Two firms produce a homogeneous product. Let p denote the product's price. The output level of firm 1 is denoted by q₁, and the output level of firm 2 by 92. The aggregate industry output is denoted by Q, Q = 91 +92. The aggregate industry demand curve for this product is given by p = 70 - Q. Assume that the unit cost of firm 1 is c₁ = 10 and the unit cost of firm 2 is c₂ = 20. a. Suppose the firms move simultaneously and compete on quantities. Derive the firms' best response functions, and find the Cournot-Nash equilibrium. What are the profits of the firms? b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2. Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2? c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findings between part b and c? Explain why.
Two firms produce a homogeneous product. Let p denote the product’s price. The output level
of firm 1 is denoted by q1, and the output level of firm 2 by q2. The
denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given by
p = 70 − Q.
Assume that the unit cost of firm 1 is c1 = 10 and the unit cost of firm 2 is c2 = 20.
a. Suppose the firms move simultaneously and compete on quantities. Derive the firms’ best
response functions, and find the Cournot-Nash equilibrium. What are the profits of the
firms?
b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2.
Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2?
c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournot
equilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findings
between part b and c? Explain why.
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