The inverse demand for a homogeneous-product Stackelberg duopoly is P = 24,000 -

Question

The inverse demand for a homogeneous-product Stackelberg duopoly is P = 24,000 -4Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 3,000QL and CF (QF) = 6,000QF..

a. What is the follower’s reaction function?

QF = _______ - _______QL


b. Determine the equilibrium output level for both the leader and the follower.

Leader output:
Follower output:


c. Determine the equilibrium market price.

$


d. Determine the profits of the leader and the follower.

Leader profits: $
Follower profits: $

Explanation / Answer

P = 24,000 -4Q

CF (QF) = 6,000QF

Profit of follower = P*QF - CF

= (24,000 - 4(QF+QL))QF - 6,000QF

dProfit/dQF = 24,000 - 8QF - 4QL - 6,000

Putting DProfit/dQF = 0

QF = 2250 - QL/2

This is the reaction for follower.

Profit function for Leader =  (24,000 - 4(QF+QL))QL - 3,000QL

=   (24,000 - 4(2250 - QL/2 +QL))QL - 3,000QL

= (24,000 - 4(2250 - QL/2 +QL))QL - 3,000QL

dProfit/dQL = 24,000 - 9000 - 4QL - 3000

Putting dProfit/dQL = 0

Leader output = QL = 12,000/4 = 3,000

Follower's Output= QF = 2,250 - QL/2 = 2250 - 3000/2 = 750

Q = QL + QF = 3000 + 750 = 3750

Market price = P = 24000 - 4*3750 = 9,000

Leader's Profit = 9,000*3000 - 3000*3000 = 18000000

Follower's Profit = 9000*750 - 6000*750 = 2250,000

If you don't understand anything then comment, I'ill revert back on the same. :)

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