Question

The rent control agency of New York City has found that aggregate demand is QD = 160 - 8P. Quantity is measured in tens of thousands of apartments. Price, the average monthly rental rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. The city’s board of realtors acknowledges that this is a good demand estimate and has shown that supply is QS = 70 + 7P.

1. If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of \(300 and all those who cannot find an apartment leave the city?

2. Suppose the agency bows to the wishes of the board and sets a rental of \)900 per month on all apartments to allow landlords a “fair” rate of return. If 50 percent of any long-run increases in apartment offerings comes from new construction, how many apartments are constructed?

Short answer

1. The free-market price will be $600. The city population will reduce by 630,000 people.

2. 105,000 apartments were constructed.

Step-by-step solution

Explanation for part (a)

The free-market price is calculated below:

Q_D = 160-8P

Q_S= 70+7P

D=S

160-8P = 70+7P

8P +7P = 160 - 70

15P=90

P=$6

P=$600

Thus, Q=160-8(6)

=160-48

=112

Q=1,120,000

At $600, 1,120,000 apartments are rented.

The agency set the apartment's rent for $300. The quantity demand and quantity supply of apartments at $300 are calculated below:

Q_D = 160-8(3)

=160-24

=136

Q_D = 1,360,000

Q_S= 70+7(3)

=70+21

=91

Q_S= 910,000

The current shortage is supply-wise, which means that the market cannot provide the apartments at the lower price; the change will be considered from the old equilibrium value to the new supply value. The supply of apartments falls short of the equilibrium level by 210,000 (=1,120,000-910,000).

Assume that in every apartment, three people live in a family; thus, there is a loss of 630,000 people (=210,000*3). At $300, there will be shortage of 450,000 apartments (=1,360,000-910,000). The city population will fall by 630,000 people as the number of apartments falls by 210,000 apartments, and in each apartment, 3 people are living.

Explanation for part (b)

At $900, the quantity demand and quantity supply of apartment will be calculated below:

Q_D = 160-8(9)

=160-72

=88

Q_D = 880,000

Q_S= 70+7(9)

=70+63

=133

Q_S= 1,330,000

The increase in supply apartments than the equilibrium level will be 210,000 (=1,330,000 – 210,000). The number of apartments were constructed will be 50% of 210,000, i.e., 105000 apartments (=0.5*210,000).