CFA Level IEconomicsHard
Two identical firms compete as Cournot duopolists in a market with inverse demand P = 120 - Q, where Q = q1 + q2, and each firm has zero marginal cost. What is the Cournot-Nash equilibrium market price?
- A$40
- B$0
- C$30
- D$60
Show answer & explanationAnswer & explanation
Correct answer: A. $40
In symmetric Cournot equilibrium with linear demand P=a-Q and zero marginal cost, each firm produces q* = a/3 = 120/3 = 40. Total quantity Q = q1+q2 = 80, so equilibrium price P = 120 - 80 = $40. This lies between the competitive outcome (P=0) and the monopoly outcome (P=60), reflecting the intermediate market power under Cournot competition.
Why the other options are wrong
- B. Incorrect—this would be the perfectly competitive price where P=MC=0, not the Cournot outcome.
- C. Incorrect—this doesn't correspond to the standard symmetric Cournot solution for this demand curve.
- D. Incorrect—$60 is the monopoly price if a single firm maximized joint profit, not the duopoly Cournot price.
Cournot Duopoly Equilibrium
In a symmetric Cournot model with linear demand P=a-Q and marginal cost c, each firm produces q*=(a-c)/3, yielding a market price between the competitive and monopoly outcomes.
- Each firm's output: q* = (a-c)/3
- Total industry output: 2(a-c)/3
- Cournot price lies between competitive (P=MC) and monopoly price
Memory trick: Two rivals split the market pie into thirds — 'Cournot cuts it into three.'