Question

3) (Symmetric Cournot) Consider a duopoly facing market demand p(Q) = 90 – 3Q, and assume each firm has cost function C(q) = 18q. For parts a-d, suppose these two firms engage in Cournot competition – that is, they simultaneously choose a quantity to produce, and then the price adjusts so that markets clear. [Recall that a firm’s Cournot best response function is the quantity that this firm will choose to produce in order to maximize its own profit, for any given quantity of the other firm. You can focus on the range in which this quantity is positive.]

a) Derive firm 1’s best-response function q1=b1(q2).

b) Derive firm 2’s best-response function q2=b2(q1).

c) Calculate the Cournot-Nash equilibrium [Find the intersection of the two best response functions].

d) In this equilibrium, what is the market price? In this equilibrium, what are the firms’ profits? How does this outcome compare to the competitive outcome?

e) Suppose the two firms could merge so that a Monopoly with the same cost function would operate in the market. Find the market price and quantity. How does this outcome compare to the Cournot-duopoly outcome in terms of price quantity and the combined total profit for the firms?

f) If instead the same market was served by an oligopoly of 5 firms, that compete according to the Cournot Model, what would be the equilibrium price.

Answer 1