Bertrand competition

Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822-1900). Specifically, it is a model of price competition between duopoly firms which results in each charging the price that would be charged under perfect competition, known as marginal cost pricing. The model has the following assumptions: There are at least two firms producing homogeneous products; Firms do not cooperate; Firms have the same marginal cost (MC); Marginal cost is constant; Demand is linear; Firms compete in price, and choose their respective prices simultaneously; There is strategic behaviour by both firms; Both firms compete solely on price and then supply the quantity demanded; Consumers buy everything from the cheaper firm or half at each, if the price is equal. Competing in price means that firms can easily change the quantity they supply, but once they have chosen a certain price, it is very hard, if not impossible, to change it, for example bars or shops or other companies that publish non-negotiable prices. Calculating the classic Bertrand model MC = Marginal cost p1 = firm 1’s price level p2 = firm 2’s price level pM = monopoly price level Firm 1s optimum price depends on what it believes firm 2 will set prices at. Pricing just below the other firm will obtain full market demand (D), while maximizing profits. If firm 1 expects firm 2 to price below marginal cost, then its best strategy is to price higher, at marginal cost. In general terms, firm 1s best response function is p1’’(p2), this gives firm 1 optimal price for each price set by firm 2.