Answer to Question #115587 in Microeconomics for Raj

Question

Mr Lim, a tuition teacher, is deciding how many hours to teach each day and how much to charge for his tuition. Each hour of lecture cost him $40. He has two students A and B with demand curves as follows: • Student A: PA= 72 - 8Q Student B: PB = 56 - 4Q • where Q is the number of hours he teaches. (a) If he teaches only one student per class in an hour, obtain the market demand curve for his tuition from the two students. To maximize social welfare, how many hours of tuition should he teach? (b) Suppose that he can broadcast his tuition online, so that both students can listen to his tuition at the same time. Obtain the marginal social benefit equation. What is the socially optimal number of hours of tuition he should provide?

Answer 1

Solution:

a)

$$72-8Q=40$$

$$Q=4$$

$$56-4Q=40$$

$$Q=4$$

b)

$$Q_A=9-\frac{1}{8}p$$

$$Q_B=14-\frac{1}{4}p$$

$$Q=23-\frac{3}{8}p$$

$$p=\frac{184}{3}-\frac{8}{3}Q$$

$$TR=\frac{184}{3}Q-\frac{8}{3}Q^2$$

$$MR=\frac{184}{3}-\frac{16}{3}Q$$

$$Q=11.5$$