What are the similarities and differences between the Cournot model and the Bertrand model?

Abstract

We revisit the classic discussion comparing price and quantity competition, but in a mixed oligopoly in which one state-owned public firm competes against private firms. It has been shown that in a mixed duopoly, price competition yields a larger profit for the private firm. This implies that firms face weaker competition under price competition, which contrasts sharply with the case of a private oligopoly. Here, we adopt a standard differentiated oligopoly with a linear demand. We find that regardless of the number of firms, price competition yields higher welfare. However, the profit ranking depends on the number of private firms. We find that if the number of private firms is greater than or equal to five, it is possible that quantity competition yields a larger profit for each private firm. We also endogenize the price-quantity choice. Here, we find that Bertrand competition can fail to be an equilibrium, unless there is only one private firm.

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Specializing in mathematical economic theory, Journal of Economics focuses on microeconomic theory while also publishing papers on macroeconomic topics as well as econometric case studies of general interest. Regular supplementary volumes are devoted to topics of central importance to both modern theoretical research and present economic reality.

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Bertrand is a model that competes on price while Cournot is model that competes on quantities (sales volume).

Bertrand Competition:
Is a Model were firms compete on price, which naturally triggers the incentive to undercut competition by lowering price, thereby depleting profit until the product is selling at zero economic profit. This effectively is the pure-strategy Nash equilibrium.

Cournot Competition:
Is a model (Oligopoly the model was built on Duopoly) where a firm competes in the Oligopoly market on quantity, maximizing profit given what it believes the other firm(s) will produce. Profit for the firm is maximized by setting its marginal revenue equal to marginal cost and determining it's quantity relative it's rival. There is no competition on price here.

| Updated Jun 26, 2020 (Published Jul 15, 2018)

An oligopoly is a market structure where only a few sellers serve the entire market. Because of their strong position in the market, these firms have the power to influence the price. That means, unlike in a market with perfect competition, they are no longer price takers, but price makers. In that sense, they can act somewaht similar to firms in a monopoly. However, unlike in a monopoly, sellers in an oligopoly also have to take into account the decisions and actions of their competitors when making pricing decisions.

There are two common models that describe the monopolistic competition in an oligopoly. They are called Cournot and Bertrand Competition (both named after their inventors). The main difference between the two is the firm’s initial decision to set a fixed price or a fixed quantity. We’ll see what exactly that means in the following paragraphs. For now, just note that the outcome of both models is based on principles of game theory (see also the prisoner’s dilemma). So with that being said, let’s look at the two models in more detail.

Cournot Competition describes an industry structure (i.e. an oligopoly) in which competing companies simultaneously (and independently) chose a quantity to produce. The total quantity supplied by all firms then determines the market price. According to the law of supply and demand, a high level of output results in a relatively low price, whereas a lower level of output results in a relatively higher price. Therefore, each company has to consider the expected quantity supplied by its competitors to maximize their own profits.

For example, let’s look at a candy seller called Sweet Candy Dreams (SCD). If the competitors of SCD are expected to sell only a small quantity of candy, it may be attractive for SCD to supply a large quantity because price (and thus profits) will be relatively high. Meanwhile, if the expected quantity supplied by its competitors is high, the company may decide to sell less candy, because it’s less profitable due to a lower price.

Thus, we have a strategic game (see also game theory) where the quantities supplied are the strategies. This situation ultimately leads to the so-called Cournot-Equilibrium. That means, the market reaches an equilibrium where all firm’s chose a quantity that is their ‘best response’ to their competitors’ quantities. We will look at how to calculate such a Cournot-Equilibrium in a different article. For now, all you need to know is that Cournot competition leads to an inefficient equilibrium, i.e. a price above the price in perfect competition and economic profits for the firms.

Bertrand Competition

Bertrand Competition describes an industry structure (i.e. an oligopoly) in which competing companies simultaneously (and independently) chose a price at which to sell their products. The market demand at this price then determines quantity supplied. As a result, each company has to consider the expected price of their competitors’ products. However, unlike in Cournot competition, in this case, the firm’s won’t share the market. Instead, the company that chooses the lowest price can serve the entire market.

To illustrate this, let’s revisit our candy seller Sweet Candy Dreams (SCD). If we assume that there is only one other competitor (Candy Corp.) in the market, SCD has to pick a price that is equal to or lower than the price Candy Corp. chooses, if the company wants to sell anything. So if Candy Corp. is expected to set its price at USD 2.00, it would be reasonable for SCD to set its price at USD 1.99, as this would allow the company to serve the entire market. However, Candy Corp. knows this, so it will chose a lower price.

Again, this can be seen as a strategic game, where the prices are the strategies. However, this results in entirely different outcome than before. All the firms need to do in order to increase their market share to 100% is set their price one cent lower than their competitors. They will repeat this process, until they reach a point where price equals their marginal costs. Therefore, in Bertrand competition the market ultimately reaches an efficient equilibrium, where price is equal to the price in perfect competition and the firm’s don’t earn economic profits.

In a Nutshell

An oligopoly is a market structure where only a few sellers serve the entire market. This gives them enough power to influence quantity and/or price of a good or service in the market. There are two common models that describe the monopolistic competition in an oligopoly: Cournot and Bertrand Competition. Cournot Competition describes an industry structure in which competing companies simultaneously (and independently) chose a quantity to produce. This sort of competition leads to an inefficient equilibrium. Meanwhile, Bertrand Competition describes an industry structure (i.e. an oligopoly) in which competing companies simultaneously (and independently) chose a price at which to sell their products. This type of competition leads to an efficient outcome.

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