Assume the market for new homes is competitive in a certain area. Demand for the

Question

Assume the market for new homes is competitive in a certain area. Demand for these homes (simple, starter homes) is given by P = 200,000 - 15Qd, supply for homes is P = 100,000 + 10Qs

A) What is the equilibrium price and quantity?

B) What is Producer, Consumer, and overall surplus?

Now assume the market is controlled by a monopolist.

C) What is the new Equilibrium Price and quantity?

D) What is Producer Surplus, Consumer surplus, and deadweight loss.

E) Now assume the market is comprised of two identical firms. Find the Equilibrium price, quantity, and consumer and producer surplus. (you will have to derive a reaction function)

Explanation / Answer

(A) In a perfectly competitive industry, in equilibrium, Qd = Qs

P = 200,000 - 15Qd

15Qd = 200,000 - P

Qd = (200,000 - P) / 15

Again,

P = 100,000 + 10Qs

10Qs = P - 100,000

Qs = (P - 100,000) / 10

Since Qd = Qs, we get

(200,000 - P) / 15 = (P - 100,000) / 10

15P - 1,500,000 = 2,000,000 - 10P

25P = 3,500,000

P = 140,000

Q = (140,000 - 100,000) / 10 = 40,000 / 10 = 4,000

(B)

Producer surplus (PS) = Area between supply curve & market price

From supply curve, if Qs = 0, P = 100,000 (Minimum acceptable price)

PS = (1/2) x (140,00 - 100,000) x 4,000 = (1/2) x 40,000 x 4,000 = 80,000,000

Consumer surplus (CS) = Area betwen demand curve & price

From demand curve, if Qd = 0, P = 200,000 (Reservation price)

CS = (1/2) x (200,000 - 140,000) x 4,000 = (1/2) x 60,000 x 4,000 = 120,000,000

Total surplus (TS) = PS + CS = 80,000,000 + 120,000,000 = 200,000,000

(C) A monopolist maximizes profits by equating marginal revenue (MR) with marginal cost (MC).

Total revenue (TR) = P x Q = 200,000Q - 15Q2

MR = dTR / dQ = 200,000 - 30Q

MC = Supply function: P = 100,000 + 10Q

200,000 - 30Q = 100,000 + 10Q

40Q = 100,000

Q = 2,500

P = 200,000 - (15 x 2,500) = 200,000 - 37,500 = 162,500

(D)

New PS = (1/2) x (162,500 - 100,000) x 2,500 = (1/2) x 62,500 x 2,500 = 78,125,000

New CS = (1/2) x (200,000 - 162,500) x 2,500 = (1/2) x 37,500 x 2,500 = 46,875,000

Deadweight loss = (1/2) x Difference in price x Difference in quantity

= (1/2) x (162,500 - 140,000) x (4,000 - 2,500) = (1/2) x 22,500 x 1,500 = 16,875,000

NOTE: First 4 sub-parts are answered.

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