Refer to table 1.1 when answering questions 13 and 14. Good X ($2 each) Quantity Total Utility Good Y ($1 each) Quantity "Total Utility 14 VON 13. If income is $13, then utility is maximized with the consumption of a. 6 units of X and 1 unit of Y. b. 5 units of X and 3 units of Y. c. 4 units of X and 5 units of Y. d. 7 units of X and 6 units of Y. e. 8 units of X and 5 units of Y.
Related textbook solutions
Related questions
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility that 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 | Ā | 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 | _____ |
||
Assume that an individual consumes two goods, X and Y. The total utility (assumed measurable) of each good is independent of the consumption rate of other goods.
The price of X and Y are respectively $40 and $60. Use the following table of total utilities to answer the following questions.
| Good | Total utility X | Total utility Y |
| Ā 1 | Ā 20 | Ā 45 |
| Ā 2 | Ā 38 | Ā 78 |
| Ā 3 | Ā 54 | Ā 108 |
| Ā 4 | Ā 68 | Ā 135 |
| Ā 5 | Ā 80 | Ā 159 |
| Ā 6 | Ā 90 | Ā 180 |
a. The marginal utility of the fourth unit of Y is__________.
b. The marginal utility of the fifth unit of X is___________.
c. The marginal utility per dollar spent on the third unit of X is__________.
d. The marginal utility per dollar spent on the second unit of Y is__________.
e. If the consumer has $420 to spend, ______ unit of X and _______units of Y maximize utility subject to the budget constraint. Explain.
f. If the consumer has $220 to spend, _______ units of X and_______ units of Y maximize utility subject to the budget constraint. Explain.
g. If the consumer wanted 4 units of X and 6 units of Y, what would have to be his/her budget constraint in order to maximize his/her utility? Explain.
