Suppose that the dancing machine industry is a duopoly. The two firms, Chuckie B

Question

Suppose that the dancing machine industry is a duopoly. The two firms, Chuckie B Corp. (CBC) and Gene Gene Dancing Machines (GGDM), compete through Cournot competition. CBC has a constant marginal cost of 4. The inverse demand curve is given by P = 28 ! 3Q, where P is the market price and Q is the sum of the two firms’ output. CBC produces 3 units in the initial Cournot equilibrium. If GGDM experiences a cost reduction that increases the amount GGDM produces in the new Cournot equilibrium (i.e. after the cost reduction) by 4 units, how much does CBC produce in the new Cournot equilibrium?

Why is the answer 1?

Explanation / Answer

P = 28 - 3Qc -3Qg

For firm CBC

Qc=3

Rc = 28Qc-3Qc^2-3QcQg

MRc = 28-6Qc-3Qg

MC = 4

MRc=MC

2Qc+Qg = 8

Qg = 2 as it given Qc=3

Now with decrease in cost of production Qg(new) = 2+4 = 6

Now 2Qc(new) + Qg(new) = 8

Qc(new) =(8-6)/2 = 1

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