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James Pizzo is president of a firm that is the price leader in the industry; 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 the 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 the other firms is equal to Qr, where Qr =49P. (P is measured in dollars per barrel; Q, Qr and Qb are measured in millions of barrels per week.)
a. If Pizzo's firm's marginal cost curve is 2.96Qb, where Qb 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?

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The point to note before answering the question is that price leadership does not imply quantity leadership, or in other words, price leadership does not imply that the price leader is the dominant firm.

Given,

Demand: P = 300 - Q
Other firms supply: Qr = 49P

In the price leadership model the price leader sets the price, lets other firms sell as much as they can, and then satisfies the remaining market. To find the numbers we need to first find ...

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