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  Stackelberg’s Duopoly-Leader-Follower Model

Stackelberg’s Duopoly (Leader-Follower Model):

In Cournot’s duopoly, we assumed that λ = 0 . But, if the decision on production is sequential or if there is a gap in competitive power, then one firm acts as a leader and the others as followers.

Stackelberg demonstrated another duopoly model with leader and followers. In his model, leader acts as if the other firm’s output is constant, and followers, however, choose optimal products in response to leader’s output.

1) If leader/follower are predetermined:

* Firm 1 (leader) and Firm 2 (follower). Identical in almost every aspect.

* Market demand: P = a − (q1 + q2) , same demand in Cournot model.

* MC1 = AC1 = c = AC2 = MC2

* If q1 is determined, q2 that maximizes π2 will be: q2 = (a - c - q1)/2 .....(i)

* And, Firm 1 (leader) can expect that Firm 2 will produce q 2 = a-c-q1 if Firm 1 produces q1. So, plugging the reaction curve of Firm 2 into π1,

270_stackelbergs.jpg

* By the way, the Firm 2 (follower) will produce q2 in response to q1*= (a - c)/2.

1457_market price.jpg

2) If leader/followers are not certain:

We know every firm wants to be a leader because the leader’s profit is always bigger than that of follower. So, if the leader and follower are not determined before they start game, we might expect different results.

Every firm has two strategies; Lead and Follow.

* If two firm act as leaders ad produce q1 and q2,

q1* = q2*= (a-c)/2, P = a − (q1 + q2) = c , π π 1 = (P − c)q1 = (P − c)q2 = 2 = 0

Identical to Perfect Competition (Stackelberg Warfare)

* If two firms act as followers and produce q1 and q2 ,

1539_cournot duopoly.jpg

It is Cournot Duopoly.

1362_stackelberg warfare.jpg

C: Cournot-Nash Equilibrium Point
S1: If Firm 1 is a leader
S2: If Firm 2 is a leader
W: Stackelberg Warfare

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