Consider a Cournot oligopoly consisting of five identical firms producing good X

Question

Consider a Cournot oligopoly consisting of five identical firms producing good X. If the firms produce good X at a marginal cost of $7 per unit and the market elasticity of demand is %u22123, determine the profit-maximizing price.
$7.50 per unit $5.25 per unit $7 per unit $4.20 per unit
Consider a Cournot oligopoly consisting of five identical firms producing good X. If the firms produce good X at a marginal cost of $7 per unit and the market elasticity of demand is %u22123, determine the profit-maximizing price.
$7.50 per unit $5.25 per unit $7 per unit $4.20 per unit

Explanation / Answer

dC(x)/dQ(x) =7

C(x)=7Q(x)

total cost,C=5*C(x)=35Q(x)

elasticity of demand=(-dP/P)*(Q/dQ)=-3

dP/P=3dQ(x)/Q(x)

P=Q(x)^3

revenue=P*Q(x)=Q(x)^4

profit=Revenue-Cost=Q(x)^4-35Q(x)

for profit maximization d(profit)/dQ(x)=0

price=$7.50 per unit

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