Duopoly Model Analysis

Joseph Louis François Bertrand was a French mathematician and economist whose impact is still evident in the modern economic world. Joseph Bertrand was a Professor at the École Polytechnique and a member of the Collège de France. What the present paper sets out to achieve is to discuss the economic contribution and impact of the French economist in the 19th century, while thoroughly analysing his own theories and how they have moulded and influenced the modern economic world as of current. Joseph Bertrand is well regarded for reviewing the work of his contemporaries, Leon Walras and Antoine Cournot. Bertrand criticized Leon Walras’s process of tatonnement as he argued that there are transactions that take place under non-balanced situations

This model differs to that of Cournot’s in that Bertrand’s model assures that duopolies competition is linked to prices and not quantity, as suggested by Cournots model.(Serrano & Feldman, 2010) Bertrand’s duopoly model rests on specific assumptions, namely; two or more firms are producing a homogenous product and are unable to cooperate. The model also assumes that firms set prices simultaneously and therefore a firm that sets a lower price will gain all the demand from the consumers as the products are homogenous. (Allian, 2012) Thus marginal and average costs are equal to the competitive price at the point of Nash equilibrium. If the price drops below the marginal and average cost firms will cease to produce as they will incur a loss. Although Bertand’s model was not formalized, 6 years later Francis Ysidro Edgeworth, an Irish mathematician, developed this idea into a mathematical model.(Authors of New World Encyclopaedia,

The reason for this is that there are other determinants that effect competition other than pricing. These determinants include transport and search costs as well as product differentiation. (Allian, 2012) Bertrand did not take into account that many firms offer various incentives to the consumers for purchasing their product, over that of their competitors, in an attempt to decrease their price elasticity of demand. If firms are able to decrease their price elasticity of demand then the competitive price will not be equal to the marginal cost and thus Nash equilibrium cannot occur. This therefore renders Bertrand’s duopoly model improbable at