IGNOU MEC 1 2016 2017 - Assume that there are four firms supplying a homogenous product. They

Question

Assume that there are four firms supplying a homogenous product. They have identical
cost functions given by C(Q) =40 Q. If the demand curve for the industry is given by
, find the equilibrium industry output if the producers are Cournot
competitors. What would be the resultant market price? What are the profits of each
firm?

11 Apr 2017

Answer :

Word Count : 460

In Cournot competition, firms compete by choosing the quantity of output they will produce, taking into account the output levels of other firms in the market. This scenario involves four firms supplying a homogeneous product with identical cost functions given by \( C(Q) = 40Q \). The demand curve for the industry is represented by \( P(Q) = 120 - Q \), where \( P \) is the price and \( Q \) is the total industry output.

The Cournot model assumes that each firm decides its output level simultaneously, considering the output decisions of the other firms as given. Let's denote the output level of each firm as \( q_i \), where \( i \) ranges from 1 to 4.

The total industry output (\( Q \)) is the sum of the output levels of all four firms:

\[ Q = q_1 + q_2 + q_3 + q_4 \]

Since the cost function is given

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