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.
a. 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?
b. 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% of any
long-run increases in apartment offerings come from new construction, how many
apartments are constructed?
ANSWER
a. 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?
Set supply
equal to demand to find the free-market price for apartments:
160 - 8P =
70 + 7P, or P = 6,
which means
the rental price is $600 since price is measured in hundreds of dollars.
Substituting the equilibrium price into either the demand or supply equation to
determine the equilibrium quantity:
QD = 160 - 8(6) =
112
and
QS = 70 + 7(6) =
112.
The
quantity of apartments rented is 1,120,000 since Q is measured in tens of
thousands of apartments. If the rent control agency sets the rental rate at
$300, the quantity supplied would be 910,000 (QS = 70 + 7(3) = 91), a decrease of 210,000
apartments from the free-market equilibrium.
Assuming
three people per family per apartment, this would imply a loss in city
population of 630,000 people. Note: At the $300 rental rate, the demand for
apartments is 1,360,000 units, and the resulting shortage is 450,000 units
(1,360,000 - 910,000).
However, excess demand (the shortage) and lower quantity demanded are
not the same concept. The shortage of 450,000 units is the difference between
the number of apartments demanded at the
new lower price (including the number demanded by new people who would have
moved into the city), and the number supplied at the lower price. But these new
people will not actually move into the city because the apartments are not
available.
Therefore,
the city population will fall by 630,000, which is due to the drop in the
number of apartments available from 1,120,000 (the old equilibrium value) to
910,000.
b. 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% of any
long-run increases in apartment offerings come from new construction, how many
apartments are constructed?
At a rental
rate of $900, the demand for apartments would be 160 - 8(9) =
88, or 880,000 units,
which is 240,000 fewer apartments than the original free-market equilibrium
number of 1,120,000. Therefore, no new apartments would be constructed.
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