QQuestionEconomics
QuestionEconomics
The Table below shows the utility a college student obtains from digital music albums and lattes. Albums are $7.00 each and lattes are $3.50. Assume the college students exhaust all of her income on these two goods.
| Units of goods | Marginal utility of digital albums | Marginal utility of albums per dollar spent | Marginal utility of lattes | Marginal utility of lattes per dollar spent |
| --- | --- | --- | --- | --- |
| First | 35 | 5 | 18 | 5.14 |
| Second | 26.25 | 3.75 | 14 | 4 |
| Third | 21 | 3 | 12 | 3.43 |
| Fourth | 17.5 | 2.5 | 10 | 2.86 |
Suppose the student receives a coffee shop gift card worth $7.00. What is the total utility she derives from the gift card?
| Number | |
| --- | --- |
| | utils |
What if she were given $7.00 in cash instead? What is her total utility in this case?
| Number | |
| --- | --- |
| | utils |
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Answer
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Step 1:: First, let's calculate the total utility the student derives from spending the $7.00 gift card on lattes.
where $$MU\_{lattes, i}$$ is the marginal utility of the ith latte.
We do this by summing up the marginal utility of each latte she buys with the gift card.
Step 2:: Plug in the marginal utilities from the table:
\text{Total utility from lattes} = 18 + 14 + 12 + 10 = 54
Step 3:: Now, let's calculate the total utility she derives from spending $7.00 in cash on digital albums.
where $$MU\_{albums, i}$$ is the marginal utility of the ith album.
We do this by summing up the marginal utility of each album she buys with the cash.
Step 4:: However, we can see from the table that after buying the first album, the student's marginal utility from albums per dollar spent drops below 1.
This means that she gets less utility from spending her money on albums than on lattes. Therefore, she will spend all of her $7.00 on lattes instead of albums.
Step 5:: Thus, the total utility she derives from the $7.00 in cash is the same as the total utility she derives from the gift card, which is 54 utils.
Final Answer
The total utility the student derives from the gift card is 54 utils, and the total utility she derives from $7.00 in cash is also 54 utils.
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