There are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4. Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. Calculate the optimal prices for the shops, and their profits in terms of N.

Answer

In this scenario, there are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4. Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. The optimal prices for the shops, and their profits in terms of N can be calculated through the Cournot Model.

The Cournot Model

The Cournot Model is a model of an oligopoly, which is a market form in which a market or industry is dominated by a small number of sellers (oligopolists). The Cournot Model suggests that each firm independently chooses a quantity to produce, taking into account the quantity produced by the other firm(s). Each firm then receives a profit or loss depending on the market price that then results from the total industry output.

Calculating Optimal Prices

In this example, the optimal price for the shop with the marginal cost of 1 will be 3. This price is determined by the inverse demand function P=4-1/N-Q, where P is the price, N is the number of consumers, and Q is the total output produced by both shops. The optimal price for the shop with the marginal cost of 2 will be 5, which is determined by the inverse demand function P=6-2/N-Q. In terms of profits, the shop with the marginal cost of 1 will have a profit of (3-1)*1/N and the shop with the marginal cost of 2 will have a profit of (5-2)*1/N.

Related Questions

• What is an oligopoly?
• What is the Cournot Model?
• What are the characteristics of an oligopoly?
• What is the inverse demand function?
• What does marginal cost mean?
• What is a fixed cost?
• What is a profit?
• What is the difference between fixed and marginal costs?
• What is the optimal price for a product?
• How do you calculate profits in terms of N?