Bertrand Paradox
Introduction to the Bertrand Model
The Bertrand model was developed by Joseph Bertrand to challenge Cournot’s work on non-cooperative oligopolies. Cournot’s model dealt with an N number of firms who will choose a specific quantity of output where price is a known decreasing function of total output. (About.com 2011) However, Bertrand’s argument was with regard to the setting of prices. He said the only factors influencing the price in an oligopolistic market were the firms themselves and therefore based his model on the fact that firms set prices rather than output. (Carlton & Perloff 2005)
As with the Cournot model, the Bertrand model makes some assumptions. There is no market entry limiting the number of firms to two (duopoly) who produce homogenous products in a single period, have the same demand curve and set prices simultaneously. These two non-cooperative firms are also identical in nature, have the same constant returns to scale signifying that both firms have the same unit cost of production and each firm believes its rival’s price is fixed. (Carlton & Perloff 2005)
In order to illustrate the Bertrand model, the following hypothetical situation can be used. There are two firms in an industry, Firm A and Firm B that are in line with the assumptions made above. Firm A charges a price PA while Firm B charges a price PB. If PA is greater than MC, then firm A will make a positive economic profit. However, the fact that both firms produce identical products makes the demand for the good perfectly elastic. Therefore if PB was less than PA, the demand for Firm A’s products would fall to zero whereas the demand for Firm B’s products will be equal to the entire market demand. As the two firms are non-cooperative they will chose the only strategy that will allow them to make a positive economic profit which is lowering their price below the competitor. This strategy will continue until both firms reach the point where they make a normal economic profit
The Bertrand model was developed by Joseph Bertrand to challenge Cournot’s work on non-cooperative oligopolies. Cournot’s model dealt with an N number of firms who will choose a specific quantity of output where price is a known decreasing function of total output. (About.com 2011) However, Bertrand’s argument was with regard to the setting of prices. He said the only factors influencing the price in an oligopolistic market were the firms themselves and therefore based his model on the fact that firms set prices rather than output. (Carlton & Perloff 2005)
As with the Cournot model, the Bertrand model makes some assumptions. There is no market entry limiting the number of firms to two (duopoly) who produce homogenous products in a single period, have the same demand curve and set prices simultaneously. These two non-cooperative firms are also identical in nature, have the same constant returns to scale signifying that both firms have the same unit cost of production and each firm believes its rival’s price is fixed. (Carlton & Perloff 2005)
In order to illustrate the Bertrand model, the following hypothetical situation can be used. There are two firms in an industry, Firm A and Firm B that are in line with the assumptions made above. Firm A charges a price PA while Firm B charges a price PB. If PA is greater than MC, then firm A will make a positive economic profit. However, the fact that both firms produce identical products makes the demand for the good perfectly elastic. Therefore if PB was less than PA, the demand for Firm A’s products would fall to zero whereas the demand for Firm B’s products will be equal to the entire market demand. As the two firms are non-cooperative they will chose the only strategy that will allow them to make a positive economic profit which is lowering their price below the competitor. This strategy will continue until both firms reach the point where they make a normal economic profit