Chapter 2: The Basics of Supply and Demand
To find the free market price for apartments, set supply equal to demand:
100 - 5P = 50 + 5P, or P = $500,
since price is measured in hundreds of dollars. Substituting the equilibrium price into
either the demand or supply equation to determine the equilibrium quantity:
Q
D
= 100 - (5)(5) = 75
and
Q
S
= 50 + (5)(5) = 75.
We find that at the rental rate of $500, 750,000 apartments are rented.
If the rent control agency sets the rental rate at $100, the quantity supplied would then
be 550,000 (Q
S
= 50 + (5)(1) = 55), a decrease of 200,000 apartments from the free
market equilibrium. (Assuming three people per family per apartment, this would
imply a loss of 600,000 people.) At the $100 rental rate, the demand for apartments is
950,000 units, and the resulting shortage is 400,000 units (950,000-550,000). The city
population will only fall by 600,000 which is represented by the drop in the number of
apartments from 750.000 to 550,000, or 200,000 apartments with 3 people each. These
are the only people that were originally in the City to begin with.
Appartments
(10,000’s)
$1,000
Rent
100
200
300
400
500
600
700
800
900
20 40 60
80 100
Excess
Demand
Demand Supply
Figure 2.4
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 percent of
any long-run increases in apartment offerings comes from new construction, how
many apartments are constructed?
At a rental rate of $900, the supply of apartments would be 50 + 5(9) = 95, or 950,000
units, which is an increase of 200,000 units over the free market equilibrium.
Therefore, (0.5)(200,000) = 100,000 units would be constructed. Note, however, that
since demand is only 550,000 units, 400,000 units would go unrented.
5. Much of the demand for U.S. agricultural output has come from other countries. From
Example 2.4, total demand is Q = 3244 - 283P. In addition, we are told that domestic demand
is Q
d
= 1700 - 107P. Domestic supply is Q
S
= 1944 + 207P. Suppose the export demand for
wheat falls by 40 percent.