Question

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 ____.

Answer 1

The market equilibrium rent is $1250 per apartment, and the equilibrium quantity is 22.5 thousand apartments. With the price ceiling of $1000, the rent is capped at that price and the quantity rented is 10 thousand apartments. The excess demand for apartments with the price ceiling is 1490.

Step-by-step explanation:

The market equilibrium rent can be found by setting the demand and supply equations equal to each other and solving for the price (P). In this case, we have:

1700 - 20Q = 80Q + 200

By rearranging and solving for Q, we find Q = 22.5. Substituting this value back into either the demand or supply equation, we can find the equilibrium price: P = 1700 - 20(22.5) = $1250.

So, the market equilibrium rent is $1250 per apartment, and the equilibrium quantity is 22.5 thousand apartments.

(b) With the price ceiling of $1000, the rent is capped at that price and the quantity rented is determined by the supply equation.

Plugging P = 1000 into the supply equation, we have:

1000 = 80Q + 200

By rearranging and solving for Q, we find Q = 10.25. However, since quantity is measured in thousands, the actual quantity rented is 10 thousand apartments.

So, with the price ceiling, the rent is $1000 per apartment, and the quantity rented is 10 thousand apartments.

(c) The excess demand for apartments with the price ceiling is the difference between the quantity demanded and the quantity supplied at the price ceiling.

Quantity demanded at P = 1000: 1700 - 20Q = 1700 - 20(10) = 1500.

Excess demand = quantity demanded - quantity supplied = 1500 - 10 = 1490.

Answer 2

(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

Step-by-step 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