Eco11, Fall 2008
Simon Board
Economics 11: Solutions to Homework 1
October 16, 2008
Due date:
Tuesday 14th October.
Instructions:
You are required to write up your solution separately and independently, al
though you are encouraged to discuss and work in groups. Please write your name, student ID
number, and the name of your TA on the front page of the assignment that you hand in. Also,
please put boxes around your final answer to each part.
1. Utility Functions
Let
X
=
{
x
∈ <
0
≤
x
≤
4
}
. Suppose an agent receives utility
u
(
x
) =
x
if 0
< x
≤
2
= 4

x
if 2
< x
≤
4
from consuming
x
slices of pizza.
Which of the following utility functions represent the same preferences as above:
(a)
v
(
x
) = 2
x
if 0
≤
x
≤
2, and
v
(
x
) = 4

x
if 2
< x
≤
4.
(b)
v
(
x
) = 2
x
if 0
≤
x
≤
2, and
v
(
x
) = 8

2
x
if 2
< x
≤
4.
(c)
v
(
x
) = 4

(2

x
)
2
if 0
≤
x
≤
4.
(d)
v
(
x
) = 4

(2

x
)
3
if 0
≤
x
≤
4.
(e)
v
(
x
) = 4

(2

x
)
4
if 0
≤
x
≤
4.
(f)
v
(
x
) =

(2

x
)
2
if 0
≤
x
≤
4.
Solution
(a) This is different since
v
(1) = 2
>
1 =
v
(3).
1
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Eco11, Fall 2008
Simon Board
(b) This is the same since
v
(
x
) = 2
u
(
x
).
(c) This is the same since
v
(
x
) is increasing for
x <
2, decreasing for
x >
2, and is symmetric
around 2.
(d) This is different since
v
(
x
) is increasing for all
x
.
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 Fall '08
 cunningham
 Economics, Utility, Simon Board

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