The inverse demand for a homogeneous-product Stackelberg duopoly is P = 16,000 -

Question

The inverse demand for a homogeneous-product Stackelberg duopoly is P = 16,000 -4Q. The cost structures for the leader and the follower, respectively are CL(QL) = 3,000QL and CF (QF) = 6,000QF. What is the follower's reaction function? QF = _____ - _____ QL. Also, determine the equilibrium output level for both the leader and the follower. Leader output:____ and Follower output:_____. Also, determine the equilibrium market price. $______. Finally, Determine the profits of the leader and the follower. Leader profit$:____ and Follower profit: $______.

Explanation / Answer

Part-1) Solution: 1,250 - 0.5QL

Working:

Qf = [(16,000 - 6,000) / 2*4] - (1/2Ql)

Qf = 1,250 - 0.5QL

Part-2) Solution: Leader output: 2,000; Follower output: 250

Working: Ql= 2000; Qf=250

Part-3) Solution: Equilibrium market price: 7,000

Working: Equilibrium market price = 16,000 - 4*2,250 = 7,000

Part-4) Solution: Leader profits: 8,000,000; Follower profits: 250,000

Working: Ql= 8,000,000; Qf=250,000

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