Question

2. The demand and supply functions for rental accommodation in Metroland are as follows:

Qd =120-P

Qs = 2P

a. Solve for the competitive equilibrium rental rate (P) and quantity (Q) of rental units in Metroland. Illustrate this equilibrium in a graph.

On your graph, show the regions that represent consumer surplus and producer surplus. Calculate the value of consumer surplus, producer surplus, and overall welfare.

b. Suppose the City of Metroland enacts a rent control ordinance that imposes a maximum rent of 30. How many rental units will be rented at this controlled price?

c. Does this policy impose a deadweight loss on society? If so, calculate the value of this deadweight loss. Which region on the graph represents this deadweight loss?

Answer 1

Qd = 120 - P

Qs = 2P

a)

In equilibrium Qd = Qs,

120 - P = 2P

120 = 3P

P = 40

Q = 80

Consumer surplus is the area above the price line and below the demand curve and is depicted by blue triangle. Area of blue trianlgle = 1/2*(120-40)*(80-0) = 3200

Producer Surplus is the area above the supply line and below the price line and is represented by the green triangle. Area of gree triangle = 1/2*(40-0)*(80-0) = 1600

Total Surplus = 3200+1600 = 4800

b)

Price = 30

Qs = 2*30 =60. Hence 60 units will be rented at this price.

c)

The deadweight loss is the area between the demand and supply curve bounded by the new quantity.

Area of blue triangle = 1/2*(60-30)*(80-60) = 300