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 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?

Answer 1

Answer on question #58688-Economics- Microeconomics

Assume that there are four firms supplying a homogenous product. They have identical cost functions given by $C(Q) = 40Q$. If the demand curve for the industry is given by $\mu = 100 - Q$

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?

Solution

Market demand $\mu = 100 - Q = a - bQ$

Cost function $C(Q) = 40Q = cQ$

Each individual firm’s output

$$\mathrm{q_i} = \frac{Q}{N} = \frac{a - c}{b(N + 1)},$$

where $N$ – number of firms

Total industry output $\sum q_i = Nq_i = \frac{N(a - c)}{b(N + 1)} = \frac{4*(100 - 40)}{1*(4 + 1)} = 48$

Market price $\mu = a - b(Nq) = \frac{a + Nc}{N + 1} = \frac{100 + 4*40}{4 + 1} = 52$

Profits of each firm $P_i = (\mu - c)(\sum q_i / N) = (52 - 40)*(48 / 4) = 144$

Answer

Equilibrium industry output equal 48

Market price equal 52

Profits of each firm equal 144

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