# Cournot Duopoly Model Characteristics

__Meaning of Duopoly__

Duopoly is exactly a special case of thesis of Oligopoly, in which there are two sellers involved and are absolutely at liberty and no contract persists between them. Notwithstanding their liberations, the variations in price and productivity of one will affect the other one indeed and the subsequent reactions are to follow. One seller nevertheless presumes that his competition is impassive by his activity; in that case he takes only his own leading persuasion on the price of that commodity.

Alternatively, every seller among the two will considers the consequence of his policy on that of his competition and the response of the competition on himself once more then he takes into account both straight and meandering power upon the price of that commodity. Furthermore, a competitive seller’s policy may stay untouched either to the sum proffered for sale or to the price at which he offers his product. In this way the complexity of duopoly can be regarded as either avoiding mutual liberty or identifying it.

__Cournot’s Model of Duopoly__

This model is the ancient models of determining duopoly complexities. Cournot’s Model is based on the following postulations.

__Postulations__

- There are two sellers at liberty. Conversely, mutually dependence of the duopolists is ignored.
- They manufacture and sell standardised goods.
- The total productivity has to be sold out, being non-durable and non-warehoused.
- The number of consumers is huge.
- Each seller among the two is very well aware of the market demand curve of the commodity.
- The cost of manufacturing is presumed to be zilch.
- Every of the two industries have like costs and like demands.
- Every of the two sellers fixes on about the volume he wants to manufacture and sell in each product.
- But both the sellers are unaware of the competitive strategies of each other regarding the productivity.
- At the same time each seller takes the supply or productivity of its competitor as invariable.
- Neither of both decides the price for their commodities but each accepts the market demand price at which the commodity can be sold.
- The entry of firm is blocked.
- Each seller aims at obtaining the maximum net revenue or profit.

An illustration would explain us clearly the duopoly situation in the market.

__Illustration 1__

Let us consider the market for Electronic devices are represented by a duopoly, where both the firms are producing productivities of Ax and Ay in that order. The inverse market demand function is denoted by V = 200 – 4A, (where A = Ax + Ay). The marginal cost that each industry expends is $8.

- What are the response tasks of the Cournot Duopolists?
- Compute each industry’s productivity and the market price at Cournot’s Equilibrium.

__Solution__ __Condition
1__

At first, we have to ascertain the market demand (A) when V = MC, (marginal cost). For this fixing the inverse demand task equalling to MC, we have the following.

200 – 4A = 8

- ⇒ 4A = 200 – 8
- ⇒ 4A = 192
- ⇒ A = 192 / 4
- ⇒ A = 48

Response task of the **Second industry** of manufacturing electronic device
is –

Ax
= __48 – Ay__ ………….
Equation (1)

2

Response task of the **First industry** of manufacturing electronic device
is –

Ay
= __48 – Ax__ …………..Equation
(2)

2

To ascertain Ax we have to substitute the value of Ay in Equation 1 and we obtain the
following

Ax
= 48 – [ 4__8 – Ax__ ]

__ 2 __

2

- ⇒
__48 – 24 + (½ Ax)__

2 - ⇒ Ax = 24 – 12 + (¼ Ax)
- ⇒ 1Ax = ¼ Ax + 12
- ⇒ 1Ax – ¼ Ax = 12
- ⇒ ¾ Ax = 12
- ⇒ Ax = 12 x 4/3
- ⇒ Ax = 16.

Similarly, Ay will also be 16 which is obtained by substituting the value of Ax in the equation (2).

__Condition 2__

Total productivity A under Cournot duopoly equilibrium will be as follows.

As told in the problem, the condition for A = Ax + Ay, hence A = 16 + 16 which is 32.

Hence Total Productivity A is 32 under Cournot duopoly equilibrium.

The inverse demand task is represented as V = 200 – 4A, by substituting value
A as 32, we get the inverse market demand task 72.* ( 200 – [4x32] = 72)*

**Hence V = 72, A = 32 and Ax and Ay is 16 each.**

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