Answer:
(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
