Explain why the intersection of the best-response functions is the Cou

Explain why the intersection of the best-response functions is the Cournot equilibrium.

What will be an ideal response?

ANSWER

On a best-response function, a firm selects the profit-maximizing level of output given the level of output it believes the other firm will produce. At the intersection of the best-response functions, what one firm believes the other firm will produce actually is the amount the other firm produces. Thus, neither firm has an incentive to change the level of output.