Chapter 1 NAME
The Market
Introduction. The problems in this chapter examine some variations on
the apartment market described in the text. In most of the problems we
work with the true demand curve constructed from the reservation prices
of the consumers rather than the “smoothed” demand curve that we used
in the text.
Remember that the reservation price of a consumer is that price
where he is just indifferent between renting or not renting the apartment.
At any price below the reservation price the consumer will demand one
apartment, at any price above the reservation price the consumer will de-
mand zero apartments, and exactly at the reservation price the consumer
will be indifferent between having zero or one apartment.
You should also observe that when demand curves have the “stair-
case” shape used here, there will typically be a range of prices where
supply equals demand. Thus we will ask for the the highest and lowest
price in the range.
1.1 (3) Suppose that we have 8 people who want to rent an apartment.
Their reservation prices are given below. (To keep the numbers small,
think of these numbers as being daily rent payments.)
Person = A B C D E F G H
Price = 40 25 30 35 10 18 15 5
(a) Plot the market demand curve in the following graph. (Hint: When
the market price is equal to some consumer i’s reservation price, there
2THE MARKET (Ch. 1)
012345678
10
20
30
40
60
50
Price
Apartments
(b) Suppose the supply of apartments is fixed at 5 units. In this case
there is a whole range of prices that will be equilibrium prices. What is
the highest price that would make the demand for apartments equal to 5
(c) What is the lowest price that would make the market demand equal
(d) With a supply of 4 apartments, which of the people A–H end up
(e) What if the supply of apartments increases to 6 units. What is the
1.2 (3) Suppose that there are originally 5 units in the market and that
1 of them is turned into a condominium.
(a) Suppose that person Adecides to buy the condominium. What will
be the highest price at which the demand for apartments will equal the
supply of apartments? What will be the lowest price? Enter your an-
NAME 3
Person A B C D E F G H
(b) Suppose that there were two people at each reservation price and 10
18. Suppose that one of the apartments was turned into a condo-
1.3 (2) Suppose now that a monopolist owns all the apartments and that
he is trying to determine which price and quantity maximize his revenues.
(a) Fill in the box with the maximum price and revenue that the monop-
Number 1 2 3 4 5 6 7 8
(c) If the monopolist were required by law to rent exactly 5 apartments,
(e) If this landlord could charge each individual a different price, and he
knew the reservation prices of all the individuals, what is the maximum
(f) If 5 apartments were rented, which individuals would get the apart-
1.4 (2) Suppose that there are 5 apartments to be rented and that the
city rent-control board sets a maximum rent of $9. Further suppose that
people A, B, C, D, and E manage to get an apartment, while F, G, and
H are frozen out.
4THE MARKET (Ch. 1)
(a) If subletting is legal—or, at least, practiced—who will sublet to whom
in equilibrium? (Assume that people who sublet can evade the city rent-
(b) What will be the maximum amount that can be charged for the sublet
(c) If you have rent control with unlimited subletting allowed, which of
1.5 (2) In the text we argued that a tax on landlords would not get
passed along to the renters. What would happen if instead the tax was
imposed on renters?
(a) To answer this question, consider the group of people in Problem 1.1.
What is the maximum that they would be willing to pay to the landlord
Person A B C D E F G H
(b) Using this information determine the maximum equilibrium price if
(c) Of course, the total price a renter pays consists of his or her rent plus
(d) How does this compare to what happens if the tax is levied on the