Varian Solution
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 demand 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 “staircase” 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 Price = A = 40 B 25 C D 30 35 E 10 F 18 G 15 H 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 will be two different quantities of apartments demanded, since consumer i will be indifferent between having or not having an apartment.)
2
THE MARKET
(Ch. 1)
Price 60 50 40 30 20 10
0
1
2
3
4
5
6 7 8 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 units?
$18. $15. A, B, C, D. $10 to $15.
(c) What is the lowest price that would make the market demand equal to 5 units?
(d) With a supply of 4 apartments, which of the
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 demand 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 “staircase” 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 Price = A = 40 B 25 C D 30 35 E 10 F 18 G 15 H 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 will be two different quantities of apartments demanded, since consumer i will be indifferent between having or not having an apartment.)
2
THE MARKET
(Ch. 1)
Price 60 50 40 30 20 10
0
1
2
3
4
5
6 7 8 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 units?
$18. $15. A, B, C, D. $10 to $15.
(c) What is the lowest price that would make the market demand equal to 5 units?
(d) With a supply of 4 apartments, which of the