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Cournots Model Of Oligopoly

   Establishment of Price and Productivity under Oligopoly Rivalry

Cournot’s Model

Illustration 82

Presume the market demand curve for a homogenous commodity is provided by R = 200 – V. There are two industries each with an invariable marginal cost MC of $20. We are to ascertain that if these two industries behave as Cournot Duopolists, what will be the symmetry price and total industry productivity.

Solution

Cournot’s solution to the duopoly problem cannot be made by obtaining the reaction functions of the two industries. For procuring the reaction function we need to evaluate the marginal revenue MR of every duopolist which is equated by him with marginal cost MC to optimum profits. Therefore, for manufacture (1),

                        TR       =          R.V1

Where TR symbolises for total revenue, which can be procured from multiplying rate with volume manufactured and sold.

As                    R         =          200 – V

                        TR1     =          (200 – V).V1

Therefore,        V         =          V1 + V2 we have

                       TR1     =          200V1 – (V1 + V2) V1

                                  =          200V1 – V1^2 – V2.V1

 Now,             MR1    =          ΔTR1   =          200 – 2V1 – V2
                                                 ΔV1

Now setting marginal revenue MR of product 1 equal to marginal cost MC to optimise profits, we have

                                   MR1    =          MC

            200 – 2V1 – V2          =          20

            200 – 20 – V2             =          2V1

                        180 – V2         =          2V1

                                    V1       =          180 – V2
                                                                   2

                                                =          90 – ½ V2                               …..Equation (1)

The Equation (1) is the reaction function of industry (1).

Likewise, reaction function of industry (2) can be formulated which will be equal to:

                        V2       =          180 – V1         =          90 – ½ V1
                                                      2

Now, the two reaction function equations can be mutually resolved to procure the values of V1 and V2. Therefore,

                        V1       =          90 – ½ V2                               ….. (1)

                        V2       =          90 – ½ V1                               ….. (2)

Substituting the value V2 in (1), we have

                        V1       =          90 – ½ (90 – ½ V1)

                                   =          90 – 45 + ¼ V1

                        V1       =          45 + ¼ V1

                       -45       =          ¼ V1 – V1

                       45        =          ¾ V1

                        V1       =          45 * 4/3           =          60

Substituting the value of V1 = 60 in (2), we obtain the value of V2 as follows:

                        V2       =          90 – ½ (60)

                                   =          90 – 30

                        V2       =          60

Therefore, under Cournot’s duopoly solution V1 = V2 = 60 and aggregate firm productivity is 120, i.e. V1 + V2 = 60 + 60 = 120.

Now substituting the value of V in the market demand function, we have,

                        R         =          200 – V

                                    =          200 – 120

                        R         =          80

Therefore, price predetermined in Cournot’s duopoly model, price or rate R will be equal to $80.

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