Question

The town council is contemplating the imposition of a R350 per month rent ceiling on apartment rooms in the town. An economist at the university estimates the demand and supply curves as: QD = 5600 - 8P QS = 500 + 4P, where P = monthly rent, and Q = number of apartments available for rent. For purposes of this analysis, apartments can be treated as identical. a) Calculate the equilibrium price and quantity that would prevail without the price ceiling.[1] b) Calculate producer and consumer surplus at this equilibrium. [3] c) Provide a rough sketch of the information calculated in (a) and (b). [2] d) What quantity will eventually be available if the rent ceiling is imposed? What is the amount of the shortage? [2] e) Calculate then resulting impact on consumer and producer surplus.[3] f) What is meant by deadweight loss? Why does a price ceiling usually result in a deadweight loss? In your answer explain the impact on both producers and consumers. [4]

Answer 1

a)

To calculate equilibrium,

set $Q_D=Q_S$

$5600-8P=500+4P\\5600-500=4P+8P\\5100=12P\\P=\frac{5100}{12}\\P=425$

Substituting p into Q_D

$Q_D=5600-8P\\\implies Q=5600-(8\times425)\\Q=2200$

b)

$Q_D=5600-8P\\8P=5600-Q_D\\P=700-0.125Q_D\\Q_S=500+4P\\4P=Q_S-500\\P=0.25Q_S-125$

Consumer surplus=Area A

$=0.5(700-425)\times2200\\=302,500$

Producer surplus = area B

$=0.5(425-125)\times 2200\\=330,000$

sum of consumer and producer surplus

$302,500+330,00=632,500$

c)

d)

Eventually, the market will settle at the quantity supplied corresponding to $350 rent.

$Q_S=500+4P\\=500+4(350)\\=1900$

Q_D at P=350

$Q_D=5600-8P\\=5600-8(350)\\=2800$

There will be a shortage of 2800-1900=900 apartments

e)

Gain=consumer surplus, Area A

$Area\space A=(425-350)\times 1900=142,500$

Loss in consumer surplus

consumer reservation price corresponding to 1900

$P=700-0.125(1900)=462.5$

Difference in Q

$=2200-1900\\=300$

$Area\space B=0.5(462.5-425)\times (2200-1900)\\=5625$

So the loss in consumer surplus is 5625

Area C is loss in producer surplus not offset by gain in consumer surplus. The net changes are thus b ( lost consumer surplus) and C ( lost producer suplus)

f)

The policy ths results in a dead weight loss.

The dead weight loss =lost C.S + lost P.S

$=5625+11250\\=16,875$

The town council should not implement the policy.