Practice Worksheet

Chapter 21 — The Theory of Consumer Choice

Part 1

Short Answer — The Dining Hall vs. Cup O' Soup Budget

Given A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O' Soup for $1.50 per meal. Her weekly food budget is $60. Put dining-hall meals on the horizontal axis and Cups O' Soup on the vertical axis.

Income I = $60 P_meal = $6 P_soup = $1.50

Question a

What are the two intercepts of the budget constraint — that is, the most meals she can afford if she spends her entire budget on meals, and the most Cups O' Soup if she spends her entire budget on soup?

Max meals

Max Cups O' Soup

Hint To find each intercept, divide the total budget by the price of that good. Max meals = I / P_meal; max soups = I / P_soup.

Explanation Max meals = $60 ÷ $6 = 10 meals.
Max Cups O' Soup = $60 ÷ $1.50 = 40 soups.

The budget line runs from (0 meals, 40 soups) on the vertical axis down to (10 meals, 0 soups) on the horizontal axis. Every bundle on the line costs exactly $60.

Question b

What is the slope of the budget constraint, in "Cups O' Soup given up per extra meal"? Enter the magnitude (a positive number).

|slope| (soups per meal)

Hint The slope of the budget line with meals on the horizontal axis is −P_meal/P_soup. It tells you how many soups you must give up to afford one more meal.

Explanation Slope = −P_meal / P_soup = −$6 / $1.50 = −4.

So the magnitude is 4. Giving up 1 meal frees up $6, which buys 4 Cups O' Soup. Equivalently, to buy 1 more meal she must give up 4 soups. This slope is the relative price of meals in terms of soups.

Part 2

Short Answer — Optimum and a Price Change

Given Suppose the student's indifference curves are such that her initial optimum has her spending equal dollar amounts on dining-hall meals and Cup O' Soup (so $30 on each).

Question c

At the initial prices ($6 per meal, $1.50 per soup), how many meals and how many Cups O' Soup does she buy at her optimum? Label this bundle point A.

Meals at A

Soups at A

Hint Equal dollar amounts means $30 on meals and $30 on soup. Divide each by its price.

Explanation Meals: $30 ÷ $6 = 5 meals.
Soups: $30 ÷ $1.50 = 20 soups.

Verify feasibility: 5 × $6 + 20 × $1.50 = $30 + $30 = $60 ✓. The bundle (5, 20) lies exactly on the budget line — it's affordable and spends every dollar.

Question d

Now suppose the price of a Cup O' Soup rises from $1.50 to $2. Her budget and the price of a dining-hall meal are unchanged. What are the new intercepts of the budget constraint (max meals, max soups)?

New max meals

New max soups

Hint Only the soup price changes. The meals intercept depends on meal price, so it stays at $60 / $6. The soup intercept drops because soup is now more expensive: $60 / $2.

Explanation Max meals = $60 ÷ $6 = 10 meals (unchanged, since the price of meals is unchanged).
Max soups = $60 ÷ $2 = 30 soups (fell from 40).

The budget line pivots inward around the meals intercept (10). The new slope is −$6 / $2 = −3, so the line is now flatter in "soups per meal."

Question e

After the soup price rises, suppose the student's new optimum has her spending 30% of her budget on dining-hall meals (and the remaining 70% on Cup O' Soup). How many meals and how many soups does she buy at the new optimum? Label this bundle point B.

Meals at B

Soups at B

Hint 30% of $60 = $18 on meals. The remaining 70% = $42 on soup. Divide each dollar amount by the new price of that good.

Explanation Spending on meals: 0.30 × $60 = $18. Meals bought: $18 ÷ $6 = 3 meals.
Spending on soup: 0.70 × $60 = $42. Soups bought: $42 ÷ $2 = 21 soups.

Verify: 3 × $6 + 21 × $2 = $18 + $42 = $60 ✓.

Pay attention to this result. Her consumption of Cup O' Soup went from 20 → 21 even though the price of soup rose. That's the signature of a Giffen good: a good whose demand curve slopes upward because the income effect dominates the substitution effect. See Question 9 below.

Part 3

Multiple Choice

Question 1

Homer buys pizza for $10 and Pepsi for $2. He has income of $100. His budget constraint will shift inward (shrink) if:

The price of pizza rises to $12 The price of Pepsi falls to $1 His income rises to $150 The prices of pizza and Pepsi, and his income, all rise by 50 percent

Hint Compute the two intercepts (max pizza = I/P_pizza and max Pepsi = I/P_Pepsi) in each case and compare to the original (10 pizzas, 50 Pepsi). Which option makes the affordable set strictly smaller?

Explanation Answer: A. Original intercepts: 10 pizzas, 50 Pepsi.
(A) Pizza $10→$12: max pizza falls to 8.33, max Pepsi unchanged (50). The pizza intercept shrinks, so the budget set contracts. ✓
(B) Pepsi $2→$1: max Pepsi rises to 100, outward. ✗
(C) Income $100→$150: both intercepts grow (15, 75), outward. ✗
(D) All prices and income scale by 1.5: intercepts I/P are unchanged (still 10 and 50). No shift at all. ✗

Question 2

At any point on an indifference curve, the slope of the curve measures the consumer's:

income willingness to trade one good for the other perception of the two goods as substitutes or complements elasticity of demand

Hint The slope of the IC has a specific name: MRS. What does MRS stand for, and what does it measure?

Explanation Answer: B. The slope of the indifference curve is the marginal rate of substitution (MRS) — the rate at which the consumer is just willing to give up one good to get one more unit of the other while staying equally happy. Income (A) determines the budget line, not the IC. Perfect substitutes vs complements (C) is determined by the shape of the curve (straight-line vs L-shape), not its slope at a point. Elasticity (D) is a property of demand curves.

Question 3

A consumer buys two goods, X and Y, with prices P_x = $4 and P_y = $2. At her utility-maximizing optimum, what must her marginal rate of substitution (MRS, in units of Y per unit of X) equal?

MRS = 0.5 (Y per X) MRS = 1 (Y per X) MRS = 2 (Y per X) MRS = 4 (Y per X)

Hint At the optimum, the slope of the IC equals the slope of the budget constraint. That's the tangency condition. MRS = P_x / P_y.

Explanation Answer: C (MRS = 2). At the optimum the IC is tangent to the budget line, so their slopes are equal: MRS = P_x / P_y = $4 / $2 = 2. Intuition: because X costs twice as much as Y, the consumer must value one X as worth 2 Y. If MRS > 2, she'd want more X (higher marginal value than market price); if MRS < 2, she'd want more Y. Only MRS = 2 is an optimum.

Question 4

Mr. Burns buys only lobster and chicken. Lobster is a normal good; chicken is an inferior good. When the price of lobster rises, Mr. Burns buys:

less of both goods more lobster and less chicken less lobster and more chicken less lobster, but the impact on chicken is ambiguous

Hint Split the price change into the two effects. Substitution: lobster is now relatively more expensive → less lobster, more chicken. Income: the price rise makes him poorer, so he buys less of the normal good (lobster) and more of the inferior good (chicken). Which direction do the two effects push for each good?

Explanation Answer: C — less lobster and more chicken.

For lobster: Substitution effect says "less lobster" (it's more expensive now). Income effect also says "less lobster" (the price rise makes him poorer, and lobster is a normal good). Both effects push the same way → unambiguously less lobster.

For chicken: Substitution effect says "more chicken" (it's relatively cheaper now). Income effect also says "more chicken" (he's poorer, and chicken is inferior, so he buys more of it when poor). Both effects push the same way → unambiguously more chicken.

This is the rare case where an inferior good makes the answer unambiguous in BOTH directions.

Question 5

Maude's labor-supply curve slopes upward if, for Maude:

leisure is a normal good consumption is a normal good the income effect on leisure exceeds the substitution effect the substitution effect on leisure exceeds the income effect

Hint When the wage rises: substitution effect says "work more" (leisure is more expensive), income effect says "work less" (you're richer and buy more leisure). Which effect must dominate for total hours worked to rise with the wage?

Explanation Answer: D. When wage rises, the substitution effect pushes toward less leisure (work more), but the income effect (for most people, leisure is normal) pushes toward more leisure (work less). For the labor-supply curve to slope upward — meaning higher wages induce more work — the substitution effect must outweigh the income effect. If the income effect dominates instead, the curve bends backward.

Question 6

A Giffen good is a good for which:

demand is perfectly inelastic it is inferior, and the income effect is so large that it dominates the substitution effect consumers treat it as a perfect substitute for another good it is a luxury good that only the rich buy

Hint A Giffen good violates the law of demand: its demand curve slopes upward. That requires the two effects of a price change to push in opposite directions, AND the "wrong" one to win. Which combination does that?

Explanation Answer: B. A Giffen good is inferior (so the income effect points opposite to the substitution effect for that good) AND the income effect dominates. Example: potatoes for a very poor household during the Irish famine. When the price of potatoes rose, the household was so much poorer that it cut out meat entirely and ate more potatoes. All Giffen goods are inferior goods, but almost no inferior goods are Giffen — they're extremely rare.

Part 4

True or False

Question 7

Two indifference curves for the same consumer can cross each other.

Hint Suppose two ICs cross at some point. Use transitivity: the intersection point would be on both curves, so they'd represent the same satisfaction level — but a higher curve is supposed to mean strictly more satisfaction. Contradiction?

Explanation False. Indifference curves cannot cross. If they did, the intersection point would lie on both curves, making the consumer equally satisfied at two different "satisfaction levels" — a logical contradiction. More concretely: if curves cross, you could find a point on one curve that has more of both goods than a point on the other curve, yet be equally happy. That violates the assumption that more is better.

Question 8

All Giffen goods are inferior goods.

Hint For a Giffen good, the income effect must push the opposite direction from the substitution effect. What kind of good has an income effect that works "backward"?

Explanation True. A Giffen good requires the income effect to point in the opposite direction from the substitution effect. For that to happen, a price drop (which effectively makes the consumer richer) must cause the consumer to buy less of the good — i.e. the good must be inferior. So every Giffen good is an inferior good.

The converse is NOT true: most inferior goods are not Giffen. For a good to be Giffen, the income effect must also be so strong that it overwhelms the substitution effect — a very unusual situation that normally only arises for a staple food that dominates a poor household's budget.

Question 9

If a consumer's income increases while the prices of all goods stay the same, her budget constraint will shift outward in a parallel way (same slope).

Hint The slope of the budget line equals −P_x/P_y. Does this expression depend on income at all?

Explanation True. The slope of the budget line is −P_x/P_y, which depends only on prices, not income. When income rises, both intercepts (I/P_x and I/P_y) scale up by the same factor, so the line shifts outward while keeping the same slope. That's exactly what "parallel shift" means. Note: what the consumer does with that shift (buy more of both goods, or less of an inferior good) depends on preferences — but the budget line itself just moves out in parallel.

Part 5

Refer to Figure 21-1

Figure 21-1 A consumer chooses between two goods, X and Y. The figure shows her budget constraint (solid black) along with three of her indifference curves (I₁, I₂, I₃) and four labeled bundles (W, X, Y, Z). P_x = $5 and P_y = $10. Use the figure to answer the next two questions.

Figure 21-1. Budget line at I = $500, P_x = $5, P_y = $10. Three indifference curves and four labeled bundles.

Question 10 — Refer to Figure 21-1

Which point represents the consumer's utility-maximizing bundle (the optimum)?

Point W (inside the budget set, on I₁) Point X (on the budget line, on I₁) Point Y (tangent to I₂ on the budget line) Point Z (on I₃, above the budget line)

Hint The optimum must be (1) affordable (on or below the budget line) and (2) on the highest indifference curve that meets that test. The tangency point is the only point where the budget line touches — but never crosses — the highest reachable IC.

Explanation Answer: C (Point Y). Point Y is where the budget line is tangent to I₂, the highest reachable indifference curve. At the tangency, MRS = P_x/P_y.

Why not the others?
W is affordable but leaves money unspent — the consumer could move to a higher IC by spending more.
X is on the budget line but on a lower IC (I₁). The consumer could slide along the budget line toward the middle and reach I₂, a higher curve.
Z is on I₃ (most preferred), but sits above the budget line — unaffordable.

Question 11 — Refer to Figure 21-1

At the optimum in Figure 21-1, what is the consumer's marginal rate of substitution (MRS), in units of Y per unit of X?

MRS = 0.2 (Y per X) MRS = 0.5 (Y per X) MRS = 2 (Y per X) MRS = 5 (Y per X)

Hint At the optimum the IC is tangent to the budget line, so MRS equals the relative price: MRS = P_x / P_y. Plug in $5 and $10.

Explanation Answer: B (MRS = 0.5). At the optimum, MRS = P_x/P_y = $5 / $10 = 0.5 Y per X.

Sanity check on the graph: the budget line runs from (0, 50) to (100, 0), so its slope magnitude is 50/100 = 0.5 units of Y per unit of X. At point Y the IC has the same slope as the budget line (that's what "tangent" means), so MRS = 0.5. Intuitively: Y costs twice as much as X, so one unit of Y must be worth two units of X at the optimum — meaning one X is only worth half a Y.

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