How to Calculate Bertrand Equilibrium

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The economic theory known as the Bertrand equilibrium describes a concept we all use every day. It's a fancy way of saying that consumers will buy the product with the cheapest price, all other things being equal. While this idea may seem like common sense, it does have a basis in economic theory.

What Is the Bertrand Equilibrium?

In 1883, Joseph Louis Francois Bertrand created a model of price competition that described how firms would set prices for their products.

His theory was based on the following assumptions:

  • The market has only two suppliers.
  • Both suppliers make the same homogeneous, undifferentiated product.
  • Each firm has the same marginal cost of production.
  • Consumers are indifferent as to which product they purchased.
  • The suppliers would set their prices simultaneously.

Pricing Strategies and Results

A firm has three choices to set prices. The manufacturer can set a price above the competition, equal to the competitor's price or below the competition.

Consumer Actions Under Bertrand Duopoly

Bertrand theorized that consumers would make their buying decisions based on price. The firm with the highest price would receive zero purchases. If both firms have the same price, consumers will split their purchases 50-50. The firm with the lowest price would win the market and receive 100 percent of purchases from consumers.

Bertrand Equilibrium Pricing

In an attempt to sell their products to price-sensitive consumers, firms will try to set their prices slightly below the competition. However, this could lead to a price war as the competitor reacts by lowering his price below the competition. Prices will continue to ratchet down until they reach the firms' marginal cost of production.

When prices are equal to the marginal cost of production, neither firm will make a profit, and they will have no desire to sell any products. The Bertrand equilibrium price, therefore, becomes the marginal cost of production. Neither firm has any incentive to sell below this price since they will lose money for each unit they sell.

Limitations of Bertrand Model

One problem with the Bertrand model is that the theory assumes the firm with the lowest price has the capacity to supply all the product demanded by consumers. For example, if consumer demand totals 1,000 units but Firm A can only manufacture 630 units, then consumers will be forced to buy the remaining 350 units at the higher price from Firm B.

Another problem is search costs. Take the price of gasoline, for example. How far would a consumer be willing to drive to save one or two cents per gallon? If the distance is far, the consumer would choose to purchase the gasoline at a higher price because the search costs to find the lowest price would exceed the savings.

Following the Bertrand Equilibrium model leads to the conclusion that all firms would continue to lower prices until they reached their marginal cost of production. At this point, neither firm would make a profit and would not have any incentive to manufacture and sell their products. Under these conditions, companies would then try to find ways to differentiate their products and justify higher prices in the minds of consumers.