A consumer finds only three products, X, Y, and Z, are for sale. The amount of u
ID: 2506747 • Letter: A
Question
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 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
_____
Explanation / Answer
Product X
Product Y
Product Z
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
1
42
4.2
1
14
7.0
1
32
4.0
2
82
4.0
2
26
6.0
2
60
3.5
3
118
3.6
3
36
5.0
3
84
3.0
4
148
3.0
4
44
4.0
4
100
2.0
5
170
2.2
5
50
3.0
5
110
1.25
6
182
1.2
6
54
2.0
6
116
.75
7
182
0.0
7
56.4
1.2
7
120
.50
(a) See completed table above.
(b) The consumer will purchase 4 units of X, 5 units of Y, and 3 units of Z to maximize utility. The marginal utility per dollar for
each of the products is equal to 3.0. Also, all income ($74) is spent on the products ($40 for X, $10 for Y, and $24 for Z equals
$74).
(c)Although the marginal utility per dollar spent is equal to 4.0 for X, Y, and Z, the consumer does not spend all available income. There is $74 available but the consumer only spends $36. More goods could be obtained by spending the income to maximize utility as shown in the answer to (b)
Product X
Product Y
Product Z
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
1
42
4.2
1
14
7.0
1
32
4.0
2
82
4.0
2
26
6.0
2
60
3.5
3
118
3.6
3
36
5.0
3
84
3.0
4
148
3.0
4
44
4.0
4
100
2.0
5
170
2.2
5
50
3.0
5
110
1.25
6
182
1.2
6
54
2.0
6
116
.75
7
182
0.0
7
56.4
1.2
7
120
.50
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