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Bertrand Competition

Bertrand's competition is an economic theory, which indicates how two firms will compete in a duopoly market, using 'price' as a weapon.
WealthHow Staff
Bertrand Competition is an economic duopoly model. Its theory was propounded by Joseph Louis Fran├žois Bertrand and is named after him. This theory was actually made to criticize the Cournot's model which stated that companies will compete with each other by changing the quantities manufactured by them. This implies that the quantities manufactured or produced is the factor that will determine their market share and profits.
Bertrand's Theory
The Bertrand's economic competition model incites the changes in the prices charged by the sellers and the quantities that consumers would prefer to buy at that price.
Assumptions of the Theory
The following assumptions were made in the theory.
  1. There are a minimum of two sellers selling homogeneous goods.
  2. The firms individually select the prices they charge for a product, and not on the basis of a mutual agreement.
  3. All the firms will be supplying to all the market demands at the changed price.
  4. Firms will compete with each other by setting up prices at the same time.
  5. Consumers buy everything from either of the firms, depending on who sells at the lowest price.
  6. If all the firms charge an equal price, then consumers will buy products on random selection. In this way, the market demand is equally shared by both the firms.
Bertrand's theory describes a duopoly market in which two firms are competing with each other through a price war. As per the assumptions made, if the price of a good from 'Firm 1' is less than the price charged by 'Firm 2' then, all the consumers will buy goods only from Firm 1. And, Firm 1 will be able to cater to all the consumer demands. However, if Firm 2 also reduces its price making it equal to the equal to the price charged by Firm 1, then, the total demand and the total sale will be equally divided between the two firms. If the price war continues, then firms eventually will reach a point where they will charge a 'Marginal Price'. After reaching this point none of the firms can further lower their prices and will reach a point of stagnancy.
Diagrammatic Explanation
bertrand competition
I have tried explaining this theory using a diagram.
In the above diagram, the following points are indicated.

Pm = Monopoly Price
MC = Marginal Cost ($50)
P1 = Price Charged By Firm 1 ($100)
P2 = Price Charged By Firm 2 ($90)
P3 = Price Charged By Firm 1 ($70)
P4 = Price Charged By Firm 2 ($60)

Initially 'Firm 1' and 'Firm 2' both are operating at monopoly prices that is indicated as Pm. Both the firms are charging the same price for the same good and the market demand is equally divided among them. Now, to compete with Firm 2, Firm 1 will charge a price lower than Pm, at $100. As, per the assumptions made in the theory all the market demand will now shift to Firm 1. As a counter response, Firm 2 will charge a price lower than Firm 1, i.e. at $90. Now, all the demand shifts to Firm 2. Both the firms continue competing by lowering their respective prices. Eventually, they lower their prices to the marginal cost (MC), which is $50. Both the firms cannot lower their prices below this level, as any price charged under the MC will prove to be a loss to the firm. Now, if either of the firms charge a price lower than the MC, then all the demand will be directed to that firm, but the firm will make no profit. That's when both the firms reach the point of 'Nash Equilibrium'. At this point, none of the firms can lower their prices further. Therefore, they reach a point of stagnation, a no-win situation. To earn profits, both the firms will have to maintain their prices at the 'monopoly prices', and enjoy the profits derived by catering to half of the market demand. As both the firms won't really reach to a mutual agreement, it is best that both continue charging the same price.
Concept of Limit Pricing
If one of the firms has a price advantage over the other firm because of an efficient technology used in manufacturing, then that firm will charge a price just below its 'Average Cost'. This will enable it to charge a lower price than the other firm, without making a loss, and will overtake the entire market demand. In Bertrand's theory, this is called "limit pricing".
Advantages of the Theory
  1. This theory can be applied when the cost involved in turning customers away is very high.
  2. It can be applied when the output of a firm can be efficiently changed.
  3. This theory can be applied to a duopoly market in which two firms are dealing with a product that cannot have much of a product differentiation.
Critical Evaluation of the Theory
  1. Only two companies are incorporated in the model. Therefore, it cannot be applied to a oligopoly market model.
  2. If the market demand is more than the market supply, companies would like to increase the price of their goods to gain higher profits.
  3. If one company is selling the same commodity at a higher price, it is implied in the theory that he will sell nothing. This is not true. This theory the effect of branding on price into consideration.
  4. In reality, just two firms cannot push the prices to the extent that it equals the marginal cost.
  5. Practically this model cannot hold true as the sales of a good does not just depend on its price but also on other factors like, brand name, product differentiation, etc.
  6. It may not be possible for a firm to be able to serve the entire market demand.
  7. When a market moves from having one firm to two firms, the price shifts from monopoly price to the Marginal cost (competitive price). But, even when more firms are added, the price remains at MC. This assumption is unrealistic.
  8. Instead of competing on the basis of price, a firm can choose to compete with other firms through product differentiation.
  9. It is not right to say that, firms will charge a price necessarily at marginal cost, as firms can also settle at an equilibrium price that lies above MC.
This theory has been criticized for its unrealistic approach and has not been termed as a better model than the Cournot's model. In fact, both the models cater to different market structures. Even though this model cannot be applied to real life models, it still holds an important place in economics, as they explain how firms can compete.