Question

The demand and supply functions for rental accommodation in New York are as
follows:
Qd = 120 - P
Qs = 2P
a. Solve for the competitive equilibrium rental rate (P) and quantity (Q) of rental units
in New York. Illustrate this equilibrium in a graph.
b. On your graph, show the regions that represent consumer surplus and producer
surplus. Calculate the value of consumer surplus, producer surplus, and overall
welfare.
c. Suppose the City of New York enacts a rent control ordinance that imposes a
maximum rent of 30. How many rental units will be rented at this controlled price?

Answer 1

a) Market equilibrium occurs where Qs = Qd

120 - P = 2P

120 = 3P

P = $40

Q = 2*40 = 80

This is the equilibrium rental price and rental units

b) CS = (Max price - current price)*current qty = 0.5*(120 - 40)*80 = $3200.

PS = (current price - minimum price)*current qty = 0.5*(40)*80 = $1600

Overall welfare = PS + CS = $4800

c) When P is fixed = 30, Qs = 2*30 = 60 and Qd = 120 - 30 = 90. Hence there is a shortage of 30 units. At this price only 60 units will be rented at this controlled price