Question #50470

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.

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.

## Comments

Assignment Expert23.09.15, 18:05Dear visitor, please use panel for submitting new questions

MANESHA23.09.15, 12:44A consumer’s utility function is given as U(x,y) = In (x+2y-

) Where x and y are two goods of consumption. (a) Find the indirect utility function of the consumer. (b) Examine if Roy’s law is satisfied by the consumer’s demand function for y. (c) Find the expenditure function of the consumer

e(p,u)

where price of x = 1 and price of y = p. (d) Find the Hicksian demand function

hy (p,u

) for commodity y, where the price of x is 1 and the price of y is p

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