Question

Ms. Aura is a psychic. The demand for her services is given by Q-2000 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200-0.2Q Ms. Aura's operation has no fixed costs, but she incurs a cost of 150 per session (going to the client's house).
a. What is Ms. Aura's yearly profit?
b. Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500-5P. Her new marginal revenue is MR = 500-0.4Q. What is her profit now?
c. Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of 1,000, but the marginal cost is only 20 per session. What is Ms. Aura's profit? Assume the demand curve is still given by Q-2500 -5P.
d. Summarize the lesson of this problem for the superstar phenomenon.

Answer 1

Answer:

a)

P 175

Q = 250

Profit6,250

b)

P 325

Q = 875

Profit 153,125

c)

Q = 1200

P = 260

Profit = 287,000

Explanation:

It maximize profit at MR = MC

MR = 200 - 0.2Q

MC = 150

150 = 200-0.2Q

Q = 50/0.2 = Q = 250

Price:

250 = 2000 - 10P

P = 1750/10 = 175

Profit: revenue - cost

$175 x 250 session - $150 per session = 6,250

At new functions:

150 = 500-0.4Q

Q = 350 / 0.4 = 875

Price:

875 = 2,500 - 5P

P = (2500-875)/5= 325

Profit

(325 - 150) * 875 = 153,125

If cost changes:

cost: 1000 + 20Q

marginal cost: 20

20 = 500 - 0.4Q

Q = 480 / 0.4 = 1,200

Price:

1,200 = 2500 - 5P

P = 1300/5 = 260

Profit

(260 - 20)Q - 1,000 = 287,000