P=30-Q

(d) Now consider a typical Cournot duopoly situation such that the market is being served by

two firms (Firm 1 and Firm 2) that simultaneously decide on the level of output to sell in the

market, while producing an identical product.

The total output of the industry is Q = q1 + q2, where q1 and q2 are the output of Firm 1 and

2, respectively. Each firm has a symmetric cost function: C(q1) = 12 q1 and C(q2) = 12 q2.

(i) Write down the (inverse) market demand function for this situation and the resultant

profit functions for both firms.

(ii) Derive the reaction functions for Firm 1 and Firm 2.

(iii) What is the Cournot-Nash equilibrium output level (qN) for each firm? Explain.

(iv) Calculate the market price of the product (pN).

(v) What will be the total market output (QN) for both firms together?

(vi) Calculate the allocative inefficiency resulting from this market structure. Compare it to

that under the monopoly market in part (a).

(e) What can you say, in general, about the Cournot-Nash equilibrium quantities and prices as

the number of sellers (n) competing in the industry rises?

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