Utility maximization formula

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Reference no: EM1315706

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

_____



Reference no: EM1315706

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