The can industry is composed of two firms. Suppose that the demand curve for cans is
P = 100 - Q
where P is the price (in cents) of a can and Q is the quantity demanded (in millions per month) of cans. Suppose the total cost function of each firm is
TC = 2 + 15q
where TC is total cost (in tens of thousands of dollars) per month and q is the quantity produced (in millions) per month by the firm.
a. What are the price and output if managers set price equal to marginal cost?
b. What are the profit-maximizing price and output if the managers collude and act like a monopolist?
c. Do the managers make a higher combined profit if they collude than if they set price equal to marginal cost? If so, how much higher is their combined profit?