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's model argued that each firm should maximise its profit by selecting a quantity level and then adjusting price level to sell that quantity. The outcome of the model equilibrium involved firms pricing above marginal cost; hence, the competitive price. In his review, Bertrand argued that each firm should instead maximise its profits by selecting a price level that undercuts its competitors' prices, when their prices exceed marginal cost. The model was not formalized by Bertrand; however, the idea was developed into a mathematical model by Francis Ysidro Edgeworth in 1889. Underlying assumptions of Bertrand competition Considering the simple framework, the underlying assumptions that the Bertrand model makes is as follows: there are firms () competing in the market that produce homogenous goods; that is, identical products; the market demand function , where Q is the summation of quantity produced by firms , is continuous and downward sloping with ; the marginal cost is symmetric, ; it is a static game; firms simultaneously set price, without knowing the other firm’s decision; and firms don't have a capacity constraint; that is, each firm has the capability to produce enough goods to meet market demand. Furthermore, it is intuitively deducible, when considering the law of demand of firms' competition in the market: the firm that sets the lowest price will acquire the whole the market; since, product is homogenous and there is no cost of switching for the customers; and if the price set by the firms is the same, , they will serve the market equally, . The Bertrand duopoly equilibrium Why is the competitive price a Nash equilibrium in the Bertrand model? First, if both firms set the competitive price with price equal to marginal cost (unit cost), neither firm will earn any profits. However, if one firm sets price equal to marginal cost, then if the other firm raises its price above unit cost, then it will earn nothing, since all consumers will buy from the