Utility maximizing condition

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Chapter 20, Problem 4CQ

To determine

Utility maximizing condition

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A consumer is currently purchasing three pairs of jeans and five T-shirts per year. The price of jeans is $30, and T-shirts cost $10. At the current rate of consumption, the marginal utility of jeans is 60, and the marginal utility of T-shirts is 30. Is this consumer maximizing his or her utility? Would you suggest that he buy more jeans and fewer T-shirts, or more T-shirts and fewer jeans?

Suppose John decides to buy 4 units of food and 4 units of clothing with his $12 budget. Would his marginal utility per dollar spent on food be greater than or less than his marginal utility per dollar spent on clothing? What does this tell you about how he should substitute food for clothing if he wanted to increase his utility without spending any more money?

Aria consumes only two goods, food and clothing. The marginal utility of the last dollar she spends on food is 12, and the marginal utility of the last dollar she spends on clothing is 9. The price of food is $1.20/unit, and the price of clothing is $0.90/unit. Is Aria maximizing her utility?