Question

Assume a duopoly (firms 1 & 2) has the following demand:

          P = 100 - 0.5 (q₁ + q₂) where

          q₁ and q₂ are outputs for firm 1 and 2 respectively.

     The cost functions are as follows:

          c₁ = 5q₁

          and c₂ = 0.5q₂²

1.   If the firms maximize individual profits (Cournot solution):

     (i) How much will each firm produce? Be sure to state each firm’s reaction function.

     (ii) How much profit does each firm make?

     (iii) What are the industry’s total output and market price?

2.   If the above firms collude and maximize industry profits:

     (i) How much will each firm produce?

     (ii) What are the industry output and market price?

     (iii) What is the industry profit?

     (iv) How do your results in part (2) compare with those obtained in part (1)? Explain.

Answer 1