Stackelberg Model

The Stackelberg model is an economic model of industry structure in which a market leader firm sets its output level first, and follower firms then decide their output levels based on the leader’s decision.

TLDR

Sequential output decisions

Assumptions

• One of the firms sets its output first
• The other firm observes this decision and sets its own output second
• Firm 1 knows that Firm 2 will react and has to take that into account when setting its output.
• Firm 2 takes the output decision of Firm 1 as given and sets its output using the cournout reaction function.

Example

Building on „Example Extreme Duopoly“ assume that firm 1 decides first on its quantity. Firm 2 observes the decision of firm 1 and decides subsequently (i.e. firm 1 is the Stackelberg-Leader). Calculate the profits of the two firms.

$F_1$ chooses $q_1$, then $F_2$ chooses $q_2$ Suppose $F_1$ choose $q_1\to q_2(q_1)=(30-q_1)/2$ $F_1$s problem: $(30-q_1-(30-q_1)/2)q_1$ → max $q_2$ $1/2(30-q_1)q_1$ $30-2q_1=0$ $q_1^{\ast }=15$ $q_2^{\ast }=7.5$

First Mover Advantage of the Stackelberg Model

Conclusions for symmetric firms:

• The output of Firm 1 is two times larger than that of Firm 2
• The profit of Firm 1 is two times larger than that of Firm 2 (first mover advantage) Nash Equilibrium reached

This is only true for symmetric firms and constant marginal costs!