Managerial Econ Scenario

James Pizzo is president of a firm that is the industry price leader; that is, it sets the price
and the other firms sell all they want at that price. In other words, the other firms act as
perfect competitors. The demand curve for this industry’s product is P=300-Q, where P is
the price of the product and Q is the total quantity demanded. The total amount supplied
by other firms is equal to Q_r, where Q_r = 49P. (P is measured in dollars per barrel; Q,
Q_r and Q_b are measured in millions of barrels per week.)
a. If Pizzo’s firm’s marginal cost curve is 2.96Q_b, where Q_b is the output of his
firm, at what output level should he operate to maximize profit?
b. What price should he charge?
c. How much does the industry as a whole produce at this price?
d. Is Pizzo’s firm the dominant firm in the industry?