Use the following information to answer the question below. Cloe is given $4 of pocket money to be spent on either hard candies or chocolates. Chocolates cost 40 cents each and hard candies cost 80 cents each. The marginal utilities derived from the consumption of each product are as shown in the following table. Number of ItemsMarginal Utility of ChocolatesMarginal Utility of Hard Candies160150250140340120430100520 80610 707 5 508 0 20 What is Cloe’s total utility at her utility maximizing bundle?Multiple Choice870 utils620 utils80 utils150 utils
Question
Use the following information to answer the question below. Cloe is given $4 of pocket money to be spent on either hard candies or chocolates. Chocolates cost 40 cents each and hard candies cost 80 cents each. The marginal utilities derived from the consumption of each product are as shown in the following table. Number of ItemsMarginal Utility of ChocolatesMarginal Utility of Hard Candies160150250140340120430100520 80610 707 5 508 0 20 What is Cloe’s total utility at her utility maximizing bundle?Multiple Choice870 utils620 utils80 utils150 utils
Solution
To find Cloe's utility maximizing bundle, we need to find the combination of chocolates and hard candies that maximizes her total utility given her budget constraint.
First, we need to calculate the marginal utility per dollar for each good. This is done by dividing the marginal utility of each good by its price.
For chocolates:
- At 1 chocolate, the marginal utility per dollar is 150/0.40 = 375 utils/dollar
- At 2 chocolates, the marginal utility per dollar is 140/0.40 = 350 utils/dollar
- At 3 chocolates, the marginal utility per dollar is 120/0.40 = 300 utils/dollar
- At 4 chocolates, the marginal utility per dollar is 100/0.40 = 250 utils/dollar
- At 5 chocolates, the marginal utility per dollar is 80/0.40 = 200 utils/dollar
- At 6 chocolates, the marginal utility per dollar is 70/0.40 = 175 utils/dollar
- At 7 chocolates, the marginal utility per dollar is 50/0.40 = 125 utils/dollar
- At 8 chocolates, the marginal utility per dollar is 20/0.40 = 50 utils/dollar
For hard candies:
- At 1 hard candy, the marginal utility per dollar is 60/0.80 = 75 utils/dollar
- At 2 hard candies, the marginal utility per dollar is 50/0.80 = 62.5 utils/dollar
- At 3 hard candies, the marginal utility per dollar is 0/0.80 = 0 utils/dollar
Cloe should consume the good with the highest marginal utility per dollar first until her budget is exhausted.
Given her budget of 0.40 each) or 5 hard candies (at $0.80 each).
Looking at the marginal utility per dollar, she should consume chocolates first. She can afford 10, but the marginal utility per dollar decreases after the 7th chocolate. Therefore, she should consume 7 chocolates. This will cost her 1.20.
With the remaining 0.80 each). The marginal utility per dollar for the first hard candy is higher than for the 8th chocolate, so she should consume 1 hard candy.
Therefore, Cloe's utility maximizing bundle is 7 chocolates and 1 hard candy.
To find her total utility at this bundle, we sum the marginal utilities of the 7 chocolates and 1 hard candy:
Total utility = (150 + 140 + 120 + 100 + 80 + 70 + 50) + 60 = 770 utils
Therefore, Cloe’s total utility at her utility maximizing bundle is 770 utils.
None of the multiple choice options match this answer. There may be a mistake in the question or the answer choices.
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