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Suppose the price of a sweater is $15. julia’s marginal benefit for purchasing each additional sweater is given in the table below. julia gets the most benefit from the first sweater and less benefit from each additional sweater. if julia is behaving rationally, how many sweaters will she purchase?

User Tuan Phan
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Final answer:

Julia will buy sweaters until the marginal benefit equals the price of the sweaters, ensuring her total utility is maximized. This is similar to José's scenario where he ensures the marginal utility per dollar is the same for T-shirts and movies to achieve the highest total utility.

Step-by-step explanation:

A rational consumer like Julia will purchase sweaters up to the point where her marginal benefit equals the price of the sweater. Each additional sweater(s) brings less satisfaction (or utility) to Julia, a concept known as diminishing marginal utility. This scenario also applies to the given example of José, who is making a decision between purchasing T-shirts and movies. The principle here is to maximize total utility by ensuring that the marginal utility per dollar is equalized across all goods.

If the last T-shirt provides more than twice the marginal utility of the last movie, this indicates greater bang for the buck. José should, therefore, purchase more T-shirts until the marginal utility per dollar of T-shirts is equal to that of movies. At José's optimal choice point S, with one T-shirt and six movies, his marginal utility per dollar is the same for both goods, signaling the highest total utility is achieved.

However, going beyond the optimal point, like from S to T, would mean a decrease in total utility for José, which rational behavior aims to avoid. This illustrated principle of balancing marginal utility per dollar across goods is the same that Julia would apply in deciding how many sweaters to buy, by purchasing up to the point where the additional benefit from the last sweater bought equals the cost.

User Abhijeet Kamble
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(Assuming the marginal benefits of the sweaters are: $50, $35, $30, $23, $12, $8, in order of purchase.)

Julia has a reducing marginal benefit for sweaters, meaning she values the first sweater she buys more than the second, which she values more than the third, and so on. The given list shows Julia’s marginal benefit for each additional sweater she buys. Julia will buy sweaters until her marginal benefit is lower than the price of a sweater, which is $15. This means Julia will buy 4 sweaters, since her marginal benefit for a 5th sweater is $12, which is lower than the price of a sweater, $15.

User WlJs
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