Differentiated Bertrand competition

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As 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.

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 ("MC"). The paradox is that in models such as Cournot competition, an increase in the number of firms is associated with a convergence of prices to marginal costs. In these alternative models of oligopoly, a small number of firms earn positive profits by charging prices above cost. Suppose two firms, A and B, sell a homogeneous 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 demand is infinitely price-elastic. 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.

Contents

An increase in a competitor's price is represented as an increase (for example, an upward shift) of the firm's demand curve.

As a result, when a competitor raises price, generally a firm can also raise its own price and increase its profits.

Calculating the differentiated Bertrand model

Berntrand differenciated.jpg

The above figure presents the best response functions of the firms, which are complements to each other.

Uses

Merger simulation models ordinarily assume differentiated Bertrand competition within a market that includes the merging firms.

Merger simulation is a commonly used technique when analyzing potential welfare costs and benefits of mergers between firms. Merger simulation models differ with respect to assumed form of competition that best describes the market as well as the structure of the chosen demand system

See also

Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at the prices set. The model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot's book Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838) in which Cournot had put forward the Cournot model. Cournot argued that when firms choose quantities, the equilibrium outcome involves firms pricing above marginal cost and hence the competitive price. In his review, Bertrand argued that if firms chose prices rather than quantities, then the competitive outcome would occur with price equal to marginal cost. The model was not formalized by Bertrand: however, the idea was developed into a mathematical model by Francis Ysidro Edgeworth in 1889.

External sources

Huw Dixon economist

Huw David Dixon, born 1958, is a British economist. He has been a professor at Cardiff Business School since 2006, having previously been Head of Economics at the University of York (2003–2006) after being a Professor of economics there (1992–2003), and the University of Swansea (1991–1992), a Reader at Essex University (1987–1991) and a lecturer at Birkbeck College 1983–1987.


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