Question

rents being charged to uni The authorities are considering the imposition of a S350 per month rent ceiling on apartments in town. The demand and supply curves have been estimated as: OD-5,600- 8P Qs 500+4P Note: In this analysis apartments are treated as identical. a. Calculate the equilibrium price and quantity that would prevail without the price ceiling. b. Calculate producer and consumer surplus at this equilibrium. Present your calculations and a diagram for both. c. What quantity will eventually be available if the rent ceiling is imposed? d. Calculate any gains or losses in consumer and producer surplus e. Would you advise the local government to implement the rent ceiling policy? Base your answer on net welfare gains.

Answer 1

A. Equate quantity demanded to supply

Q_D = Q_S

5600 - 8P = 500 + 4P

12P = 5100

Equilibrium price, P* = $ 425

Equilibrium Quantity, Q* = 2200 (=5600-8*425)

B. Consumer Surplus = (1/2)*(700-425)*2200 = $ 302,500

Producer surplus = (1/2)*(425-(-125))*2200-(1/2)*125*500

Producer surplus = $ 605,000 - 31,250

Producer surplus = $ 573,750

C. When rent ceiling is imposed

Qd = 5600 - 8*350 = 2,800

Qs = 500 + 4*350 = 1900

When rent ceiling is imposed

Quantity Demanded = 2,800

Quantity Supplied = 1900

D. Consumer Surplus after rent control

= (1/2)*(700-462.5)*1900 + (462.5-350)*1900

= 225,625 + 213750

= $ 439,375

Producer surplus = (1/2)*(350-(-125))1900- (1/2)*125*500 = $ 451,250 - 31,250 = $ 420,000

Deadweight loss = (1/2)*(462.5-350)*(2200-1900 ) = $ 16,375

Please refer the attached picture.

E. Due to price ceiling a shortage of 800 units I created. At the same time quantity supplied had declined. Thus, i would suggest not to imposed price ceiling.

In addition to these the quality of rent houses will detoriate with time.