The Cournot model, in which firms compete on output, and the
Bertrand model, in which firms compete on price, describe duopoly
dynamics.
LEARNING OBJECTIVE [ edit ]
Discuss the characteristics of a duopoly
KEY POINTS [ edit ]
The Cournot model focuses on the production output decision of a single firm. A firm determines
its competitor's output level and the residual market demand. It then determines its profitmaximizing output for that residual demand as if it were the entire market, and produces
accordingly.
In the Bertrand model, firms set profit-maximizing prices in response to what they expect the
competitor to charge. The model predicts that both firms will lower prices until they reach
the marginal cost limit, arriving at an outcome equivalent to what prevails under perfect
competition.
The accuracy of the Cournot or Bertrand model will vary from industry to industry, depending on
how easy it is to adjust output levels in the industry.
TERMS [ edit ]
Bertrand duopoly
A model that describes interactions among firms competing on price.
Cournot duopoly
An economic model describing an industry in which companies compete on the amount of output
they will produce, which they decide on independently of each other and at the same time.
Give us feedback on this content: FULL TEXT [edit ]
A true duopoly is a specific type of oligopolywhere only two producers exist in a market.
There are two principle duopoly
models: Cournot duopoly and Bertrand
duopoly.
Cournot Duopoly
Cournot duopoly is an economic model
that describes an industry structure in
which firms compete on output levels. The
model makes the following assumptions:
There are two firms, which produce a
homogeneous product;
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The number of firms is fixed;
Firms do not cooperate (there is no collusion);
Firms have market power, and each firm's output decision affects the good's price;
Firms are economically rational and act strategically, seeking to maximize profit given
their competitor's decisions; and
Firms compete on quantity, and choose quantity simultaneously.
The Cournot model focuses on the production output decision of a single firm. The firm
determines its rival's output level, evaluates the residual market demand, and then changes
its own output level to maximize profits. It is assumed that the firm's output decision will not
affect the output decision of its competitor. For example, suppose that there are two firms in the market for toasters with a given demand
function. Firm A will determine the output of Firm B, hold it constant, and then determine
the remainder of the market demand for toasters. Firm A will then determine its profitmaximizing output for that residual demand as if it were the entire market, and produce
accordingly. Firm B will be conducting similar calculations with respect to Firm A at the same
time. Bertrand Duopoly
The Bertrand model describes interactions among firms that compete on price. Firms set
profit-maximizing prices in response to what they expect a competitor to charge. The model
rests on the following assumptions:
There are two firms producing homogeneous products;
Firms do not cooperate;
Firms compete by setting prices simultaneously; and
Consumers buy everything from a firm with a lower price. If all firms charge the same
price, consumers randomly select among them. In the Bertrand model, Firm A's optimum price depends on where it believes Firm B will set
its price . Pricing just below the other firm will obtain full market demand, though this choice
is not optimal if the other firm is pricing below marginal cost, as this would result in negative
profits. If Firm B is setting the price below marginal cost, Firm A will set the price at marginal
cost. If Firm B is setting the price above marginal cost but belowmonopoly price, then Firm A
will set the price just below that of Firm B. If Firm B sets the price above monopoly price,
Firm A will set the price at monopoly level. Bertrand Duopoly
The diagram shows the reaction function of a firm competing on price. When P2 (the price set by Firm 2)
is less than marginal cost, Firm 1 prices at marginal cost (P1=MC). When Firm 2 prices above MC but
below monopoly prices, Firm 1 prices just below Firm 2. When Firm 2 prices above monopoly price (PM),
Firm 1 prices at monopoly level (P1=PM).
Imagine if both firms set equal prices above marginal cost. Each firm would get half the
market at a higher than marginal cost price. However, by lowering prices just slightly, a firm
could gain the whole market. As a result, both firms are tempted to lower prices as much as
they can. However, it would be irrational to price below marginal cost, because the firm
would make a loss. Therefore, both firms will lower prices until they reach the marginal cost
limit. According to this model, a duopoly will result in an outcome exactly equivalent to what
prevails under perfect competition. The result of the firms' strategies is a Nash equilibrium--a
pair or strategies where neither firm can increase profits by unilaterally changing the price. Colluding to charge the monopoly price and supplying one half of the market each is the best
that the firms could do in this scenario. However, not colluding and charging the marginal
cost, which is the non-cooperative outcome, is the only Nash equilibrium of this model. The accuracy of the Cournot or Bertrand model will vary from industry to industry.
If capacity and output can be easily changed, Bertrand is generally a better model of duopoly
competition. If output and capacity are difficult to adjust, then Cournot is generally a better
model.