Competition is the foundation of the market model of the economy. It is on its basis that the so-called equilibrium price is established, which satisfies both consumers and buyers. Bertrand's model describes this fundamental phenomenon of a market economy. It was formulated in 1883 in a review of the book "Mathematical Principles of the Theory of Wealth." In the latter, the author described the Cournot model. Bertrand did not agree with the conclusions made by the scientist. In the review, he formulated a model, but mathematically described it by Francis Edgeworth only in 1889.
Assumptions
Bertrand’s model describes oligopoly situations. There are at least two companies on the market that produce homogeneous products. They cannot cooperate. Firms compete among themselves, setting prices for their products. Since the products are homogeneous, the demand for cheaper goods immediately takes off. If both firms set the same price, then it is divided into two equal parts. Bertrand's model is suitable not only for the situation of duopoly, but also when there are many manufacturers on the market. However, the key assumption is the homogeneity of their products. It is also important that technology firms are no different. This means that their marginal and average costs are the same and equal to the competitive price. Firms can increase production indefinitely. Obviously, they will do this as long as the market price covers their costs. If it is less, then production does not make sense. No one will work at a loss.
Bertrand Model: Key Points and Characteristics
But what strategy will firms choose in this case? It seems that all manufacturers will benefit if each of them sets high prices. However, the Bertrand model shows that in a situation where firms do not cooperate with each other, this will not happen. Competitive price is equal to marginal cost in accordance with the Nash equilibrium. But why is this happening? Indeed, in this case no one can make a profit?
Suppose that one firm sets a price that is higher than its marginal costs, and the second does not. It is not difficult to predict what will happen in this case. All buyers will opt for the products of the second company. The conditions of the Bertrand model are such that the latter will be able to increase production indefinitely.
Suppose that both firms set the same price, which is greater than their marginal costs. This is a very volatile situation. Each of the firms will strive to bring down the price in order to capture the entire market. So she will be able to increase her profit almost twice. There is no stable equilibrium in a situation where both firms set different prices, which are more than marginal costs. All customers will go where goods are cheaper. Therefore, the only possible equilibrium is a situation where both firms set prices that are equal to marginal costs.
Cournot Model
The author of the "Mathematical Principles of the Theory of Wealth" believed that prices are always higher than the marginal value of goods produced, because firms themselves choose the volume of their output. Bertrand's model proves that this is not so. However, all the assumptions she uses were made by Cournot. Among them:
- There is more than one company on the market. However, the products they produce are homogeneous.
- Firms cannot or do not want to cooperate.
- The decision of each of the companies regarding the volume of output affects the price established on the market for products.
- Producers act rationally and think strategically, striving to maximize their profits.
Model Comparison
Competition for Bertrand is to minimize prices, for Cournot - to maximize output. But which model is more correct? Bertrand says that under the conditions of a duopoly, firms will be forced to set prices at the level of their marginal costs. Therefore, in the end, it all comes down to perfect competition. However, in practice it turns out that it is not so easy to change the volume of output in all sectors, as Bertrand suggested. In this case, the Cournot model better describes the situation. In some cases, you can use both. At the first stage, firms choose output volumes, at the second - they compete, as in the Bertrand model, setting prices. Separately, you need to consider the case when the number of firms in the market tends to infinity. Then the Cournot model shows that prices are equal to marginal costs. Thus, under these conditions, everything works in accordance with Bertrand's conclusions.
Criticism
Bertrand's model uses assumptions that are very far from real life. For example, it is believed that buyers seek to buy the cheapest product. However, in real life there is non-price competition in the market. Products are differentiated, not homogeneous. There are also transportation costs. No one wants to go twice as far to buy a product 1% cheaper if they spend more than 1% of the price on it. Manufacturers also understand this. Therefore, in real life, the Bertrand model often does not work.
Another important difference is that no company in practice can endlessly increase production capacity. This was noted by Edgeworth. Prices in real life do not correspond to the marginal costs of producers. This is due to the fact that the choice of strategy is not as simple as the Nash equilibrium shows.
