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Stackelberg duopoly

I have changed the values and need the model to plug my numbers in.
Please solve with explanations.

1. The inverse demand curve for a Stackelberg duopoly is

P = 5,000 - 3Q.

The leader's cost structure is

CL(QL) = 1250 + 10QL.

The follower's cost structure is

CF(QF) = 250 + 20QF.

a. Determine the reaction function for the follower.
b. Determine the equilibrium output levels for both the leader and the follower.
c. What are the profits for the leader? For the follower?

Solution Preview

<br><br>In a Stackelberg Model the price of the good depends on the quantity produced by both the leader and the follower. Hence the price function becomes:
<br><br>P = 5,000 - 3(QF+QL)
<br><br>Now, let us start with the follower's problem. He is a profit maximizer. Hence the profit maximizing equation for the follower becomes:
<br><br>Max: P*QF -CF
<br><br>Substituting the above from the equations given in the problem:
<br><br> Max: [5,000 - 3(QF+QL)]*QF -[250 + ...

Solution Summary

Stackelberg duopoly is exemplified.