Question

Suppose demand for apartments in Honolulu is P=6600-0.5q 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 $1800, 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

P = 6600 - 0.5q (demand)

P = 0.25q (supply)

Making supply = demand

6600 - 0.5q = 0.25q

0.75q = 6600

q = 8800

P = 0.25q = 0.25*8800 = 2200

Equillibrium P = 2200, q = 8800

If q = 0, in demand curve P = 6600, so highest possible price is 6600, but demand is zero

If P = 0, in demand curve q = 13200, so at zero price quantity demanded is 13200.

Plotting in a graph

a)

CS = 19360000

PS = 9680000

b)

CS = 21600000

PS = 6480000

DWL = 960000

Supply = 7200

Demand = 9600

Shortage = 2400

c)

Highest rent = 3000 (as shown for supply of 7200)

The new producer surplus will increase by the area of the rectangle abcd

i.e. 7200*1200 = 8640000

CS = 21600000 - 8640000 = 12960000

PS = 6480000 + 8640000 = 15120000

Price controls are in place to help middle and lower income tenants.

As price were controlled, CS increased and PS decreased.

But, due to black market, price control became ineffective. Infact highly ineffective, as now CS is even lower than part a. PS increases a low. Prices are highest with a price control in place along with a black market.