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# Bertrand's model: main provisions and characteristics

Competition is the basis 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. The Bertrand model describes this fundamental phenomenon of a market economy. It was formulated in 1883 in a review to 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 the model, but mathematically it was described by Francis Edgeworth only in 1889.

## Assumptions

The Bertrand model describes the situation of oligopoly. At the market there are at least two firms that produce homogeneous products. They can not 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. The Bertrand 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 the products they produce. It is also important that the technologies of firms do not differ. This means that their marginal and average costs are the same and equal to the competitive price. Increase the production of firms can endlessly. Obviously, they will do this as long as the price on the market covers their costs. If it is smaller, then production does not make sense. No one will work at a loss.

## Bertrand's model: main provisions and characteristics

But what strategy will firms choose in this case? It seems that all producers will benefit if each of them sets high prices. However, Bertrand's model shows that in a situation where firms do not cooperate with each other, this will not happen. The competitive price is equal to the marginal cost in accordance with the Nash equilibrium. But why does this happen? After all, in this case, no one can make a profit?

Suppose that one firm sets a price that is greater 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 second company's products. The conditions of the Bertrand model are such that the latter can increase production volumes indefinitely.

Suppose that both firms set the same price, which is greater than their marginal costs. This is a very unstable situation. Each of the firms will seek to bring down the price to capture the entire market. So it will be able to increase its profits almost twice. There is no stable equilibrium in a situation where both firms set different prices, which are greater than marginal costs. All buyers will go where goods are cheaper. Therefore, the only possible equilibrium is the situation where both firms set prices that are equal to marginal costs.

## The Cournot model

The author of the "Mathematical Principles of the Theory of Wealth" believed that prices are always greater than the marginal cost of manufactured goods, because firms themselves choose the volume of their output. The Bertrand model proves that this is not so. However, all the assumptions that she uses were formulated by Cournot. Among them:

- There is more than one company on the market. However, the products produced by them are homogeneous.
- Firms can not or do not want to cooperate.
- The decision of each of the firms on the volume of output affects the price of the products established on the market.
- Producers act rationally and think strategically, striving to maximize their profits.

## Comparison of models

The competition for Bertrand is to minimize prices, according to Cournot - in maximizing output. But which of the models is more correct? Bertrand says that in conditions of duopoly, firms will be forced to set prices at the level of their marginal costs. Therefore, in the final analysis, everything will be reduced to perfect competition. However, in practice it turns out that it is not easy to change the output volume in all branches, as Bertrand assumed. In this case, the Cournot model is better described. In some cases, you can use both. At the first stage, firms choose output volumes, at the second stage they compete, as in Bertrand's model, setting prices. Separately, we need to consider the case when the number of firms on 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 the conclusions of Bertrand.

## Criticism

The Bertrand model uses assumptions that are very far from real life. For example, it is believed that buyers are eager to buy the cheapest product. However, in real life there is non-price competition on the market. The products are differentiated, not homogeneous. There are also transportation costs. No one will want to go two times farther to buy goods at 1% cheaper, if he spends more than 1% of the price for this. Understand this and the producers. Therefore, in real life, the Bertrand model often does not work.

Another important difference is that no firm in practice can not infinitely increase production capacity. This was noted by Edgeworth. Prices in real life do not correspond to marginal costs of producers. This is due to the fact that the choice of strategy is not so simple, as Nash equilibrium shows.

## On practice

The Bertrand model shows that the oligopoly is an intermediate stage. If firms can not agree and refuse to cooperate, they will sell their goods at prices equal to marginal costs. No one will lose, but will not make a profit. A more winning situation is in practice. Several firms that produce similar products are easily negotiated. Especially it is beneficial to all. In this case, a price equal to the monopoly price is set on the market. Each of the firms produces the volume of the goods within their capabilities. The advantage in real life of a firm can only be obtained through new technologies.

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