A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend.
a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places.
b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula.
c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?
|
Product X
|
Product Y
|
Product Z
|
|
Quantity
|
Utility
|
Marginal
Utility
per $
|
Quantity
|
Utility
|
Marginal
Utility
per $
|
Quantity
|
Utility
|
Marginal
Utility
per $
|
|
|
|
1
|
42
|
_____
|
1
|
14
|
_____
|
1
|
32
|
_____
|
|
|
|
2
|
82
|
_____
|
2
|
26
|
_____
|
2
|
60
|
_____
|
|
|
|
3
|
118
|
|
3
|
36
|
_____
|
3
|
84
|
_____
|
|
|
|
4
|
148
|
_____
|
4
|
44
|
_____
|
4
|
100
|
_____
|
|
|
|
5
|
170
|
_____
|
5
|
50
|
_____
|
5
|
110
|
_____
|
|
|
|
6
|
182
|
_____
|
6
|
54
|
_____
|
6
|
116
|
_____
|
|
|
|
7
|
182
|
_____
|
7
|
56.4
|
_____
|
7
|
120
|
_____
|
|
|