Question

If the inverse market demand function facing a duopoly is $p=a-b Q,$ what are the NashCournot equilibrium quantities if the marginal cost of Firm 1 is $m$ and that of Firm 2 is $m+x,$ where $x>0 ?$ Which firm produces more and which has the higher profit? $\mathbf{A}$

          If the inverse market demand function facing
a duopoly is $p=a-b Q,$ what are the NashCournot equilibrium quantities if the marginal cost of Firm 1 is $m$ and that of Firm 2 is $m+x,$ where $x>0 ?$ Which firm produces more and which has the higher profit? $\mathbf{A}$

Added by Andrea C.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Oluwadamilola Ameobi

05/31/2023

Step 1

First, we need to find the profit functions for both firms. The profit function for Firm 1 is given by: $\pi_1 = (p - m)q_1 = (a - bQ - m)q_1 = (a - b(q_1 + q_2) - m)q_1$ Similarly, the profit function for Firm 2 is given by: $\pi_2 = (p - (m+x))q_2 = (a - bQ - Show more…

Show all steps

Thanks for your feedback!

If the inverse market demand function facing a duopoly is $p=a-b Q,$ what are the NashCournot equilibrium quantities if the marginal cost of Firm 1 is $m$ and that of Firm 2 is $m+x,$ where $x>0 ?$ Which firm produces more and which has the higher profit? $\mathbf{A}$