The can industry is composed of two firms. Suppose that the demand curve for can
ID: 1193361 • Letter: T
Question
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 + 15 q 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. What are the price and output if managers set price equal to marginal cost? What are the profit-maximizing price and output if the managers collude and act like a monopolist? Do the managers make a higher combined profit if they collude than It they set price equal to marginal cost? If so, how much higher is their combined profit?Explanation / Answer
From the total cost function we can derive that the marginal cost is 15
When the price is set equal to marginal cost then P = 15
P = 100 – Q
Q = 100 – P
Q = 100 – 15 = 85
Total Revenue = 85 x 15 = 1275
Total Cost = 2 + 85 x 15 = 1277
Profit = 1275 – 1277 = (-2)
When the firms collude and act like monopolist the profit maximization occurs when the MR = MC
P = 100 – Q
MR = 100 – 2Q
MC = 15
Profit maximization at 100 – 2Q = 15
Q = 100 – 15 / 2 = 42.5
P = 100 – 42.5 = 57.5
Total Revenue = 57.5 x 42.5 = 2443.75
Total Cost = 2 + 15 x 42.5 = 639.5
Profit = 2443.75 – 639.5 = 1804.25
The managers make a higher profit when they collude and act like a monopolist.
They make 1804.25 – (-2) = 1806.25 more profit combined.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.