Bertrand paradox (economics)
Encyclopedia
In economics and commerce, the Bertrand paradox—named after its creator, Joseph Bertrand—describes a situation in which two players (firms) reach a state of Nash equilibrium
where both firms charge a price equal to marginal cost. The paradox is that in reality, it usually takes a large number of firms to ensure that prices equal marginal cost. Typically, a small number of firms (oligopoly) earn positive profits by charging prices above cost.
Suppose two firms, A and B, sell an identical commodity
, each with the same cost of production and distribution
, so that customers choose the product solely on the basis of price. It follows that neither A nor B will set a higher price than the other because doing so would yield the entire market to their rival. If they set the same price, the companies will share both the market and profits.
On the other hand, if either firm were to lower its price, even a little, it would gain the whole market and substantially larger profits. Since both A and B know this, they will each try to undercut their competitor until the product is selling at zero economic profit. This is the pure-strategy Nash equilibrium
. Recent work has shown that there may be an additional mixed-strategy Nash equilibrium with positive economic profits (see Kaplan & Wettstein, 2000, and Baye & Morgan, 1999).
The Bertrand paradox rarely appears in practice because real products are almost always differentiated
in some way other than price (brand name, if nothing else); firms have limitations on their capacity to manufacture and distribute; and two firms rarely have identical costs.
Bertrand's result is paradoxical because if the number of firms goes from one to two, the price decreases from the monopoly
price to the competitive price and stays at the same level as the number of firms increases further. This is not very realistic, as in reality, markets featuring a small number of firms with market power typically charge a price in excess of marginal cost. The empirical analysis shows that in most industries with two competitors, positive profits are made. Solutions to the Paradox attempt to derive solutions that are more in line with solutions from the Cournot model
of competition, where two firms in a market earn positive profits that lie somewhere between the perfectly competitive and monopoly levels.
Some reasons the Bertrand paradox do not strictly apply:
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
where both firms charge a price equal to marginal cost. The paradox is that in reality, it usually takes a large number of firms to ensure that prices equal marginal cost. Typically, a small number of firms (oligopoly) earn positive profits by charging prices above cost.
Suppose two firms, A and B, sell an identical commodity
Commodity
In economics, a commodity is the generic term for any marketable item produced to satisfy wants or needs. Economic commodities comprise goods and services....
, each with the same cost of production and distribution
Distribution (business)
Product distribution is one of the four elements of the marketing mix. An organization or set of organizations involved in the process of making a product or service available for use or consumption by a consumer or business user.The other three parts of the marketing mix are product, pricing,...
, so that customers choose the product solely on the basis of price. It follows that neither A nor B will set a higher price than the other because doing so would yield the entire market to their rival. If they set the same price, the companies will share both the market and profits.
On the other hand, if either firm were to lower its price, even a little, it would gain the whole market and substantially larger profits. Since both A and B know this, they will each try to undercut their competitor until the product is selling at zero economic profit. This is the pure-strategy Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
. Recent work has shown that there may be an additional mixed-strategy Nash equilibrium with positive economic profits (see Kaplan & Wettstein, 2000, and Baye & Morgan, 1999).
The Bertrand paradox rarely appears in practice because real products are almost always differentiated
Product differentiation
In economics and marketing, product differentiation is the process of distinguishing a product or offering from others, to make it more attractive to a particular target market. This involves differentiating it from competitors' products as well as a firm's own product offerings...
in some way other than price (brand name, if nothing else); firms have limitations on their capacity to manufacture and distribute; and two firms rarely have identical costs.
Bertrand's result is paradoxical because if the number of firms goes from one to two, the price decreases from the monopoly
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...
price to the competitive price and stays at the same level as the number of firms increases further. This is not very realistic, as in reality, markets featuring a small number of firms with market power typically charge a price in excess of marginal cost. The empirical analysis shows that in most industries with two competitors, positive profits are made. Solutions to the Paradox attempt to derive solutions that are more in line with solutions from the Cournot model
Cournot competition
Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot who was inspired by observing...
of competition, where two firms in a market earn positive profits that lie somewhere between the perfectly competitive and monopoly levels.
Some reasons the Bertrand paradox do not strictly apply:
- Capacity constraints–Sometimes firms do not have enough capacity to satisfy all demand
- Product differentiation–If products of different firms are differentiated, then consumers may not switch completely to the product with lower price
- Dynamic competition–Repeated interaction or repeated price competition can lead to the price above MC in equilibrium.
- More money for higher price–It follows from repeated interaction: If one company sets their price slightly higher, then they will still get about the same amount of buys but more profit for each buy, so the other company will raise their price, and so on (only in repeated games, otherwise the price dynamics are in the other direction).
- Oligopoly If the two companies can agree on a price, it is in their long-term interest to keep the agreement: the revenue from cutting prices is less than twice the revenue from keeping the agreement, and lasts only until the other firm cuts its own prices.
See also
- Joseph Bertrand
- Bertrand model
- Differentiated Bertrand competitionDifferentiated Bertrand competitionAs a solution to the Bertrand paradox in economics, it has been suggested that each firm produces a somewhat differentiated product, and consequently faces a demand curve that is downward-sloping for all levels of the firm's price....
- Edgeworth paradoxEdgeworth paradoxIn economics, the Edgeworth paradox describes a situation in which two players cannot reach a state of equilibrium with pure strategies, i.e. each charging a stable price....
- Prisoner's dilemmaPrisoner's dilemmaThe prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...