# Implications of the Bertrand Model

Pages: 5 (1876 words) Published: May 14, 2011
In 1893 French economist Joseph Bertrand developed his Bertrand model of competition from his review of Antoine Cournots study of a Spring Water duopoly. His criticism lay with how firms in oligopolies compete. In his model firms compete with prices rather than Cornots quantities. (REFERENCE TO SPANISH JOURNAL) The model consists of two firms who set prices simultaneously and independently (HUGH GRAVIELLE AND AY REES, MICROECONOMICES), jean tiral explains this as when one firm sets its price it is ignorant to its rival’s price, rather it “anticipates” what they will charge. It is assumed products are homogeneous and perfect substitutes (ECCSTRAT) and due to the nature of the product the firm supplying output at the lowest price will gain the entire market demand. (GB!) This firm will have to supply all the forthcoming demand at the price they have set; gb1 from this an important assumption of the model is that there are no capacity constraints, that both firms have the same marginal cost, which remains constant, and that demand is liner. GB2 As stated, the entire market demand for homogeneous products will go to the firm offering the lowest price, although if both firms were to sell at the same price “a sharing rule must be assumed” GB2. Using an example from the ((((((( lets suppose the market demand for a homogeneous product is given by, Q = 120-p (where Q is quantity demanded and p is price charged). The marginal cost (MC) for both producers is, C=\$30, and both producers sell output at p=c=\$30. The demand for each producer is Q=0.5*120-p=45. Lets say producer A increased their price to c=\$31, the entire market demand would transfer to producer B who would now have a demand function of Qb=120-c=90, while producer A would have zero demand. However if producer A had reduced their price to c=\$29, they would capture the entire market demand through charging the lowest cost, however they would make a \$1 loss in each product sold. From this, the Nash equilibrium for the Bertrand model lies where P=MC, with demand so heavily influenced by price producers do not want to be undercut by rivals. With P=MC no rival will undercut as zero profits are preferable to negative profits, and any firm trying to charge above the MC and make positive profits will receive no sales. The suggestion is the addition of one firm restores perfect market competition (Jean Tirole, 1998), moving the market form monopoly power and profits (maximum inefficiency) to perfectly competitive (maximum efficiency). It had been deemed a paradox as it is difficult to believe that two firms in a duopolistic market can make zero profits. We are able to resolve Bertrand’s paradox through relaxing and of the three integral assumptions of the model (intro to industrial org l. M. B Cabrail). In order to analyse its practical relevance and its implications, this essay will now give examples of where the paradox can be deconstructed. The first example of a solution comes from a combination of two assumptions, the first is the absence of capacity constraints, and the second firms make decisions independently. In the model whichever firm firm is charging the lowest price will receive the entire market demand, and is “expected to supply all forthcoming demand at the price it has set” (old xavior). There are few situations in the real world where one firm could satisfy the demand of the whole market. Using the previous example, producer B gained the entire market demand (Q=120-\$30=90). Let’s assume producer B has a capacity constraint below 90 units. There is now a proportion of the market that can only be satisfied by producer A, who can use monopoly power and make positive profits as the only producer. (managerial Economics a strategic approach). This example shows how with the inclusion of a common real world problem, Bertrand’s proposed equilibrium of price equal to marginal cost is deconstructed. A second implication of capacity constraints is their effect on...