model focuses on two firms competing in the market.
- Homogenous Product: The products offered by both firms are perfect substitutes.
- Simultaneous Decision-Making: Firms decide on their output levels simultaneously, without knowing the other firm’s choice.
- Profit Maximization: Each firm aims to maximize its profits.
- Market Demand: A known market demand curve exists.
Each firm’s output decision affects the market price. The market price is determined by the total quantity supplied by both firms. Each firm derives its residual demand curve by assuming the other firm’s output is fixed. The firms then choose their output levels to maximize profit, leading to a Nash Equilibrium where neither firm has an incentive to change its output given the other firm’s output. The equilibrium quantities are lower than in perfect competition but higher than in monopoly. The price is lower than in monopoly but higher than in perfect competition.
Mathematically, if the market demand is P = a - bQ (where Q = q1 + q2, q1 and q2 are the outputs of firm 1 and firm 2 respectively), each firm’s profit maximization problem leads to reaction functions. Firm 1’s reaction function is q1 = (a - c1) / (2b) - q2/2, and Firm 2’s is q2 = (a - c2) / (2b) - q1/2, where c1 and c2 are the marginal costs of firm 1 and firm 2 respectively. Solving these simultaneously yields the Cournot equilibrium quantities.
Cournot Model with Differentiated Products
The Cournot model with differentiated products acknowledges that firms may offer products that are not perfect substitutes. This introduces a crucial element: the degree of product differentiation. The key modifications are:
- Differentiated Products: Products are not identical; they possess unique characteristics, branding, or perceived quality differences.
- Residual Demand Curves: Each firm faces a residual demand curve that is downward sloping but less elastic than in the homogenous product case. This is because some consumers are loyal to a particular brand or prefer a specific product feature.
- Strategic Interdependence: A firm’s output decision still affects the market price, but the impact is lessened because its product is not a perfect substitute for the other firm’s product.
The profit maximization problem for each firm now considers the impact of its output on its own price, as well as the impact of the other firm’s output. The reaction functions become more complex, reflecting the interdependence of prices and quantities. The equilibrium quantities are generally higher than in the homogenous product case, and the prices are also higher. This is because firms have some market power due to product differentiation.
The demand function for firm i can be represented as Pi = a - bQi - γQj, where Pi and Qi are the price and quantity of firm i, and Qj is the quantity of firm j. γ represents the cross-price elasticity of demand, indicating the extent to which a change in one firm’s output affects the other firm’s price. A higher γ indicates greater product similarity, while a lower γ indicates greater product differentiation.
Comparison of the Two Models
| Feature | Similar Products | Differentiated Products |
|---|---|---|
| Product Nature | Homogenous (Perfect Substitutes) | Differentiated (Imperfect Substitutes) |
| Residual Demand Curve | Highly Elastic | Less Elastic |
| Equilibrium Quantities | Lower | Higher |
| Equilibrium Prices | Lower | Higher |
| Cross-Price Elasticity | High | Low |
| Market Power | Limited | Greater |
Conclusion
In conclusion, the Cournot model provides a valuable framework for understanding duopolistic competition. While the basic principles remain consistent, the nature of the product – whether similar or differentiated – significantly alters the market outcomes. Similar products lead to greater price competition and lower profits, while differentiated products allow firms to exercise more market power and achieve higher profits. The model’s adaptability highlights its enduring relevance in analyzing a wide range of industries, from commodities to branded goods. Further extensions of the Cournot model incorporate factors like dynamic competition, product innovation, and entry/exit of firms, providing a more nuanced understanding of real-world market dynamics.
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.