Free Economics Dissertations - Due To Its Representation As A One-period Game, The Cournot Outcome Assumes
Due to its representation as a one-period game, the Cournot outcome assumes that firm j will not change its behaviour in response to a change in the behaviour of firm i, signified by the fact that dqj/dqi = 0. This conjecture is patently false as firms would in reality observe across time that they can influence each other through changes in their behaviour and subsequently alter their quantity choices accordingly.
The Bertrand Model
The Bertrand model of duopoly is assumed to have the same characteristics as the Cournot model, with the exception that firms compete in price whilst allowing industry demand to determine quantity. Again firms are assumed to act simultaneously upon interaction with one another.
In the simple model presented below, each firm faces a constant marginal cost c. Note that if firms were to set price lower than marginal cost they would face losses. Also, there exists a profit maximising monopoly price which is the maximum price that firms could be expected to charge. A firm could potentially capture the industry by setting price one unit lower than its rival, or share the industry by setting price equal to its rival’s price.
This gives rise to the following set of best responses for player i:
If firm j sets price less than or equal to marginal cost, firm i will set price equal to marginal cost and neither firm will make profits.
If firm j sets price greater than marginal cost but less than the monopoly price, firm i will set price at pi = pj - x, where x is greater than 0.
If firm j sets price greater than or equal to the monopoly price, firm i will set price equal to the monopoly price.
There is a unique equilibrium where each firm’s price maximises their profit given the price set by the other firm. This is where pi = pj = c. To see this note that if one firm sets a price lower than c it will make losses and if it sets price higher than c then the other firm will capture the market. In stark contrast to Cournot, this model states that in equilibrium firms set price at the socially optimal level, and do not make profits.
The Bertrand model, unlike the Cournot model, provides a formal mechanism for determining prices. However, the outcome improbably signifies that a firm could capture the market by simply setting price one unit lower than its rival. Hotelling (1929) developed a model in which products were identical in price but differentiated by location and subsequently reached the more realistic conclusion that one firm will not necessarily capture the market by pricing one unit of currency lower than the other firm. As with the Cournot model, the static framework of the Bertrand model leads to the unrealistic assumption that rivals will not play a repeated game in which they change their behaviour in response to changes in the behaviour of rivals.
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