All questions
Question 1
Morgan views Coke and Pepsi as perfect substitutes and is always willing to trade one can of Coke for one can of Pepsi. The price of Coke is $1.25 per can and the price of Pepsi is $1.50 per can. If Morgan has a budget of $15 to spend on soda, what is her utility-maximizing consumption bundle?
- 12 cans of Coke and 0 cans of Pepsi (correct answer)
- 0 cans of Coke and 10 cans of Pepsi
- 6 cans of Coke and 5 cans of Pepsi
- Any combination of Coke and Pepsi costing $15, since she is indifferent between them.
Explanation: For perfect substitutes, a rational consumer will spend their entire budget on the good that is less expensive, as it provides the same utility at a lower cost. In this case, Coke is priced at $1.25 and Pepsi at $1.50. Since Coke is cheaper, Morgan will maximize her utility by purchasing only Coke. With a budget of 15, she can buy \(15 / $1.25) = 12 cans of Coke.
Question 2
Maria currently consumes 5 units of good X and 3 units of good Y. The marginal utility of the 5th unit of X is 20, and the marginal utility of the 3rd unit of Y is 30. Good X costs $4 per unit and good Y costs $5 per unit. If Maria's income increases by $9, and she spends all of this additional income on one more unit of each good, what can we conclude about her decision?
- Her decision is optimal because she maintains proportional consumption of both goods with her increased income
- Her decision is suboptimal because the marginal utility per dollar of good Y exceeds that of good X initially (correct answer)
- Her decision is optimal because the additional expenditure exactly equals her additional income, satisfying the budget constraint
- Her decision is suboptimal because she should spend the entire additional income on good Y since it provides higher marginal utility
Explanation: Initially, MU_X/P_X = 20/4 = 5 utils per dollar, and MU_Y/P_Y = 30/5 = 6 utils per dollar. Since MU_Y/P_Y > MU_X/P_X, Maria should consume more Y and less X to maximize utility. When she buys one more unit of each (spending $4 + $5 = $9), she's not optimizing because she's still not equalizing marginal utility per dollar. Choice A incorrectly focuses on proportional consumption rather than marginal optimization. Choice C incorrectly assumes that satisfying the budget constraint alone ensures optimality. Choice D is wrong because it focuses on absolute marginal utility rather than marginal utility per dollar, and suggests spending all additional income on one good.
Question 3
Lisa consumes only apples and bananas. She currently buys 6 apples at $1 each and 4 bananas at $2 each, spending her entire $14 weekly budget. The marginal utility of the 6th apple is 8 utils and the marginal utility of the 4th banana is 20 utils. If Lisa wants to maximize her utility and can only make whole-unit changes, what should she do in the following week?
- Buy 8 apples and 3 bananas to increase apple consumption since apples are cheaper per unit
- Buy 4 apples and 5 bananas to better align marginal utility per dollar ratios between the two goods (correct answer)
- Buy 5 apples and 4.5 bananas to achieve perfect equalization of marginal utility per dollar
- Maintain current consumption since changing whole units would overshoot the optimal consumption balance
Explanation: Current MU/P ratios: apples = 8/1 = 8, bananas = 20/2 = 10. Since bananas provide higher marginal utility per dollar, Lisa should consume more bananas and fewer apples. Option B (4 apples, 5 bananas) costs $4 + $10 = $14, fitting the budget. This moves consumption toward equalizing MU/P ratios. Choice A incorrectly focuses on absolute price rather than marginal utility per dollar. Choice C is impossible since Lisa can't buy half bananas. Choice D incorrectly suggests the current allocation is optimal when MU/P ratios are unequal.
Question 4
A consumer optimization problem involves two goods where the consumer has reached equilibrium. If the price of good A increases by 25% while the price of good B and the consumer's income remain constant, and the consumer maintains the same quantity of good A, what must be true about the marginal utility of good A after this price change?
- The marginal utility of good A must have increased by exactly 25% to maintain the equilibrium condition
- The marginal utility of good A must have decreased due to income effects reducing overall consumption capability
- The marginal utility of good A must have increased by more than 25% to compensate for reduced consumption of good B (correct answer)
- The marginal utility of good A must remain unchanged since the consumer chose to maintain the same quantity
Explanation: Initially at equilibrium: MU_A/P_A = MU_B/P_B. After the 25% price increase in good A, if the consumer maintains the same quantity of A, they must reduce consumption of B (since income is fixed but A is more expensive). Reduced consumption of B increases MU_B due to diminishing marginal utility. For equilibrium to be restored: MU_A/1.25P_A = MU_B(new)/P_B. Since MU_B increased, MU_A must increase by more than 25% to maintain equality. Choice A incorrectly assumes MU_A increases by exactly 25%. Choice B wrongly focuses on income effects rather than the substitution needed for equilibrium. Choice D incorrectly assumes marginal utility is constant when consumption patterns change.
Question 5
Alex consumes goods A and B and is currently in equilibrium. The marginal utility of good A is 24 utils and the marginal utility of good B is 18 utils. If the price of good A is $6, and Alex's income increases by $15 while prices remain constant, what is the minimum number of additional units Alex must purchase to potentially reach a new equilibrium?
- 1 additional unit total, since any change in consumption can potentially establish a new equilibrium point (correct answer)
- 2 additional units total, since equilibrium requires consuming at least one more unit of each good
- 3 additional units total, since the income increase allows for substantial expansion of consumption possibilities
- 5 additional units total, since this equals the ratio of income increase to the lower-priced good
Explanation: Currently in equilibrium: MU_A/P_A = MU_B/P_B, so 24/6 = 18/P_B, meaning P_B = $4.5. With 15additionalincome,Alexcouldpurchasevariouscombinations.Theminimumadditionalunitsforanewequilibriumis1,sincepurchasingjustoneadditionalunitofeithergoodwillchangethemarginalutilities(duetodiminishingmarginalutility)andrequirerebalancing.Alexcouldbuy1moreunitofA(6) and have $9 left over, or other combinations, but needs only 1 additional unit minimum to disrupt and then reestablish equilibrium. Choices B, C, and D incorrectly assume multiple units are necessary when a single unit purchase can establish a new equilibrium. Question 6
The price of rice, an inferior good for a particular consumer, decreases. The substitution effect causes the consumer to purchase 10 more pounds of rice. The income effect causes the consumer to purchase 4 fewer pounds of rice. Which of the following accurately describes the total effect of the price change?
- The quantity demanded of rice increases by 6 pounds, and rice is a Giffen good for this consumer.
- The quantity demanded of rice increases by 14 pounds, and the law of demand is violated.
- The quantity demanded of rice increases by 6 pounds, and the law of demand holds for this consumer. (correct answer)
- The quantity demanded of rice decreases by 6 pounds, and rice is a Giffen good for this consumer.
Explanation: The total effect of a price change is the sum of the substitution and income effects. The substitution effect of a price decrease is always to increase quantity demanded (+10 pounds). Since rice is an inferior good, the income effect of a price decrease (which increases real income) is to decrease quantity demanded (-4 pounds). The total effect is 10+(−4)=+6 pounds. Because the price decreased and the total quantity demanded increased, the law of demand holds. A Giffen good is a special type of inferior good where the income effect is stronger than the substitution effect, causing quantity demanded to fall when the price falls; that is not the case here. Question 7
A consultant chooses how many hours to work each week. Her utility depends on both her total income and her hours of leisure. Her hourly wage rate increases significantly. If leisure is a normal good for this consultant, which of the following must be true regarding her decision?
- She will necessarily work more hours because the opportunity cost of leisure has increased.
- She will necessarily work fewer hours because she can afford more leisure with the higher income.
- The substitution effect encourages her to work more, while the income effect encourages her to work less. (correct answer)
- Both the substitution and income effects encourage her to work more hours and take less leisure.
Explanation: A higher wage has two effects on the labor-leisure choice. First, the substitution effect: a higher wage increases the opportunity cost of leisure, making leisure more expensive. This incentivizes the consultant to substitute away from leisure and toward work (work more). Second, the income effect: a higher wage increases her income for any given number of hours worked. Since leisure is a normal good, this increase in income will cause her to demand more leisure (work less). The total effect on hours worked is ambiguous and depends on the relative strengths of these two opposing effects.
Question 8
A consumer with an income of $120 per week buys two goods, X and Y. The price of good Y is $10 per unit. The price of good X is $20 per unit for the first 3 units purchased, and $10 per unit for all additional units. What is the maximum quantity of good Y the consumer can purchase if they buy exactly 5 units of good X?
- 2 units
- 4 units (correct answer)
- 6 units
- 7 units
Explanation: This is a multi-step calculation involving a kinked budget constraint. First, calculate the total cost of purchasing 5 units of good X. The first 3 units cost $20 each, and the next 2 units cost $10 each. Total cost for X = (3 units × $20/unit) + (2 units × $10/unit) = $60 + $20 = $80. Second, find the remaining income: $120 (total income) - $80 (spent on X) = $40. Third, calculate the quantity of good Y that can be purchased with the remaining income: 40/(10/unit of Y) = 4 units of Y. Question 9
A consumer's budget constraint is given by the equation 10X+5Y=100. If the government imposes a quantity tax of $2 per unit on good X and provides a lump-sum income subsidy of $20, what is the new equation for the consumer's budget constraint?
- 12X+5Y=100
- 12X+5Y=120 (correct answer)
- 10X+5Y=120
- 8X+5Y=80
Explanation: The original budget constraint is PXX+PYY=I, where PX=10, PY=5, and I=100. A quantity tax of $2 on good X increases its price to PX′=10+2=12. A lump-sum income subsidy of $20 increases total income to I′=100+20=120. The new budget constraint is therefore PX′X+PYY=I′, which is 12X+5Y=120. Question 10
A government program provides low-income families with a choice between a $1,000 cash grant or a $1,500 voucher that can only be spent on housing. A rational consumer who would have spent $800 on housing in the absence of the program will:
- be indifferent between the cash and the voucher because both allow for the purchase of the original housing bundle.
- prefer the cash grant because it provides greater flexibility in spending.
- prefer the housing voucher because it has a higher monetary value. (correct answer)
- be made worse off by either program because they distort consumption choices.
Explanation: The consumer initially plans to spend $800 on housing. With the $1,000 cash grant, the consumer has complete flexibility and would likely spend more than $800 but less than $1,500 on housing, using the remainder for other goods. The 1,500housingvoucherconstrainstheconsumertospendthefullamountonhousing,whichismorethantheywouldfreelychoose.However,sincethevoucher′svalue(1,500) significantly exceeds the cash grant ($1,000), the consumer can achieve a higher overall utility level despite the spending restriction. The large value difference outweighs the loss of flexibility, making the voucher preferable. Question 11
Alex paid a non-refundable, non-transferable $100 fee to enter a theme park. After a few hours, Alex begins to feel ill. Alex places a value of $30 on the enjoyment from the remaining rides. The cost of medicine that would alleviate the illness and allow Alex to stay is $40. From an economic perspective, Alex should:
- stay, because the $100 entry fee combined with the $30 of remaining enjoyment exceeds the $40 cost of medicine.
- leave, because the marginal cost of staying (40)exceedsthemarginalbenefitofstaying(30). (correct answer)
- stay, because leaving the park would mean wasting the $100 entry fee.
- leave, because the total expenditure ($100 + $40) is greater than the total benefit from the day.
Explanation: The rational decision should be based on marginal analysis at the time of the decision. The $100 entry fee is a sunk cost; it has already been paid and cannot be recovered, so it should not influence the decision to stay or leave. The relevant comparison is between the marginal benefit of staying (the $30 value of the remaining rides) and the marginal cost of staying (the $40 for medicine). Since the marginal cost exceeds the marginal benefit, the rational decision is to leave.
Question 12
The law of demand can be derived from the principle of diminishing marginal utility. As a rational consumer consumes more of a good, holding consumption of other goods constant, what is the sequence of events that explains why they are willing to buy an additional unit only if its price falls?
- Total utility increases at a decreasing rate, causing the marginal utility per dollar to fall unless the price also falls. (correct answer)
- The marginal utility of the good increases, but the consumer's income remains fixed, requiring a lower price.
- The consumer's total utility begins to decline, so the price must fall to compensate for the disutility.
- The opportunity cost of consuming the good increases, which must be offset by a lower price.
Explanation: The principle of diminishing marginal utility states that as consumption of a good increases, the additional satisfaction (marginal utility) from each extra unit decreases. A rational consumer will purchase a good up to the point where its marginal utility per dollar equals that of other goods. If the consumer is to be induced to buy one more unit, which provides lower marginal utility than the previous unit, the price must fall to keep the ratio of marginal utility to price (MU/P) in equilibrium with other purchasing options.
Question 13
Casey consumes coffee and sugar as perfect complements, always using two spoons of sugar for every one cup of coffee. The price of coffee is $2 per cup and the price of sugar is $0.25 per spoon. If the price of sugar increases to $0.50 per spoon, what is the substitution effect on Casey's consumption of coffee?
- The substitution effect causes Casey to consume more coffee to substitute away from the relatively more expensive sugar.
- The substitution effect is zero because coffee and sugar cannot be substituted for one another in consumption. (correct answer)
- The substitution effect causes Casey to consume less coffee because the coffee-sugar bundle is now more expensive.
- The substitution effect cannot be determined without also knowing the income effect on consumption.
Explanation: The substitution effect measures how a consumer substitutes one good for another when the relative price changes, holding utility constant. For perfect complements, goods are consumed in a fixed ratio (in this case, 1 coffee to 2 sugars). There is no possibility of substitution. Therefore, when the price of one of the complements changes, the substitution effect is zero. The entire change in quantity demanded is due to the income effect.
Question 14
A consumer is spending their entire budget on apples and bananas. The price of an apple is $2 and the price of a banana is $1. At their current consumption bundle, the marginal utility of the last apple consumed is 12 utils, and the marginal utility of the last banana consumed is 8 utils. To maximize total utility, this consumer should:
- buy more apples and fewer bananas.
- buy fewer apples and more bananas. (correct answer)
- buy more of both goods, as both provide positive marginal utility.
- make no change to their consumption bundle.
Explanation: The utility maximization rule states that a consumer should allocate their budget such that the marginal utility per dollar spent is equal across all goods: MUA/PA=MUB/PB. In this case, the marginal utility per dollar for apples is 12 / \2 = 6,andforbananasitis8 / $1 = 8.Since8 > 6$, the consumer is getting more utility per dollar from bananas than from apples. Therefore, to maximize utility, the consumer should reallocate their spending by buying more bananas and fewer apples. Question 15
A consumer buys only two goods, food and clothing. If the price of food falls, and the consumer's demand curve for food is downward-sloping and linear, the consumer's marginal rate of substitution of food for clothing will:
- increase at all points along the new budget constraint.
- decrease as the consumer moves down along their new indifference curve.
- be constant because the demand curve is linear.
- decrease as the consumer moves to a new, higher indifference curve. (correct answer)
Explanation: When the price of food falls, the budget constraint pivots outward. The consumer moves to a new optimal bundle on a higher indifference curve. At the new equilibrium, the indifference curve is tangent to the new, flatter budget constraint. The slope of the budget constraint is the price ratio (P_food / P_clothing), and the slope of the indifference curve is the marginal rate of substitution (MRS). Since the price of food has fallen, the price ratio is smaller, and the budget line is flatter. Therefore, at the new tangency point, the MRS must also be smaller (a flatter slope on the indifference curve).
Question 16
The 'water-diamond paradox' describes the observation that water, which is essential to life, is very inexpensive, while diamonds, which are not essential, are very expensive. The principles of marginal analysis resolve this paradox by explaining that:
- the consumer surplus from water is very small, while the consumer surplus from diamonds is very large.
- a good's price is determined by its marginal utility, not its total utility. (correct answer)
- the supply of water is highly elastic, while the supply of diamonds is perfectly inelastic.
- water is a normal good, whereas diamonds are a luxury good with high income elasticity of demand.
Explanation: The paradox is resolved by distinguishing between total utility and marginal utility. The market price of a good is related to its marginal utility—the utility of the last unit consumed—not its total utility. Water is abundant, so people consume it to the point where the marginal utility of the last gallon is very low. Thus, its price is low, even though the total utility from all water consumed is immense. Diamonds are scarce, so the marginal utility of an additional diamond is very high, leading to a high price, even though their total utility is much lower than that of water.
Question 17
An economic model of consumer choice assumes that utility is ordinal rather than cardinal. Which of the following is a direct implication of this assumption?
- The concept of diminishing marginal utility is invalid because utility cannot be measured.
- The consumer's indifference curves can be mapped, but the numerical utility levels assigned to them are meaningful only for ranking. (correct answer)
- The utility-maximizing rule MUX/PX=MUY/PY is no longer applicable for finding the optimal consumption bundle.
- Consumer surplus cannot be measured because the difference between willingness to pay and price is not quantifiable.
Explanation: Ordinal utility means that consumers can rank their preferences (e.g., bundle A is preferred to bundle B), but it does not assume that the intensity of those preferences can be measured in meaningful units ('utils'). This is the foundation of indifference curve analysis. We can say that an indifference curve further from the origin represents a higher level of satisfaction, but the numerical labels (e.g., U=10, U=20) only serve to rank the curves; we cannot say that the 'U=20' bundle is twice as good as the 'U=10' bundle.
Question 18
For a good to be classified as a Giffen good, which of the following conditions must be met?
- The good must be inferior, and the substitution effect of a price change must be larger than the income effect.
- The good must be normal, and the income effect of a price change must be larger than the substitution effect.
- The good must have no close substitutes, and it must account for a very small portion of the consumer's budget.
- The good must be inferior, and the income effect of a price change must be larger than the substitution effect. (correct answer)
Explanation: A Giffen good is a rare case where an increase in price leads to an increase in quantity demanded, violating the law of demand. This requires two conditions to be met simultaneously. First, the good must be an inferior good, meaning that the income effect is negative (a decrease in real income from a price rise leads to an increase in quantity demanded). Second, this negative income effect must be so strong that it outweighs the normal substitution effect (which always pushes quantity demanded down when price rises).
Question 19
If a consumer's indifference curves are L-shaped, it implies that the two goods are:
- perfect substitutes, and the marginal rate of substitution is constant.
- perfect complements, and the substitution effect of a price change is zero. (correct answer)
- unrelated goods, and a change in the price of one has no effect on the other.
- inferior goods, and the income elasticity of demand is negative.
Explanation: L-shaped indifference curves represent preferences for perfect complements, which are goods consumed together in a fixed proportion (e.g., left shoes and right shoes). The right angle of the 'L' indicates that having more of one good without more of the other does not increase utility. Because the goods cannot be substituted for one another, a change in their relative prices does not cause a substitution effect; the consumer will not change the proportion in which they are consumed. The entire response to a price change is an income effect.