24) Suppose a consumer spends all his income. His marginal utility per dollar on X is 4 and marginal utility per dollar on Y is 2. We know that A) utility can be increased by decreasing the consumption of X and increasing the consumption of Y. B) the price of Y must be eight times the price of X. C) utility can be increased by increasing the consumption of X and decreasing the consumption of Y. D) utility is maximized. E) the price of Y must be one-third the price of X.
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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 |
| 1 | 20 | 45 |
| 2 | 38 | 78 |
| 3 | 54 | 108 |
| 4 | 68 | 135 |
| 5 | 80 | 159 |
| 6 | 90 | 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.
