Question

1. Consider two monopolists: Up and Down. Up makes a good, then sells it to Down, who puts a better label on it then sells to the public. It costs Up $150 to make each good. Down’s only cost is what it has to pay Up for each good.

Up has demand and marginal revenue functions:

Price_U = 500 – 0.25Q_U                        MR_U = 500 – 0.5Q_U

Down has demand and marginal revenue functions:

Price_D = 600 – 0.25Q_D                        MR_D = 600 – 0.5Q_D

A. How do you know these are monopolists rather than competitive firms?

Besides the fact that the question says they are.

B. To maximize its profit, what quantity should Up produce?

C. To maximize its profit, what price should Up charge?

D. What is the maximum profit that Up can earn?

E. To maximize its profit, what quantity should Down produce?

F. To maximize its profit, what price should Down charge?

G. What is the maximum profit that Down can earn?

Answer 1

(A)

Each firm has downward sloping demand curve, indicating they have price-setting power and are monopolists.

(B)

Profit is maximized when MRU = MCU = 150.

500 - 0.5QU = 150

0.5QU = 350

QU = 700

(C)

PU = 500 - 0.25 x 700 = 500 - 175 = 325

(D)

Profit = QU x (PU - MCU) = 700 x (325 - 150) = 700 x 175 = 122,500

(E)

For Down, MC = PU = 325

Profit is maximized when MRD = MCD = 325.

600 - 0.5QD = 325

0.5QD = 275

QD = 550

(F)

PD = 600 - 0.25 x 550 = 600 - 137.5 = 462.5

(G)

Profit = QD x (PD - MCD) = 550 x (462.5 - 325) = 550 x 137.5 = 75,625