Implications of the Bertrand Model
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
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