Solution
Stackelberg Leadership
Show the problem again
In the same market as the Cournot duopoly (price P = 120 − Q, zero costs), Firm 1 commits to its quantity first and Firm 2 observes it before choosing its own. In the subgame perfect equilibrium, what quantity does the leader (Firm 1) produce?
Worked solution
The leader produces 60 (and the follower 30). The follower best-responds with q₂ = (120 − q₁)/2. The leader substitutes this in and maximizes q₁(120 − q₁ − (120 − q₁)/2) = q₁(120 − q₁)/2, giving q₁ = 60, then q₂ = 30. Price is 30; the leader earns 1800 (up from Cournot's 1600) and the follower 900: a clean quantification of first-mover advantage.
Source: Heinrich von Stackelberg, 'Marktform und Gleichgewicht' (1934). Statement written for AxiomIQ.