Suppose that a developer has market power in first hand market but can only prac

Question

Suppose that a developer has market power in first hand market but can only practice unit price because of easy resale and arbitrage among buyers in a second hand market, which is a competitive market. Let the market demand curve it is facing be Q=40-2P. (To make it simple we do not specify unit here, which could be, say, a million unit for dollar price and a hundred for flat unit Q ---- assuming each flat is same and somehow is divisible). Let the MC= Q Assuming that the developer aims at maximizing profit

a) Show that the MR=20 Q

b) What is the profit maximizing quantity, price, producer and consumer surplus?

c) For simplicity assume that government imposes a unit tax, 2, on every property transaction in both first and second hand property market. You might assume that the sale side pays the tax to the government.

I. How the answer in part (B) above be changed?

II. How the burden of unit tax shared between the buyer and developer?

III. Will such a unit tax affect increase the ability of developer to practice price discrimination? Offer your argument according to the given scenario and above results. Hint: no math, maximum 50 words.

Explanation / Answer

Q=40-2P

a. P = (40- Q) / 2 = 20 - Q/2

TR = PQ = 20Q - Q2/2

MR = dTR/dQ = 20- Q

b. Profit maximising quality and price is obtained at MR = MC

20-Q = Q =>2Q = 20

=> Q = 20/2 = 10 and P = 20-10/2 = 20- 5 = 15

Consumer surplus = 1/2 * (20-15) * 10 = 1/2 * 5*10 = 25

Producer surplus is (15-10) * 10= 50

c. i) Unit tax shifts th MC curve upward by the amount of tax

MC = Q+ 2

New equilibrium = 20- Q = Q +2

=> 2Q = 18 => Q =9

P = 20- 9/2 = 20- 4.5 = 15.5

ii) Burden of tax is shared by both seller and buyers but mostly borne by the seller as the price paid by buyer has incrased only 0.5, Therefore the rest of the amount of tax is paid by the seller.

iii) Price discrmination allows the producers to differentiate prices among different customer groups. Unit tax incraases the marginal cost hence the price charged yby them. A monopolist absorb some part of the tax. Any incraese in price change may increase the sell in th esecondary market. Therefore, price discrimination may be a strategy to incraese revenue.

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