Suppose a town council is thinking of implementing the impos

Suppose a town council is thinking of implementing the imposition of a $350 per week rent ceiling on apartments in a city. Demand and supply curves are: QD 5600- 8P and Qs4004P product) Where P-weekly rent, and Q = number of apartments (apartments can be treated as identical (a) Calculate the equilibrium price and quantity that would prevail before implementing the price ceiling. Calculate consumer surplus and producer surplus at this (b) What quantity will be available if the rent ceiling is imposed? Calculate any gains or (c) Does the proposed rent ceiling result in net welfare gains? Would you advise the equilibriunm losses in consumer surplus and producer surplus. town council to implement this policy? Explain

Solution

a) Q_D = 5600-8P and Q_S = -400+4P

At equilibrium point, Quantity demanded = Quantity supplied

Therefore, 5600-8P = -400+4P or, 12P =6000

or, P = $500 and Q= Q_D =Q_S = -400+4*500= 1600 which are the equilibrium rent and quantity before implementation of the price ceiling.

Also, consumer will be willing to pay rent at the point where Q_D =0

Therefore, 5600-8P=0 or P=$700

Therefore, consumer surplus = $700-equilibrium rent = $700-$500=$200

and producer i.e., apartment owners will be willing to rent the apartment at the point where, Q_S =0

or, -400+4P=0 or P=200

Therefore, producer surplus= $200-$500=-$300

b. Q_S=-400+4P or 4P= 400+Q_S or P = 100+Q_S /4

d(PQ_S)/dQ_S = 100+Q_S /2

Therefore, after implementation of rent ceiling on apartments.

Marginal revenue of the town council = Proposed rent ceiling rate

or 100+Q_S /2 = 350 or Q_S = 500 which is number of apartments available after implementation of rent ceiling.

Also from the demand function, substituting Q_D =Q_S =Q =500, we get,

      500=5600-8P or P= 637.5

Consumer surplus = rent that consumer is willing to pay-equilibrium rent rate = $637.5-$500= $137.5

Producer supply= Rent ceiling rate- Equilibrium rent =$350-$500=-$150.

Change in consumer surplus after implementation of rent ceiling = $137.5-$200=-$62.5

Change in producer surplus after implementation of rent ceiling =-$150+$300= $150

c) Total surplus before implementation of rent ceiling = $200-$300=-$100   (From part a.)

total surplus after implementation of rent ceiling =$137.5-$150=-$12.5

Net surplus = -$12.5+$100=$87.5 which reflects net welfare gain of $87.5 after implementation of rent ceiling. Therefore, the town council should implement the rent ceiling policy as it will maximize the revenue of apartment owners.