Stackelberg (1934) proposed a dynamic model of Duopoly in which a dominant (or leader) firm moves first and a subordinate (or follower) firm moves second. Consider a model in which firms choose quantities sequentially and then compete according to the Cournot model. Timing: firm 1 chooses quantity q1>0, firm 2 observes q1 and then chooses q2>0. Demand: let Q=q1+q2 be the total quantity sold, then P=a-Q is the inverse demand function where a is a positive constant. Cost: both firms have constant marginal costs equal to c.
1. Write down the profit function of each firm as a function of q1 and q2.
2. Sequential games like the Stackelberg model are solved using backward induction. Therefore, given that player 1 chose q1, what is the best reaction function of player2? Compare this reaction function to the one you would obtain for firm 2 if this was a simultaneous move Cournot.
3. Given firm 2’s reaction function what will be the optimal q1 that firm 1 chooses?
4. What are the equilibrium quantities, equilibrium price, equilibrium profits and equilibrium shares?
5. Compare the above to those coming from the simultaneous Cournot