Problem: Consider an industry dominated by one firm that acts as a price leader. The industry also has a large number of smaller price followers that can sell as much as they want at the price set by the dominant firm. The demand curve for the output of all firms in the industry is:
QT = - 42,500 + 70P
The total cost curve for the dominant firm and the aggregate cost curve for the price followers are:
TCD = 50,000 + 150Q + 0.005Q2
ΣMCf = 250 + 0.05Q
Determine the price and output combination that the dominant firm would need to maximize profit for itself.