Cournot's Duopoly Model

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Duopoly
Introduction
A duopoly is a form of oligopoly. Situation in which two companies own nearly all/all of the market for a given product/service.
It is a specific type of oligopoly where only 2 producers existing one market.in reality, this definition is generally used where only 2 firms have dominant control over a market.
In the field of industrial & organization, it is the most commonly studied form of oligopoly due to its simplicity.
Example 1: In market Pepsi & Coca-Cola rule in soft drinks, so they come under Duopoly. Though other soft drinks companies are also there but these two companies cover large share in soft drinks market.
Example 2: P&G & Uniliver, they have all the products.

Duopolies are most effective when the demand
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However, classical and modern economists have developed a variety of models based on different behaviour assumptions.
1. The Cournot’s Duopoly Model
2. The Chamberlin Duopoly Model
3. The Bertrand’s Duopoly Model
4. The Edgeworth Duopoly Model

1. Cournot’s Duopoly Model:
Augustin Cournot, a French economist, was the first to develop a formal duopoly model in 1838.
To illustrate his model, Cournot assumed:

(a) Two firms, each owing an artesian mineral water well;
(b) Both operate their wells at zero marginal cost;

(c) Both face a demand curve with constant negative slope;
(d) Each seller acts on the assumption that his competitor will not react to his decision to change his and price. This is Cournot’s behavioural assumption.
On the basis of this model, Cournot has concluded that each seller ultimately supplies one-third of the market and charges the same price. While one-third of the market remains
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A has his demand curve DDB and as DDB Let us also assume that seller A has a maximum capacity of output OM and B has a maximum output capacity of OM’. The ordinate ODA measures the price.
To explain Edgeworth’s model, let us assume, to begin with, that A is the only seller in the market. Following the profit maximising rule of a monopoly seller, he sells OQ and charges a price, OP2. His monopoly profit under zero cost, equals OP2EQ Now, let B enter the market. B assumes that A will not change his price since he is making maximum profit. He sets his price slightly below A’s price (OP2) and is able to sell his total output. At this price, he captures a substantial part of A’s market.
Seller A, on the other hand , that his sales have gone down. In order to regain his market, A sets his price slightly below B’s price. This leads to price-war between the sellers.
The price- war takes the form of price-cutting which continues until price reaches OP1 At this price both A and B are able to sell their entire output- A sells OQ and B sells OQ The price OP1 could therefore be expected to be stable. But, according to Edgeworth, price OP1 should not be
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