Question

Suppose demand for apartments in Honolulu is P=6000-0.5q and supply is P=0.25q.

a. Derive the equilibrium price and quantity for apartments. Show on a graph. Calculate the producer and consumer surplus.

b. If the city of Honolulu passes a rent control, forcing a rent (or price) ceiling equal to $1600, what is the quantity supplied, quantity demanded, and the shortage? Calculate the new consumer surplus, producer surplus, and deadweight loss, and show these on your graph.

c. If a black market develops after the rent control, allowing landlords to charge an illegal rent, what is the highest rent that they could charge for the quantity supplied of apartments in part b? What is the new producer surplus? Comment on the effectiveness of price controls in allocating apartments to middle to lower income tenants.

Answer 1

A) Equilibrium at demand= supply

6000-0.5q=0.25q

Q=6000/0.75=8000

P=0.25*8000=2000

CONSUMERs surplus=1/2*8000*(6000-2000)=4000*4000=16,000,000

Producer surplus=1/2*8000*2000=8,000,000

B)Qs=1600/0.25=6400

Qd=12,000-2*1600=8800

Shortage=8800-6400=2400

Produer surplus=1/2*6400*1600=5,120,000

Willingness to for q=6400

P=6000-0.5*6400=2800

CONSUMERs surplus=(2800-1600)*6400 + 1/2*6400*(6000-2800)=7,680,000 +10,240,000=17,920,000

Deadweight loss=initial total SURPLUS- new Total surplus=(16 M + 8M)-(5.12+17.92)=0.96 M or 960,000

C)They can charge MAXIMUM:

Willingness to for q=6400

P=6000-0.5*6400=2800

New producer surplus=1/2*6400*1600+ (2800-1600)*6400=5,120,000+7,680,000=12,800,000