We showed that, when demand is linear and marginal cost is constant, the Stackelberg leader produces the monopoly output while the Stackelberg follower produces half the monopoly output. If the leader and follower now enter a simultaneous quantity setting game, why can't the leader maintain the same equilibrium?

Question

What will be an ideal response?

Answer 1

If the two firms move simultaneously, firm 1 might tell firm 2 that it will produce the monopoly quantity (just as if it were the Stackelberg leader). If firm 2 believes firm 1, it will produce half the monopoly quantity as a best response (just like a Stackelberg follower). But if firm 2 were to produce half the monopoly quantity, firm 1's best response is to produce less than the monopoly quantity (according to the best response functions we have derived). Firm 2 knows this -- and so it knows that if firm 1 believes firm 2 will produce half the monopoly quantity, firm 1 will not in fact produce the monopoly quantity as it said it would. Thus, firm 1's claim that it will produce the monopoly quantity is not credible. It becomes credible in the Stackelberg game because firm 1 moves first and can actually show that it has produced the monopoly quantity.