Question

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

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

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

d) When price is fixed at 30 and is binding the deadweight loss is the area above the shortage.
It is equal to 0.5*(90 – 60)*(40 – 30) = 150.

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