In May and June, Mary spent all her clothing budget on bathing suits and beach bags. Each bathing suit cost $73. At Mary’s optimal choice, her marginal utility from the last bathing suit purchased is 337 and her marginal utility from the last beach bag purchased is 232. This means that each handbag must cost: Please calculate the answer to two decimals.
In economic decision-making, rational consumers aim to maximize their satisfaction, or utility, given their budget constraints. This involves making choices that ensure the marginal utility per dollar spent is equal across all goods. Mary, in this scenario, spent her entire clothing budget on bathing suits and beach bags. To determine the cost of each beach bag, we can leverage the concept of marginal utility and consumer choice theory.
Marginal utility represents the additional satisfaction or pleasure a consumer derives from consuming one more unit of a particular good. In this case, Mary’s marginal utility from the last bathing suit purchased is 337, and the marginal utility from the last beach bag purchased is 232. These values indicate the incremental satisfaction Mary gains from the last unit of each product.
The principle of rational consumer choice suggests that a consumer should allocate their budget in a way that ensures the marginal utility per dollar spent is the same for all goods. In other words, Mary should spend her budget in a manner that makes the marginal utility per dollar spent on bathing suits equal to the marginal utility per dollar spent on beach bags.
To determine the optimal cost of each beach bag, we need to calculate the marginal utility per dollar spent for both bathing suits and beach bags. This calculation is straightforward:
Marginal Utility per Dollar Spent = Marginal Utility / Cost
For bathing suits, the calculation is as follows:
Marginal Utility per Dollar Spent on Bathing Suits = 337 / $73 ≈ 4.61
Now, we need to set the marginal utility per dollar spent on beach bags equal to this value, as follows:
232 / x = 4.61
Where “x” represents the cost of each beach bag. Solving for “x,” we find:
x = 232 / 4.61 ≈ 50.22
Mary should spend approximately $50.22 on each beach bag to maximize her overall satisfaction while adhering to her budget constraints. Rounded to two decimal places, this calculation ensures that she receives the same level of additional satisfaction for each dollar spent on bathing suits and beach bags, making her choices economically rational.
In the realm of consumer economics, rational choice theory emphasizes the importance of allocating one’s budget in a way that maximizes overall satisfaction. By applying this principle and considering Mary’s marginal utility data, we’ve determined that each beach bag should cost approximately $50.22. This allocation ensures that Mary gets the most value for her budget, making her choices economically sensible and optimizing her utility
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