- If a consumer's indifference curves are L-shaped, it implies that the two goods are:
Answer: perfect complements, and the substitution effect of a price change is zero.
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.
- 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?
Answer: Buy 4 apples and 5 bananas to better align marginal utility per dollar ratios between the two goods
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.
- 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?
Answer: 12X+5Y=120
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. - 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?
Answer: The quantity demanded of rice increases by 6 pounds, and the law of demand holds for this consumer.
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. - 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:
Answer: leave, because the marginal cost of staying ($40) exceeds the marginal benefit of staying ($30).
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.
- 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?
Answer: Total utility increases at a decreasing rate, causing the marginal utility per dollar to fall unless the price also falls.
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.
- 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:
Answer: prefer the housing voucher because it has a higher monetary value.
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 $1,500 housing voucher constrains the consumer to spend the full amount on housing, which is more than they would freely choose. However, since the voucher's value ($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.
- 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?
Answer: Her decision is suboptimal because the marginal utility per dollar of good Y exceeds that of good X initially
Initially, MU_X/PX = 20/4 = 5 utils per dollar, and MU_Y/PY = 30/5 = 6 utils per dollar. Since MU_Y/PY > MU_X/PX, 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. - 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?
Answer: The substitution effect encourages her to work more, while the income effect encourages her to work less.
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.
- 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?
Answer: The substitution effect is zero because coffee and sugar cannot be substituted for one another in consumption.
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.
- 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:
Answer: a good's price is determined by its marginal utility, not its total utility.
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.
- 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?
Answer: 12 cans of Coke and 0 cans of Pepsi
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.
- 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?
Answer: 4 units
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.
- For a good to be classified as a Giffen good, which of the following conditions must be met?
Answer: The good must be inferior, and the income effect of a price change must be larger than the substitution effect.
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).
- 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?
Answer: 1 additional unit total, since any change in consumption can potentially establish a new equilibrium point
Currently in equilibrium: MU_A/PA = MU_B/PB, so 24/6 = 18/PB, meaning PB = $4.5. With $15 additional income, Alex could purchase various combinations. The minimum additional units for a new equilibrium is 1, since purchasing just one additional unit of either good will change the marginal utilities (due to diminishing marginal utility) and require rebalancing. Alex could buy 1 more unit of A ($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. - 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:
Answer: decrease as the consumer moves to a new, higher indifference curve.
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).
- 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?
Answer: The marginal utility of good A must have increased by more than 25% to compensate for reduced consumption of good B
Initially at equilibrium: MU_A/PA = MU_B/PB. 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)/PB. 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. - 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:
Answer: buy fewer apples and more bananas.
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, and for bananas it is 8/$1=8. Since 8>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. - 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?
Answer: The consumer's indifference curves can be mapped, but the numerical utility levels assigned to them are meaningful only for ranking.
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.
