Cournot's Duopoly model

DUOPOLY
MUHAMMED SUHAIB M
Head of the Department,
Department of Economics,
KR’s Sree Narayana College, Thozhuvanoor

Duopoly
• Duopoly is a special type of Oligopoly, where only two Producers/Sellers
exist in one market.
• There exists Non-collusive oligopoly, means Sellers are completely
independent.
• The pricing and output of one firm will affect the another and may set a
chain reaction.
• Cournot and Edgeworth ignored mutual dependence but Chamberlin
recognised the mutual dependence.

Cournot’s Duopoly Model
• This is the earliest duopoly model, Developed by French
Economist AUGUSTIN COURNOT in 1838.
• He considered only two firms and they are owing Mineral well.
• Each firm act on the assumption that its competition will not
change its output and decides its own output so as to maximise
his profit.

Major Assumptions
• They are two independent sellers.
• They produce and sell homogeneous products.
• The number of buyers is large.
• Each producer know the market demand for the product.
• Cost of production is assumed to be zero.
• Both firms have identical cost and identical demand.

Major Assumptions
• Each firm decides their own quantity of output and ignores the role of
rival.
• Consider the supply curve of the rival is constant.
• Entry of a new firm is blocked.
• Both firms are aiming maximum profit.
• Neither of them will fixes the price for its product, but each accepts
the market demand price at which the product can be sold.

Price and Output under Duopoly
• Initially, firm A is the only seller
of mineral water in the market.
• By assuming cost of production is
zero, A charges 0P2 price and
supply 0Q quantity.
When MC=MR1, (MC is zero)
• Here he charges monopoly price
and Total Revenue is 0P2PQ

• When firm B entered into the market, He got half of the market share for
his product.
• Firm B assumes that firm A will not change his price and output, then
market available for B is PM of demand curve.
• Here firm B supplies his product to the half of his market control (when
MR2-MC(MC is zero))
• Firm B’s Price is 0P1 and output is QN and Total Revenue is QRP’N

• Here both firm A&B are supplying half of the market share they have.
• Firm B supplies only ¼ of the total market demand, (which is ½ x ½ = ¼ ).
• The low price of firm B will compel firm A to reduce the Price, the firm A will
restructure his Price and Output.
• When firm A assumes that firm will continue its production at ¼ of market
demand, the total market share available for firm B is ¾ , which is (1- ¼ = ¾ ).
• To maximise his profit (firm A), he will supply half of the total market share
available for him, (which is ½ x ¾ = 3/8 )

• Here, firm A’s share will fall from ½ to 3/8.
• Then, firm B also assumes that firm A will
continue to supply 3/8 of the market
demand, the total market demand available
for firm B is 1- 3/8 = 5/8.
• To maximise his profit (firm B) under new
market condition B will supply half of his
market demand, which is ½ x 5/8 = 5/16.
• Then firm A will also change his Price and
Output accordingly.

• This process of action and reaction continues in successive periods, means
firm A will loss his market share and firm B will gain till both firms get equal
share in the market.
• At the end of this process both firms will have 1/3 share of market demand.
• The final price will be greater than the competitive price and less than the
monopoly price.
• In case of industry or market 1/3 portion of demand will be unsupplied.
• In general, if there are ‘n’ firms in the industry, each will provide 1/n+1 of
the market and the industry output will be n/n+1

Criticism
• The model does not say how long the adjustment period will be.
• The costless production is unrealistic.
• This is closed model because it does not allow entry of firms.
• This is a no-learning by doing model .
• He assumed the supply of rival is fixed but here supply is repeatedly
changing.

Cournot's Duopoly model

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