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Cournot's Duopoly model

This document summarizes the Cournot duopoly model of market competition between two firms. It explains that under Cournot's assumptions, the two firms will each capture 1/3 of the market share and settle at an equilibrium price point between the competitive and monopoly prices. The model involves the firms reacting to each other's output and price decisions in successive rounds until they split the market evenly. Some criticisms of the model are that it assumes costless production and does not allow for new firm entry or learning over time.

Education◦
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
Price and Output under Duopoly • 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
Price and Output under Duopoly • 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 )
Price and Output under Duopoly • 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.
Price and Output under Duopoly • 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