Edgeworth Duopoly Model: Assumptions, Diagram with Explanation
EDGEWORTH DUOPOLY MODEL
F. Y. Edgeworth, a famous French
economist criticized Cournot’s assumption that each duopolist believes that his
rival will continue to produce the same output irrespective of what he himself might
produce.
Edgeworth’s model follows Bertrand’s assumption that each duopolist believes that his rival will keep his price constant irrespective of what price he himself sets. With this assumption, and taking the example of Cournot’s “mineral wells”, Edgeworth showed that no determinate equilibrium would be reached in duopoly.
Assumptions:
1- It has two firms.
2- It is not essential in this model that the product
of duopolists should be perfectly homogenous. This model will be applicable for
slightly differentiated product or we can say close substitute also. However,
in our analysis below we assume that the products of the two duopolists are perfectly
homogeneous.
3- Both firms compete with price.
4- Both
the firms have equal per unit cost.
5- The
productive capacity of each duopolist is limited.
6- Both
the firms sell their maximum possible output at the competitive price, where
price becomes equal to average cost.
7- In Edgeworth’s model also each producer believes that his rival will keep his price constant at the present level whatever price he might himself set.
The main difference between
Edgeworth’s model and Bertrand’s model is that whereas in Bertrand, productive
capacity of each duopolist is practically unlimited so that he could satisfy
any amount of demand but in Edgeworth’s model, the productive capacity of each duopolist
is limited so that neither duopolist can meet entire demand at the lower price
ranges.
Each duopolist accepts as much demand of the product at a price as he can meet.
In
Edgeworth’s model it is assumed that there are two sellers, A and B, in the
market who face identical demand curves.
A has his demand curve DA and B, as DB. OA2 and OB2 are the maximum possible output of each seller. [OA2=OB2] OD shows the price for both.
If both the sellers combined, they would sell OA1and
OB1 outputs at OP price. Suppose there is no collusion between the two. Seller
A is already in the market selling OA1 units at OP price. Now seller B believes
that A will not change the OP price whatever he does. He, therefore, by setting
a slightly lower price [OP1] than OP can attract a number of seller A's
customers to dispose of his entire output OB2. Seller A finding his sales being
reduced, will reduce his price to P2 and sell his entire
maximum possible outputs. This will lead to a price
war between the two till the price reaches OQ at which both A and B sell the
entire output OA2 and OB2 which they produce.
According to Edgeworth, OQ should not be regarded as a
stable price. For at this price only A2B2 customers are served by both the
sellers, leaving A A2 and BB2 customers unserved. The latter customers will be
glad to be served at any price less than OD. So, suppose seller A decides to
serve them at OP price, the most advantageous to him. B, on finding that A is
earning larger profit OA1EP, follows him by raising his price to OP and earns
the benefit OB1CP which is equal to seller A. According to Edgeworth: “we
return to the position from which we started and are ready to begin a new
cycle.” Price, in Edgeworth's solution, moves periodically between OP and OQ,
never stopping for even a moment. In Edgeworth's words: “There will be an
indeterminate tract through which the index of value will oscillate, or rather
will vibrate irregularly for an indefinite length of time.”
Thus, no determinate and unique
equilibrium of duopoly is suggested by Edgeworth’s duopoly model.
Edgeworth’s model is definitely an
improvement upon Cournot’s model. As in this model, price rather than output is
used as the decision variable.
You are great Mam.
ReplyDelete