The table below shows the marginal utilities in utils that Sarah derives from consuming two goods, snacks, and movies. Quantity of Snacks Marginal Utility of Snacks Quantity of Movies Marginal Utility of Movies
0 - 0 -
1 20 1 50
2 18 2 35
3 15 3 24
4 12 4 20
5 10 5 15
6 8 6 10
Sarah has a limited weekly income of $50, and she spends it all on snacks and movies. Assume the price of snacks is $5 per unit, the price of a movie ticket is $10, and Sarah is a utility-maximizing consumer.
(a) Would Sarah be able to consume 3 snacks and 5 movies? Explain.
(b) How many snacks and movies will Sarah consume to maximize her utility? Explain.
(c) Calculate the total utility Sarah will receive from consuming the utility-maximizing combination of snacks and movies indicated in your answer in part (a). Show your work.
(d) Suppose Sarah's income increases to $60.
(i) What will happen to the marginal utility per dollar spent on movies?
(ii) Will Sarah be better off buying two more snacks or one more movie ticket? Explain.

(a) No, Sarah would not be able to consume 3 snacks and 5 movies.

(b) Sarah will maximize her utility.

(c) The total utility Sarah will receive is 174 utils.

(d(i)) The marginal utility per dollar spent on movies will fall from 1.50 utils to 1.00 utils.

(d(ii)) Sarah will not be better off if she buys two more snacks or one more movie ticket.

Explanation:

Note: See the attached excel file for the calculation of marginal utility per dollar of Snacks and Movies.

(a) Would Sarah be able to consume 3 snacks and 5 movies? Explain.

No, because the total expenses would $65 would be greater than her weekly income of $50.

That is, if Sarah consumes 3 snacks and 5 movies, her total expenses would be:

Total expenses = (Units of snacks * Price of snacks) + (Units of movies * Price of movies) = (3 * $5) + (5 * $10) = $65.

Since the total expenses would $65 would be greater than her weekly income of $50, Sarah would not be able to consume 3 snacks and 5 movies.

(b) How many snacks and movies will Sarah consume to maximize her utility? Explain.

Sarah will maximize her utility at the point where marginal utility per dollar of Snacks is equal to the marginal utility per dollar of Movies. That is, where the following condition holds:

Marginal Utility of Snacks / Price of Snacks = Marginal Utility of Movies / Price of Movies

In the attached excel file, the above condition holds where Sarah consumes 4 snacks and 3 movies. At this point (see the red color in the attached excel file), we have:

Marginal Utility of Snacks / Price of Snacks = Marginal Utility of Movies / Price of Movies = 2.40

Therefore, Sarah will maximize her utility when she consumes 4 snacks and 3 movies. Because at this point, marginal utility per dollar of Snacks is equal to the marginal utility per dollar of Movies which is equal to 2.40.

(c) Calculate the total utility Sarah will receive from consuming the utility-maximizing combination of snacks and movies indicated in your answer in part (a). Show your work.

Total utility Sarah will receive from consuming the utility-maximizing combination of snacks and movies is the addition of the total utility from consuming utility maximizing quantities of the two goods.

The total utility from consuming a utility maximizing quantity of one good is the addition of the marginal utility from the first unit up to the utility maximizing units. From the attached excel file, we have:

Total utility from consuming utility maximizing quantity of Snacks = 20 + 18 + 15 + 12 = 65 utils

Total utility from consuming utility maximizing quantity of Movies = 50 + 35 + 24 = 109 utils

Therefore, we have:

Total utility from consuming the utility-maximizing combination of snacks and movies = 65 + 109 = 174 utils

(d(i)) Suppose Sarah's income increases to $60. What will happen to the marginal utility per dollar spent on movies?

To determine this, we assume that Sarah spends all her weekly income on movies alone. Therefore, we have:

Number of movies tickets when weekly income is $50 = $50 / Price of movie ticket = $50 / 10 = 5

Number of movies tickets when weekly income is $60 = $60 / Price of movie ticket = $60 / 10 = 6

Marginal utility per dollar spent on movies when weekly income is $50 = Marginal utility when 5 tickets is bought / Price of movie ticket = 15 / 10 = 1.50 utils

Marginal utility per dollar spent on movies when weekly income is $60 = Marginal utility when 6 tickets is bought / Price of movie ticket = 10 / 10 = 1.00 utils

Therefore, the marginal utility per dollar spent on movies will fall from 1.50 utils to 1.00 utils.

(d(ii)) Suppose Sarah's income increases to $60. Will Sarah be better off buying two more snacks or one more movie ticket? Explain.

If Sarah buys two snacks

From the attached excel file, this makes the total unit of snacks to increase from 4 to 6. This makes the marginal utility per dollar spent on snacks to fall from 2.40 to 1.60 while the marginal utility per dollar spent on movies still remains at 2.40.

This implies that Sarah will not be better off if she buys two more snacks because she is not maximizing her utility as the marginal utility per dollar spent on snacks of 1.60 is not equal to the marginal utility per dollar spent on movies of 2.40.

If Sarah buys one more movie ticket

From the attached excel file, this makes the total unit of movie ticket to increase from 3 to 4. This makes the marginal utility per dollar spent on movies to fall from 2.40 to 2.00 while the marginal utility per dollar spent on movies still remains at 2.40.

This implies that Sarah will not be better off if she buys one more movie ticket because she is not maximizing her utility as the marginal utility per dollar spent on snacks of 2.40 is not equal to the marginal utility per dollar spent on movies of 2.00.

Bailey has a taxable short-term capital gain of the amount of $350, but no deductible loss for the car.

Explanation:

Based on the information given In a situation where Bailey purchased the new game system for the amount of $600 in which it was sold for the amount of $950. Which means that the taxable nature of these transactions is that she has a TAXABLE SHORT-TERM CAPITAL GAIN of the amount of $350, which is calculated as ($950-$600) while on the other hand their won't be any deductible loss amount for the car.