# Topic 2: Consumer Theory

# Topic 2 Practice Questions

1. Suppose the price of a hamburger is $8 and the price of Coke is $3. Assume that the consumer has spent all of his income. If the marginal utility of a hamburger is 32 and the marginal utility of Coke is 15, is the current consumption bundle optimal?

*Correct Answer: No*

**Solution:**

MU_{c}/ P_{c} = 15 / 3 = 5

MU_{h} / P_{h} = 32 / 8 = 4

MU_{c}/ P_{c} > MU_{h} / P_{h}

So, this consumer should purchase fewer hamburgers and more Coke.

2. Tony has a utility function of U(X,Y) = XY. The price of a t-shirt (denoted by X) is $10, while the price of a coffee (denoted by Y) is $5. Tony’s budget to spend on t-shirts and coffee is $100. Which of the following represents Tony’s optimal basket of t-shirts and coffee? (Note: it must maximize his utility given his income).

A) X = 7, Y = 3

B) X = 6, Y = 6

C) X = 5, Y = 10

D) X = 0, Y = 15

E) X = 15, Y = 0

*Correct Answer: C*

**Solution:**

U = XY

MU_{X }= Y

MU_{Y} = X

Tangency condition: MRS_{X,Y} = P_{X }/ P_{Y}

MRS_{X,Y} = MU_{X }/ MU_{Y} = Y / X

P_{X }/ P_{Y} = 10 / 5 = 2

So Y = 2X

Sub Y = 2X into the budget constraint:

100 = 10X + 5Y

100 = 10X + 5(2X)

100 = 20X

X = 5

Y = 2X = 10

3. If two indifference curves for a single consumer cross each other, which assumption about preferences is violated?

A) Preferences are complete

B) Diminishing marginal rate of substitution

C) The goods are perfect substitutes

D) Transitivity

E) More is preferred to less

*Correct Answer: D*

4. Amy spends her income on two goods: x and y. She considers them to be perfect substitutes. Which of the following is correct? (where “I” is the income level.)

A) If MRS_{x, y} < P_{x} / P_{y}, then the optimal allocation of goods is X = I / P_{x} and Y= 0

B) If MRS_{x, y} > P_{x} / P_{y}, then the optimal allocation of goods is X = 0 and Y = I / P_{y}

C) If MRS_{x, y} = P_{x} / P_{y}, then there are only two optimal allocations of goods: X = I / P_{x} and Y = 0; or X = 0 and Y = I / P_{y}

D) If MRS_{x, y} > P_{x} / P_{y}, then the optimal allocation of goods is X = I / P_{x} and Y = 0

*Correct Answer: D*

5. When Amanda wakes up in the morning, she will either purchase Timbits (T) or a bagel (B). This is represented by the utility function U(T, B) = 15T + 10B.

In addition, the price of a bagel is $2 and the price of Timbits is $0.50 apiece. Amanda has a daily budget of $5 to spend on breakfast. She is planning to purchase 1 Bagel (B) and 6 Timbits (T). Is this allocation of goods utility-maximizing?

A) No, Amanda should consume Timbits only and no bagels

B) No, Amanda should consume bagels only and no Timbits

C) Yes, since this bundle lies on Amanda’s budget line

D) Yes, since MU_{t}/P_{t} = MU_{b}/P_{b}

*Correct Answer: A*

**Solution:**

Step 1: Verify that the budget constraint is satisfied.

I = P_{t}*T + P_{b}*B

$5 = ($0.50 * 6) + ($2 * 1)

$5 = 3 + 2

$5 = 5

Step 2: Is it utility-maximizing?

MU_{t} = 15

MU_{b} = 10

MU_{t} / P_{t} = 15 / 0.5 = 30

MU_{b} / P_{b} = 10 / 2 = 5

30 > 5

The current allocation of goods is not optimal. Amanda should consume Timbits only and no bagels.

6. AJ consumes two goods: fries and soda. Suppose that his marginal utility from drinking soda equals 1 / s, and his marginal utility from consuming fries is 1 / f. If the price of soda is $0.50, the price of fries is $4, and AJ’s income is $120, how much soda will he purchase?

A) 12

B) 24

C) 0

D) 120

E) 48

*Correct Answer: D*

**Solution:**

MRS_{s,f} = (1 / s) / (1 / f) = f / s

The optimal basket occurs where MRS_{s,f} = P_{s }/ P_{f}

f / s = 0.5 / 4 = 1 / 8, so s = 8f

The budget constraint is 0.5s + 4f = 120

Substituting s = 8f into the budget constraint:

0.5(8f) + 4f = 120, so f = 15

s = 8*15 = 120

The optimal quantity of s is 120 units.

7. The price of apples equals one-third the price of oranges. When drawing the budget line for apples and oranges, apples are on the horizontal axis. The slope of this budget line is _____.

*Correct Answer: -1/3*

**Solution:**

The slope of this budget line equals – (p_{a }/ p_{o}) = -(1/3)p_{o }/ p_{o }= -1/3

8. According to the *Equal Marginal Principle*, when consuming the optimal combination of goods X and Y, a consumer has:

A) MU_{X }= MU_{Y}

B) MU_{X }/ P_{Y }= MU_{Y }/ P_{X}

C) MU_{X }/ P_{X }= MU_{Y }/ P_{Y}

D) Constant MRS_{X,Y}

*Correct Answer: C*

9. Sarah is an environmentalist. She hates pollution. She neither likes nor dislikes meat. Which of the following graphs could be the indifference map for Sarah between beef hamburgers and water pollution? (Assume beef hamburgers are on the vertical axis and water pollution is on the horizontal axis and U_{1} < U_{2} < U_{3}).

*Correct Answer: B*

**Explanation:**

Sarah neither likes nor dislikes meat. The number of beef hamburgers will not influence her utility. Thus, the indifference curves should be vertical. Since summer hates pollution, less water pollution would make her happier.

10. Andrew has always wanted to explore and travel the world. After graduating from McMaster, Andrew was able to secure a well-paying job, and he could afford to travel once a year. Andrew enjoyed his annual trips but wished he could travel more. Recently, Andrew received a promotion, and he can now afford to travel five times a year. Although Andrew is happy that he can travel more, every additional trip seems to be less and less exciting for him. Which of the following is true about Andrew?

A) Travel has become an inferior good to Andrew

B) Andrew’s preferences are changing

C) Andrew would prefer to travel less

D) Andrew is experiencing diminishing marginal utility

E) Both B and D are correct

*Correct Answer: D*

**Solution: **

Diminishing marginal utility is defined as the consumption of additional units of a good that yields smaller additions to total utility as more of the goods are consumed. In this case, travelling provided high utility to Andrew when he could only afford to go once a year since he was doing it infrequently. As Andrew began to travel more, the trips felt less special since they were not as scarce as before, which gave Andrew less incentive to make the most out of each trip. We can see that this scenario fits the above definition and is an example of Andrew’s diminishing marginal utility for travelling.

11. A solution to a consumer’s optimal choice problem where one good is not being consumed at all (i.e., the optimal basket lies on the axis), is known as:

A) an endpoint solution

B) a corner solution

C) a single optimum solution

D) an axis solution

*Correct Answer: B*

12. The vending machine in Katherine’s office building offers cans of pop and candies. Katherine’s utility function is U = 3PC, where P is the amount of pop consumed per week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, what is the optimal combination of pop and candy?

A) 10 cans of pop

B) 10 bags of candy and 5 cans of pop

C) 20 bags of candy

D) 6 bags of candy and 7 cans of pop

E) 8 bags of candy and 6 cans of pop

*Correct Answer: B*

**Explanation:**

The optimal basket occurs when MU_{p} / P_{p} = MU_{c} / P_{c}.

MU_{p} = 3C, MU_{c} = 3P, P_{p} = $1, P_{c} = $0.5. We therefore have 3C/1 = 3P/0.5, which means 1.5C = 3P, or C = 2P. We now know that Katherine should buy twice as many candies as she should pop.

Her budget constraint will be $10 = P + 0.5C. Substituting C = 2P in the budget constraint. Then, solve for P. P = 5. C = 2P =10.

Katherine should consume 10 bags of candy and 5 pops.

13. Bailey consumes two goods, X and Y, and has the utility function:

U(X,Y) = 3X^{4/5}Y^{4/5}

Which of the following conditions **must** be true for the “*more is preferred to less*” assumption to be satisfied for good X?

A) Marginal utility of X is greater than 0 for all positive values of X and Y

B) Marginal rate of substitution is equal to the price ratio

C) Marginal utility of Y is greater than 0 for all positive values of X and Y

D) Marginal utility of X increases as the quantity of good X increases

E) Both A and C

*Correct Answer: A*

**Explanation:**

For the “more is preferred to less” to be satisfied for the good X, marginal utility of X (the extra satisfaction a consumer gets from receiving one more unit of X) must always be positive. If it is negative, the consumer would become less satisfied with receiving one more unit of a good. This would mean that more is not preferred to less.

14. When the indifference curves between two goods appear as L-shaped curves, we can say that the goods are:

A) normal goods

B) inferior goods

C) perfect substitutes

D) perfect complements

E) bads

*Correct Answer: D*

15. Suppose Zia has two goods: cookies and chips. They are perfect substitutes. The price of cookies is $2, and the price of chips is $4. Zia has $8 to spend. The marginal utility of cookies is 1, and the marginal utility of chips is also 1. Which of the following statements is false?

A) Zia should buy only cookies and no chips, in order to reach her optimal consumption basket

B) Zia should buy 4 cookies to reach her optimal consumption basket

C) Zia’s optimal basket is a corner solution

D) Zia’s budget line is tangent to her indifference curve at her optimal basket. The tangency condition holds

*Correct Answer: D*

**Explanation:**

The two goods, cookies and chips, are perfect substitutes with different prices and the same marginal utility. Zia’s optimal basket is a corner solution.

MU_{cookie} / P_{cookie} = 1 / 2

MU_{chip} / MU_{chip} = 1/4

Because MU_{cookie} / P_{cookie} > MU_{chip} / MU_{chip}, Zia only consumes cookies and no chips.

Income / P_{cookie} = 8 / 2 = 4. So, Zia will consume 4 units of cookies.

16. Mary uses the entirety of her income to buy face masks (f) and hand sanitizer (h). She currently buys 10 face masks and 1 hand sanitizer. The price per unit of face masks is $0.5, and the price per unit of hand sanitizer is $4. Her marginal utility from face masks is 1, and her marginal utility from hand sanitizer is 8. Is her current basket choice optimal?

A) Yes, her optimal basket contains 10 face masks and 1 hand sanitizer.

B) No, she should buy more of both hand sanitizer and face masks.

C) No, she should buy more hand sanitizer and fewer face masks.

D) No, she should buy less of both.

*Correct Answer: A*

**Explanation:**

Mary is at her optimal basket. Her MU_{f} / P_{f} = 1/0.5 = 2. MU_{h} / P_{h} = 8/4 = 2.

MU_{f} / P_{f} = MU_{h} / P_{h}. Thus, Mary’s current consumption basket is optimal.

17. Mark’s income is $60. The price of clothing is $1 per unit, and the price of food is $6 per unit. With clothing on the horizontal axis and food on the vertical axis, what is the equation of his budget line, and what is the slope of the budget line?

A) C = 2 -(4/7)F, 3/8

B) F = 10 -(1/6)C, -1/6

C) F = 10 -(1/2)C, 1/6

D) C = 4 -(2/7)F, -2/7

*Correct Answer: B*

**Explanation:**

The budget constraint is C + 6F = 60

6F = 60 – C

6F / 6 = 60 / 6 – C / 6

F = 10 – (⅙)C

The slope of the budget line is -1/6

18. Anny has four baskets of goods that she may choose from: A, B, C or D. Anny prefers A to B, and prefers A to D. She is indifferent between B and C, but prefers C to D.

I.B and C lie on the same indifference curve.

II.Her order of preference can be determined as A > B > C > D.

III.There are 3 different utility values associated with the four baskets: A, B, C, D.

A) I is false, II and III are true.

B) I and II are true, III is false.

C) I, II and III are true.

D) I and III are true and II is false.

*Correct Answer: D*

**Explanation:**

Basket A has the highest utility as it is preferred to B, C and D.

Since Anny is indifferent between B and C, the two baskets lie on the same indifference curve.

All baskets are preferred to D.

19. Looking at the utility of perfect substitutes, if the slope of the budget line is -P_{x }/ P_{y} = -3, and the MRS_{x,y} = 7, what will that tell us about the consumer’s optimal choice?

A) Optimal choice will occur when Y = I / P_{y} and X = 0.

B) Optimal choice will occur on any point on the budget line.

C) Optimal choice will occur when X = I / P_{x} and Y = 0.

D) Optimal choice will occur on any point on the indifference curve.

*Correct Answer: C*

**Explanation:**

Since MRS_{x,y} > P_{x }/ P_{y}, the optimal consumption basket would occur when X = I / Px and Y = 0.

20. Assume Jim consumes two goods: X and Y. He has a utility function of U=X^{2}Y on bundles of (X, Y). The price for good X is twice the price of good Y. If Jim bought a combination of the two goods, and in doing so achieved a utility of 1000, how much of good X did Jim buy?

A) 5

B) 20

C) 10

D) 25

*Correct Answer: C*

**Explanation:**

MRS_{x,y} = MU_{x} / MU_{y} = 2XY / X^{2} = 2Y / X

Tangency condition: MRS_{x,y} = P_{x }/ P_{y}

2Y / X = 2P_{y} / P_{y}

Y / X = P_{y} / P_{y}

Y / X = 1

So, when Jim maximizes his utility, Y = X

U = X^{2}Y = 1000

substitute Y = X into X^{2}Y = 1000

1000 = X^{2}Y

1000 = X^{3}

*So, X = 10*

21. Robert’s utility function on bundles of (x, y) is given by: U = 2x^{4}y^{5}. What is the value of MRS_{x,y} when x = 3 and y = 2?

A) 2/7

B) 1/4

C) 8/15

D) 3/4

E) 5/2

*Correct Answer: C*

**Solution:**

U = 2x^{4}y^{5}

MU_{x} = dU / dx = 8x^{3}y^{5}

MU_{y} = dU / dy = 10x^{4}y^{4}

MRS_{x,y} = MU_{x} / MU_{y} = 8y/10x=4y/5x

When x=3 and y=2

MRS_{x,y}= 4y/5x=8/15

22. Suppose Eric has a total income of $100. He uses all the income to purchase apples and oranges. Assume the price of apples is $5 per bag, and the price of oranges is $15 per bag. With apples on the horizontal axis and oranges on the vertical axis, what is Eric’s budget constraint? Assume the price of oranges dropped by $5, what is the slope of the new budget constraint?

A) 5X + 15Y = 100; -1/2

B) 15X + 5Y = 100; -1/2

C) 5X + 15Y = 100; 1/2

D) 15X + 5Y = 100; 1/2

*Correct Answer: A*

**Explanation: **

Slope of the new budget constraint = -Pₓ/P_{y} = -5/(15-5) = -1/2

23. Suppose Jane loves jam but neither likes nor dislikes peanut butter. If jam is plotted on the horizontal axis and peanut butter is plotted on the vertical axis, what is the shape of her indifference curve?

A) upward sloping

B) downward sloping

C) horizontal

D) vertical

*Correct Answer: D*

**Explanation:**

Jane’s utility solely depends on the quantity of jam. Peanut butter is neutral to her.

24. Claire has two meal options at work to buy for her lunch break: pasta (P) and sushi (S). Pasta costs $5 per meal (P_{p}), and sushi costs $7 per meal (P_{s}). Claire has $35 dollars (I) for this week’s lunches. If sushi is on the horizontal axis, which equation represents Claire’s budget line? What is the vertical intercept of the budget line?

A) 7S + 5P = 35, 5

B) 5S + 7P = 35, 7

C) 7S + 5P = 35, 7

D) 7S + 7P = 35, 5

*Correct Answer: C*

**Solution:**

Claire’s budget line is 7S + 5P = 35. The vertical intercept represents the amount of good Y that an individual could have if she only consumed that one good. I/P_{p} = 35/5 = 7

25. John has separate yearly subscriptions to comic books(C) and auto magazines(M). He spends his income on these two goods. He considers these goods to be perfect substitutes. The cost of comic books is $30, while the cost of auto magazines is $45. The marginal utility for comic books is 40, while the marginal utility for auto magazines is 50. John was recently promoted, which enabled him to have more income and consume more of these goods. To maximize his utility, John should:

A) Increase comic book consumption and decrease auto magazine consumption

B) Increase auto magazine consumption and decrease comic book consumption

C) Use all his income to buy only comic books

D) Use all his income to buy only auto magazines

E) Spend his new income equally on comic books and auto magazines

*Correct Answer: C*

**Explanation: **

MU_{c} / P_{c} = 40/30 = 1.33. MU_{m} / P_{m} = 50/45 = 1.11

MU_{c} / P_{c} > MU_{m} / P_{m}.

John considers these goods to be perfect substitutes. Thus, John’s optimal solution is a corner solution. His optimal choice is to spend all his income on only comic books.

26. Which of the following is FALSE with regards to optimal baskets?

A) It must be located on the budget line.

B) A higher level of satisfaction can be attained.

C) It must give the consumer the most preferred combination of goods and services.

D) The marginal utility (x) per dollar spent on one good (x) is equal to the marginal utility (y) per dollar spent on another good (y).

*Correct Answer: B*

**Explanation:**

When consuming the optimal basket, a consumer’s utility is maximized. A higher level of satisfaction cannot be attained given the current income and prices of the two goods.

27. Diminishing marginal utility is defined as:

A) Additional happiness from consuming one more unit of a good.

B) The consumption of additional units of a good will yield larger additions to utility as more of a good is consumed.

C) The consumption of additional units of a good will yield smaller additions to utility as more of a good is consumed.

D) The amount of a good that a consumer is willing to give up to consume one additional unit of another good.

*Correct Answer: C*

**Explanation:**

A is the definition of marginal utility. D is the definition for marginal rate of substitution.

28. Stacey consumes both apples and bananas. Suppose apples are on the x-axis and bananas are on the y-axis. Assume her income remains constant. An increase in the price of apples will affect her budget by:

A) rotating the budget line to the right along the x-axis

B) rotating the budget line to the left along the x-axis

C) shifting the budget line to the right

D) shifting the budget line to the left

**Correct Answer: B**

**Explanation:**

Stacey’s income is constant. If the price of an item increases, the maximum amount of that item Stacey can purchase will decrease.

29. Which of the following goods would be best represented by indifference curves that are downward sloping straight lines?

A) pancake mix and maple syrup

B) pancake mix and cinnamon buns

C) pancake mix and pizza

D) pancake mix and bacon

*Correct Answer: B*

**Explanation:**

Pancakes and cinnamon buns are the main components of a breakfast meal. Most people view them as perfect substitutes in consumption.

30. Every week since lockdown, Jack spends his entire budget to purchase 2 boxes of fried chicken and 3 cream puffs. Each box of fried chicken costs $8 and each cream puff costs $5. Suppose Jack’s marginal utility from fried chicken and cream puffs is 12. What should Jack do if he wants to increase his utility?

A) Increase fried chicken consumption and reduce cream puff consumption.

B) Increase cream puff consumption and reduce fried chicken consumption.

C) Increase both cream puff and fried chicken consumption.

D) Maintain current consumption.

*Correct Answer: B*

**Explanation**:

MU_{f} / P_{f} = 12/8 = 1.5.

MU_{c} / P_{c} = 12/5 = 2.4.

MU_{c} / P_{c} > MU_{f} / P_{f} . Jack can increase his utility by consuming more cream puffs and less fried chicken.

31. Suppose Judy only consumes hamburgers (H) and pizza (P). Her utility function is given as:

U = 0.5H^{2}P^{2}

Her weekly salary is $280. The unit price of hamburgers is $5, and the unit price of pizza is $10. Find Judy’s optimal daily consumption basket.

*Correct Answer:*

P = 14, H = 28

Judy should consume 14 pizzas and 28 hamburgers.

**Solution:**

MU_{h} = HP^{2}, MU_{p} = H^{2}P

MRS_{h,p} = MU_{h} / MU_{p} = P / H

To maximize utility, set MRS_{h,p} = P_{h }/ P_{p}

P / H = 5/10

H = 2P

Budget constraint: 5H + 10P = 280

Substituting H = 2P into the budget constraint:

5*(2P) + 10P = 280, P = 14, H = 2P = 28