5. Suppose Ann consumes only X and Y and her utility is given by U(X, Y) = min (3X, 5Y). The price of X is , and the price of Y is . She has income I = $90 to spend on X and Y
(a) Are good X and good Y perfect substitutes or perfect complements? Why?
(b) Write down the consumption ratio of good X and good Y.
(c) Write down the budget constraint.
(d) What is the consumption bundle to maximize the utility level? What is the maximum utility level?
5. Suppose Ann consumes only X and Y and her utility is given by U(X, Y) = min (3X, 5Y). The price of X is , and the price of Y is . She has income I = $90 to spend on X and Y
(a) Are good X and good Y perfect substitutes or perfect complements? Why?
(b) Write down the consumption ratio of good X and good Y.
(c) Write down the budget constraint.
(d) What is the consumption bundle to maximize the utility level? What is the maximum utility level?
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Related questions
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.
