Each week, Bill, Mary, and Jane select the quantity of two goods, Xl and x2" that they will consume in order to maximize their respective utilities. They each spend their entire weekly income on these two goods.
a. Suppose you are given the following information about the choices that Bill makes over a three-week period:
| Â |
Xl
|
X2
|
Pl
|
P2
|
l
|
|
Week 1
|
10
|
20
|
2
|
1
|
40
|
|
Week 2
|
7
|
19
|
3
|
1
|
40
|
|
Week 3
|
8
|
31
|
3
|
1
|
55
|
Each week, Bill, Mary, and Jane select the quantity of two goods, Xl and x2" that they will consume in order to maximize their respective utilities. They each spend their entire weekly income on these two goods.
a. Suppose you are given the following information about the choices that Bill makes over a three-week period:
| Â |
Xl
|
X2
|
Pl
|
P2
|
l
|
|
Week 1
|
10
|
20
|
2
|
1
|
40
|
|
Week 2
|
7
|
19
|
3
|
1
|
40
|
|
Week 3
|
8
|
31
|
3
|
1
|
55
|
Did Bill"s utility increase or decrease between week 1 and week 2? Between week 1 and week 3? Explain using a graph to support your answer.
b. Now consider the following information about the choices that Mary makes:
| Â |
Xl
|
X2
|
Pl
|
P2
|
l
|
|
Week 1
|
10
|
20
|
2
|
1
|
40
|
|
Week 2
|
6
|
14
|
2
|
2
|
40
|
|
Week 3
|
20
|
10
|
2
|
2
|
60
|
Did Mary"s utility increase or decrease between week 1 and week 3? Does Mary consider both goods to be normal goods? Explain.
c. Finally, examine the following information about Jane"s choices:
| Â |
Xl
|
X2
|
Pl
|
P2
|
l
|
|
Week 1
|
12
|
24
|
2
|
1
|
48
|
|
Week 2
|
16
|
32
|
1
|
1
|
48
|
|
Week 3
|
12
|
24
|
1
|
1
|
36
|
Draw a budget line-indifference curve graph that illustrates Jane"s three chosen bundles. What can you say about Jane"s preferences in this case? Identify the income and substitution effects that result from a change in the price of good Xl.