Question

1. (Monopoly and Price Control)

Suppose that a developer has market power in the first-hand market for

luxury apartments in a district but can only sell those apartments at a unit

price, p, because of easy resale and arbitrage among buyers in a second

hand market, which is competitive. Let the market demand curve it is facing

be q = 55/2-1/2p [to make it simple, we do not specify the unit of measurement

here] where q stands for number of apartment units, which are assumed to be homogeneous and divisible.

Symbol
TC The total cost of production

What it stands for
MC The marginal cost of production

MR The marginal revenue LetTC= 100-Sq+q2•

Assuming that the developer aims at maximizing profit.

1. (a) Show that MR= 55 - 4q and MC= 2q - 5. And does the production function satisfy the law of diminishing marginal product all the time?
2. (b) What is the profit-maximizing quantity, price, and producer and consumer surplus?
3. (c) For simplicity, assuming that the government concerns about the high price of luxury apartments having any spillover effect to lower-end housing market, and imposes a price ceiling at 25 on every new luxury apartment unit.

(i) How would the answers in (b) be changed? What will be the deadweight loss?

(ii) Could the government achieve the same results as in c(i) by imposing a per unit tax on the developer instead of placing price ceiling?
[Hint: words (60 words max) and/or graphic argument suffice)

Answer 1

Solution; (1) monopoly and price contro). Given, q= 50 - 1 Te = 100 - 59 +02 @ show that mR = 55-49 mc=gq -5 and production function: - 9 = sq - ţP = 5=P » 29=55-4 p=55-29 TR = PQ = $5-29) (0) = 559-292 :: MR = d.TR = 55-49] dor

Glen 10 = 100 --5V +92 me = da (10) - (29-5 | © profit maximising quantity, price / ps and c: >) Pulit maximising price is obtained af mRame 55-49 = 29-5 60=609 V=10] p=55-29 =55-2000) IP = 35 cs =() (55-35) (10) = 9(20)(6) = 1100 PS = ( 35-10) (10) = (20) (to) -[ 2ao

© If price ceiling of 25 on every luxuary appartment is imposed othen: > it means price is set at 25 (p=25 Now at p=25 25=55-29 29=30 cs = () (55-25)(15) =+) (30) (15) = (225 ps = [25-15) (15) = (10) (15) PWL = (12-,)(Q2 -0,) =(+) (85-35)(15-10) = (+) (-10) (5) -625