Consider a market with the inverse demand py7y Two firms ope

Consider a market with the inverse demand p(y)=7-y. Two firms operate in this market as Cournot competitors. Both firms have the cost function c(y)=y+F. If both firms are making nonnegative profits in the Cournot equilibrium, the fixed cost F must be no greater than ________.

Solution

The fixed cost F must be no greater than 6y - y²

Explanation:

TR = p*y = 7y - y²

TC = y + F

Prfit = TR - TC = 7y - y² - y - F = 6y - y² -F

Therefore, Profit will be positive if 6y - y² is greater than F