Meaning and Features of Duopoly and COURNOT’S DUOPOLY MODEL-Assumptions, Diagram with Explanation, it's Defects
DUOPOLY
Duopoly is a market situation where
there are only two sellers. Both the sellers are completely independent and no
agreement exits between them. In spite of being independent, each seller has to
carefully consider the indirect effects of its own decision to change its price
or output or both, as it will affect the other.
Duopoly can be with or without product
differentiation.
Features of duopoly
1-There are only two companies that share the
market.
2- Both sellers within a duopoly are interdependent.
Even each seller may affect the other by his market policies. That’s why each
seller attempts to make a correct guess of the rival’s motives and actions.
3- Seller makes different policies basically price
reduction for increasing the demand for the product. If a seller reduces the
price of the product, the other will also do the same and it won’t impact on
demand, but if the seller will increase the price, other will not follow it and
it will cause to decrease in demand.
4-Since companies in a duopoly take different
measures to develop brand loyalty and implement
low-pricing strategies, there is the barriers for new firms to enter. So, there
is only one competitor.
Duopoly models
A model of duopoly was first of all put forth by Cournot, a French economist, in 1838. Cournot’s model was criticized in1883 by Joseph Bertrand, a French mathematician, and developed another model of duopoly. In 1897, Edgeworth, a famous Italian mathematician and economist, offered another model of duopoly in an article published in an Italian journal.
These three duopoly models are
based upon a behavioral assumption about an individual firm that it does not
take into account rival’s reactions to the output or price fixed by it.
COURNOT’S
DUOPOLY MODEL
The earliest duopoly model was developed in 1838 by the French economist A.A. Cournot. In this model, there are two sellers. There are barriers for the other sellers to enter in the market. Collusive behavior is prohibited.
Assumptions
The Cournot model is
based on the following assumptions:
(1) There are two independent sellers who
produce and sell a homogeneous product. Cournot
takes the case of two identical mineral springs operated by two owners who are
selling the mineral water in
the same market. Their waters are identical.
(2) The total output
must be sold out, being perishable and non-storable.
(3) The number of
buyers is large.
(4) Each seller knows the demand curve for the
product. Both sellers fully know the
market demand for the mineral water. Moreover, the market demand for the
product is assumed to be linear, that is, market demand curve facing the two
producers is a straight line.
(5) It is based on
the assumption of zero cost of production. Cournot assumed that the owners
operate mineral springs and sell water without any cost of production for the
sake of simplicity. Thus, in Cournot’s model, cost of production is taken as
zero.
(6) Each seller
decides about the quantity he wants to produce and sell in each period.
(7) Each seller takes the supply of his rival as constant. Cournot assumes that each seller believes that regardless of his actions and their effect upon market price of
the product, the rival
firm will keep its output constant.
(8) Each seller
decides its level of output independently.
(9) Neither of them
fixes the price for his product, but each accepts the market demand price at
which the product can be sold.
(10) Each seller aims
at obtaining the maximum net revenue.
Cournot’s
Approach to Equilibrium
Suppose there are two mineral springs exploited by two entrepreneurs, A and B. The demand for the mineral water is given by the straight-line demand curve MD.
For
the simple reason it is assumed that total cost is zero, the marginal cost is
also zero and if a marginal revenue curve is drawn, it would be a straight line
from M to N Therefore, at ON output MC=MR at zero price. Let’s assume that entrepreneurs
A is the first to produce and sell this amount ON at NK[=OP] price and thus
earn ONKP as monopoly profit. (Since the costs are zero,
the whole revenue ONKP will
be profits). Here
the Cournot solution actually begins. B who starts production now knows that A
will not change his output from ON units. According to
Cournot’s behavioral assumption, the producer B
believes that the former producer A
will continue to produce ON (=1/2
OD] amount of output,
regardless of what output he himself decides to produce. He regards the segment KD as
his demand curve. He accordingly produces NH= [1/2 ND] units and sells them at
HL(=OP2) price. Because when KD is the demand curve its corresponding MR curve will pass through H, halfway between ND. Since each seller
is assumed to sell his product at the ruling market price, the total
supply OH will be sold at OP2 price. Total profit decreases to OHLP2 of which
ONGP2 is A's and NHLG is B's profit. Now it is A's move for he knows that B
will continue to produce NH units. In his attempt to restore his profits,
seller A reduces his supply to 1/2 (OD-B’s supply).
Now that producer B
has been surprised by the reduction of output by producer A
and he will also find that his share of total profits is less
than that of producer A, he will
reappraise his situation and raise his supply by 1/2(OD-New Output of A). This process will
continue whereby A will be forced to reduce his supply gradually by B's moves
and B will continue to increase his supply side by side, until the total output OT is produced (OT=2/3 OD) and each is
producing the same amount of output equal to 1/3
OD. Thus ultimately, the total supply OT will be sold at
OP1[ST] price, consisting of OC units of producer A's and CT units of B's
output, where OT=OC +CT. This is the determinate position-one of stable
equilibrium because 1/2(OD-OC) =CT, and A's profit OCEP1=CTSE, B's profit. Thus,
the total produce will ultimately be of equally divided between the two
producers, and TS(=OP1) price will be charged.
Firm will adjust its output as I have shown with an example below.
Thus, in Cournot’s model of duopoly, stable equilibrium is reached when total output produced is 2/3rd of OD and each producer is producing 1/3rd of OD.
Cournot’s model’s defects- According to Cournot model, while deciding its output, each firm
assumes that the other firm will keep its output constant, independent of what
output it produces. Yet in the adjustment process to the equilibrium position
the other firm reacts to the output decision of its rival as it affects it's profits except at the unique Cournot equilibrium point.
A rational behavior demands
that duopolistic should quickly recognize their mutual interdependence and act
accordingly. Thus, Cournot model has been described as “no
learning by doing model”.
Joseph
Bertrand, a French mathematician, criticizing Cournot in 1883 pointed out that
seller A in order to regain all the customers lost to B, will fix a price slightly
below that fixed by B and price cutting may continue until the price becomes
zero. Thus, Bertrand argued that there would not be any limit to the fall in
price since each seller could by doubling his produce underbid his rival. He,
therefore, suggested a solution based on rival's constant price. Marshall also
regarded Cournot's cases as "incapable of a universal solution."
Pareto, however, supported Cournot and found it realistic to assume some fixed supply. Cournot model is also useful as it presents a simple model of market structure from which the relationship between market power and market shares supplied by an individual firm can be derived and the tendency towards collusion and monopoly pricing and output fixation is clearly brought out.
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