Question

The monthly demand for one-bedroom apartment rentals is given by P = 2000 - 10Q, the supply is given by 500 + 20Q, where P is monthly rent per apartment, and Q is thousands of apartments. Suppose the city council imposes a rent ceiling of $1000. The rent ceiling will change renters' surplus from $12.5 million to $ million. It will change owners' surplus from $25 million to $ million. It will create a deadweight loss equal to $ million. (Express your answer in millions of dollars, and round the final answer to one decimal place. For example, if the answer is 2.678 million, enter 2.7 in the blank.

Answer 1

Demand: P=2000-10Q

X Intercept ( keeping P=0)= 200

Y intercept (keeping Q=0) = 2000

Supply : P=500+20Q

X intercept (keeping P=0) = -25

Y intercept (keeping Q=0) = 500

At Equilibrium demand= supply

2000-10Q=500+20Q

1500= 30Q

Q*= 50

P*= 2000-10Q or 500+20Q

P*= 1500

1) New renter's surplus= Yellow region

Renter's surplus= Area of triangle ABC + Area of rectangle CBEI

•Area of triangle ABC= (1/2)*base*height

base= 25

Height= (2000-1750)= 250

Area of triangle ABC= (1/2)*25*250 = 3125

•Area of rectangle CBEI= Length* breadth

Length= 25

Breadth= (1750-1000) = 750

Area of rectangle CBEI= 25*750 = 18750

Total renters surplus= 3125+18750= 21875 = 21.875 or 22 miliion

•Rent ceiling changes renter's surplus from 12.5 million to 22 million

2) New owner's surplus= Red region

New owner's surplus= Area of triangle EFI

Area of triangle EFI= (1/2)*base*height

Base= 25

Height= 1000-500= 500

New owner's surplus= (1/2)*25*500= 6250= 6.25 or 6 million

• Rent ceiling changes owner surplus from 25 to 6 million

3) Dead weight loss= Green region

Dead weight loss= Area of triangle BDE

Area of triangle BDE= (1/2)*base*height

Base= (1750-1000) = 750

Height= (50-25) = 25

Dead weight loss= (1/2)*750*25= 9375 or 9.375 or 9 million