Suppose apples come in two quality levels, low quality and high quality. At a store in the apple-growing region, the price of low-quality apples is $3 per pound, and the price of high-quality apples is $6 per pound. Johnny lives in the apple-growing region and buys 8 pounds of each type. His marginal utility of low-quality apples is 9 utils and his marginal utility of high-quality apples is 18 utils. Is Johnny maximizing his utility? A. Yes. The marginal utility of high quality apples is > the marginal utility of low quality apples. B. Yes. The marginal utility per dollar of each good is equal. C. No. The marginal utility per dollar of low-quality apples is > the marginal utility per dollar of high-quality apples. D. No. The marginal utility per dollar of high-quality apples is > the marginal utility per dollar of low-quality apples.

Question

Keely Lane

Business

11 September, 21:57

Suppose apples come in two quality levels, low quality and high quality. At a store in the apple-growing region, the price of low-quality apples is $3 per pound, and the price of high-quality apples is $6 per pound. Johnny lives in the apple-growing region and buys 8 pounds of each type. His marginal utility of low-quality apples is 9 utils and his marginal utility of high-quality apples is 18 utils. Is Johnny maximizing his utility? A. Yes. The marginal utility of high quality apples is > the marginal utility of low quality apples. B. Yes. The marginal utility per dollar of each good is equal. C. No. The marginal utility per dollar of low-quality apples is > the marginal utility per dollar of high-quality apples. D. No. The marginal utility per dollar of high-quality apples is > the marginal utility per dollar of low-quality apples.

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Answers (1)

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Romeo Harmon · Answer 1

B

Explanation:

According to the consumer theory, consumers maximize its utility if the marginal rate of substitution (MRS) is equal to the price ratio: MgUx/MgUy=Px/Py. The MRS is the relationship between the marginal utility of each good and the price ratio is the relationship between the price per unit of each good. In this case, the problem is asking about the marginal utility per dollar (MU/$), so we transform the equation above to have it for good x and for good y: MgUx/Px=MgUy/Py. We can infer from this new equation that consumers maximize their utility when the MU/$ for good x is equal to the MU/$ for good y. If the MU/$ for good x is higher than the MU/$ for good y then the consumer should consume more of good x and an additional budget dollar should be spent on this good. and viceversa.

In this case, the problem is giving us de marginal utility for each good and its price per unit. For low-quality apples the MU/$ is 9/3=3 and the high-quality apples MU/$ is 18/6=3. This means consumer is indifferent between consuming low-quality apples or high-quality apples. Johnny bought 8 pounds each and so he is maximizing its utility.

If MU/$ of low-quality apples was higher than the MU/$ of high-quality apples, then Johnny would not maximize its utility because he bought the same quantity for both kinds of apples when he should buy more low-quality apples. The same if MU/$ of high-quality apples was higher than the MU/$ of low-quality, he would not maximize his utility.