Eco 405
Assignment 3 (Due Feb. 20, Wednesday)
1.
The rent control agency of New York City has found that aggregate demand is
Q
D
= 160  8
P
.
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 threeperson 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
Q
S
= 70 + 7
P
.
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 rental of $300, and all those who cannot find an apartment leave
the city?
To find the free market price for apartments, set supply equal to demand:
160  8
P
= 70 + 7
P
, or
P
= $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:
Q
D
= 160  (8)(6) = 112
and
Q
S
= 70 + (7)(6) = 112.
We find that at the rental rate of $600, the quantity of apartments rented is 1,120,000.
If the rent control agency sets the rental rate at $300, the quantity supplied would then
be 910,000 (
Q
S
= 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 of 630,000 people.)
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 Spring '08
 Mingaling
 Supply And Demand, rental rate

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