Question #50573

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 µ = 100 – Q, 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?

Expert's answer

An essential assumption of this model is the "not conjecture" that each firm aims to maximize profits, based on the expectation that its own output decision will not have an effect on the decisions of its rivals. The market price is set at a level such that demand equals the total quantity produced by all firms. Each firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a monopoly.

If the firms have identical cost functions given by C (Q) = 40 Q, so every firm produce the quantity, for which MR = MC.

MC = C' = 40

MR = TR' = (P*Q)' = ((100 - Q)*Q)' = 100 - 2Q

So, 100 - 2Q = 40,

Q = 30

So, the equilibrium industry output if the producers are Cournot competitors is 30*4 = 120 units.

The market price is P = 100 - 30 = $70.

Total profits of each firm are: TP = TR - TC = P*Q - TC = 70*30 - 40*30 = $900.

If the firms have identical cost functions given by C (Q) = 40 Q, so every firm produce the quantity, for which MR = MC.

MC = C' = 40

MR = TR' = (P*Q)' = ((100 - Q)*Q)' = 100 - 2Q

So, 100 - 2Q = 40,

Q = 30

So, the equilibrium industry output if the producers are Cournot competitors is 30*4 = 120 units.

The market price is P = 100 - 30 = $70.

Total profits of each firm are: TP = TR - TC = P*Q - TC = 70*30 - 40*30 = $900.

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