Suppose a city is considering placing a ceiling on rent for one-bedroom apartments, at $1,000 per apartment.
Demand is given by:
P = 1700 - 20Q
and supply by:
P = 80Q + 200,
where Q is measured in thousands of apartments.
Instructions: Round your answers to the nearest whole number.
(a) The market equilibrium rent is $ , and the equilibrium quantity is thousand apartments.
(b) With the price ceiling, the rent is $ per apartment, and the quantity rented is thousand apartments.
(c) The excess demand for apartments with the price ceiling is .

(a) The market equilibrium rent is $1,400 and the equilibrium quantity is 15 thousand apartments.

(b) With the price ceiling, the rent is $1,000 per apartment and the quantity rented is 10 thousand apartments.

(c) The excess demand for apartments with the price ceiling is 20

Explanation:

(a) At equilibrium, demand function equals supply function

1700 - 20Q = 80Q + 200

1700 - 200 = 80Q + 20Q

100Q = 1500

Q = 1500/100 = 15

Substitute the value of Q in the demand function

P = 1700 - 20Q = 1700 - 20(15) = 1700 - 300 = 1400

Equilibrium rent = $1,400

Equilibrium quantity is 15 thousand apartments

(b) Rent with price ceiling is $1,000 per apartment

Substitute the value of P in the supply function

P = 80Q + 200

1000 = 80Q + 200

1000 - 200 = 80Q

80Q = 800

Q = 800/80 = 10

Quantity rented is 10 thousand apartments

(c) Quantity demanded (Q) with price ceiling = (1700 - P)/20

P = 1000

Q = (1700 - 1000)/20 = 700/20 = 35

Excess demand = 35 - 15 = 20