CHAPTER 3

Provide definition, meaning and example with all. Diagram where needed
must draw.

1. What are the four basic assumptions about individual preferences?

Explain the significance or meaning of each.
Four Basic Assumptions about Individual Preferences
Definition: These are assumptions economists make about how
people rank different choices.
Assumptions:
1. Completeness: You can compare any two bundles.
Example: You know if you like tea more than coffee or if you like
both equally.
2. Transitivity: Preferences are consistent.
Example: If you prefer A over B, and B over C, then you prefer A
over C.
3. More is Better (Non-satiation): More of a good is preferred to
less.
Example: If you like chocolate, you prefer 3 bars over 2.
4. Diminishing Marginal Rate of Substitution (MRS): Willingness
to trade one good for another decreases as you have more of one.
Example: The more apples you have, the fewer extra apples you're
willing to trade for bananas.

2. Can a set of indifference curves be upward sloping? If so, what

would this tell you about the two goods?

No, usually not.

If they were, it would mean:

→ You like more of both goods worse, or one good is "bad", like pollution.
Example: If one good is trash, more trash would require more of the other good (like
money) to keep you happy.

3. Explain why two indifference curves cannot intersect.

Why Can’t Indifference Curves Intersect?
Reason: It would violate transitivity.
Example: If point A = point B, and B = C, but A ≠ C, that makes no sense.

4. Jon is always willing to trade one can of Coke for one can of Sprite,
or one can of Sprite for one can of Coke. a. What can you say about
Jon’s marginal rate of substitution? b. Draw a set of indifference
curves for Jon. c. Draw two budget lines with different slopes and
 illustrate the satisfaction-maximizing choice. What conclusion can
you draw?
Jon's Coke and Sprite Preferences
 a. MRS = 1 (he’s willing to swap 1 for 1 always).
 b. Indifference curves are straight lines with slope -1.
 c. Different budget lines (from prices) still give max satisfaction
where the budget line touches the highest indifference curve.
→ Conclusion: Perfect substitutes lead to corner solutions
depending on prices.

5. What happens to the marginal rate of substitution as you move

along a convex indifference curve? A linear indifference curve?
MRS Along Curves
 Convex curve: MRS decreases as you move right.
 Linear curve: MRS is constant.

6. Explain why an MRS between two goods must equal the ratio of the
price of the goods for the consumer to achieve maximum
satisfaction.

To maximize utility, you should spend money where bang-for-buck is equal across
goods.

MRS = Price of Good X / Price of Good Y

7. Describe the indifference curves associated with two goods that are
perfect substitutes. What if they are perfect complements?

Perfect Substitutes vs Complements

 Perfect Substitutes: Straight line indifference curves.
Example: Jon with Coke/Sprite.
 Perfect Complements: L-shaped indifference curves.
Example: Left and right shoes.

8. What is the difference between ordinal utility and cardinal utility?

Explain why the assumption of cardinal utility is not needed in order
to rank consumer choices.
Ordinal vs Cardinal Utility
 Ordinal: Just rank preferences (don’t need numbers).
 Cardinal: Assign actual numbers to satisfaction.
We only need ordinal to explain choices.
9. Upon merging with the West German economy, East German
consumers indicated a preference for Mercedes-Benz automobiles
over Volkswagens. However, when they converted their savings into
deutsche marks, they flocked to Volkswagen dealerships. How can
you explain this apparent paradox
East Germany Car Paradox
They liked Mercedes more (in theory), but bought Volkswagens due to price.
→ Shows that budget constraint matters more than just preference.

10. Draw a budget line and then draw an indifference curve to

illustrate the satisfaction-maximizing choice associated with two
products. Use your graph to answer the following questions. a.
Suppose that one of the products is rationed. Explain why the
consumer is likely to be worse off. b. Suppose that the price of one
of the products is fixed at a level below the current price. As a
result, the consumer is not able to purchase as much as she would
like. Can you tell if the consumer is better off or worse off?
Budget Line, Indifference Curve, and Changes
Budget Line and Indifference Curve Diagram:
A budget line shows all combinations of two goods (say, apples
and oranges) a consumer can afford.
An indifference curve shows combinations of two goods that give
the same satisfaction.
Satisfaction-Maximizing Choice:
Occurs where the indifference curve is just tangent to the
budget line.
(a) One Product Is Rationed
If you're limited in how much of one good you can buy (e.g., only 2
oranges allowed), your choice is restricted.
→ You can’t reach the highest indifference curve possible, so
you're worse off.
Example: You want 5 oranges, but can only buy 2 → lower utility.
(b) Price is Fixed Below Market Price, but Quantity Is Limited
You get a discount, but can't buy as much as you want.
Effect: Unclear – depends on your preferences.
 If you value the product a lot, you'll be worse off.
 If you didn't want much anyway, you might be better off.

11. Describe the equal marginal principle. Explain why this

principle may not hold if increasing marginal utility is associated
with the consumption of one or both goods.
Equal Marginal Principle (Equal Marginal Utility per Dollar)
Definition: You maximize utility when:
 MUXPX=MUYPY\frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}PXMUX=PYMUY
→ The extra satisfaction per dollar should be equal across goods.
Why It Might Not Hold:
If marginal utility increases with consumption (which is rare), then more = more
joy.
This violates the usual assumption of diminishing marginal utility.Example: If
eating more chocolate somehow makes you enjoy each new piece more, then you
might not balance spending.

12. The price of computers has fallen substantially over the past
two decades. Use this drop in price to explain why the Consumer
Price Index is likely to overstate substantially the cost-of-living index
for individuals who use computers intensively.
Why CPI Overstates Cost of Living When Computer Prices Fall
The Consumer Price Index (CPI) uses fixed bundles of goods.
Issue: If computer prices fall, people buy more computers and shift their spending.
CPI doesn’t account for this shift, so it overstates how much more expensive life is.
Example: If a laptop was $1,000 and now it’s $500, your real purchasing power has
increased—but CPI might not show that properly.

13. plain why the Paasche index will generally understate the
ideal cost-of-living index.
Why Paasche Index Understates Cost-of-Living Index
Paasche Index uses current prices and current quantities.
Problem: It assumes people already adapted to price changes by changing what they
buy (which lowers cost).
→ It understates the true cost of maintaining original utility.
Example: If apples get expensive and you switch to bananas, the Paasche index says
cost of living didn’t rise much—but in truth, you gave up apples, so satisfaction might
be lower.

EXCERCISE

1. In this chapter, consumer preferences for various commodities did

not change during the analysis. In some situations, however,
preferences do change as consumption occurs. Discuss why and
how preferences might change over time with consumption of these
two commodities: a. cigarettes. b. dinner for the first time at a
restaurant with a special cuisine.
How Preferences Change Over Time
a. Cigarettes: People may initially dislike them but develop addiction →
preferences change due to habit formation.
b. Special cuisine: You may be unsure at first. After tasting it, you might like it more
or less → preferences update with experience.
 2. Draw indifference curves that represent the following individuals’
preferences for hamburgers and soft drinks. Indicate the direction in
which the individuals’ satisfaction (or utility) is increasing. a. Joe has
convex indifference curves and dislikes both hamburgers and soft
drinks. b. Jane loves hamburgers and dislikes soft drinks. If she is
served a soft drink, she will pour it down the drain rather than drink
it. c. Bob loves hamburgers and dislikes soft drinks. If he is served a
soft drink, he will drink it to be polite. d. Molly loves hamburgers and
soft drinks, but insists on consuming exactly one soft drink for every
two hamburgers that she eats. e. Bill likes hamburgers, but neither
likes nor dislikes soft drinks. f. Mary always gets twice as much
satisfaction from an extra hamburger as she does from an extra soft
drink.
Indifference Curves for Preferences
a. Joe: Dislikes both → curves slope upward, utility increases as you move away
from both goods.
b. Jane: Loves burgers, hates drinks → vertical lines (only burger matters).
c. Bob: Same as Jane, but tolerates drinks → similar curves but slightly bowed.
d. Molly: Perfect complements (2 burgers : 1 drink) → L-shaped curves.
e. Bill: Likes burgers, neutral to drinks → horizontal lines.
f. Mary: Gets 2x satisfaction from burgers → curves flatter, she prefers more burgers.

3. If Jane is currently willing to trade 4 movie tickets for 1 basketball

ticket, then she must like basketball better than movies. True or
false? Explain

True. Willingness to give up 4 movies for 1 basketball ticket means she

values basketball more.

4. Janelle and Brian each plan to spend $20,000 on the styling and gas
mileage features of a new car. They can each choose all styling, all
gas mileage, or some combination of the two. Janelle does not care
at all about styling and wants the best gas mileage possible. Brian
likes both equally and wants to spend an equal amount on each.
Using indifference curves and budget lines, illustrate the choice that
each person will make.
Janelle vs Brian – Car Purchase
 Janelle: Only cares about gas mileage → choose all gas mileage.
 Brian: Equal preference → spends $10,000 on each.
→ Indifference curves:
 Janelle's: vertical lines,
 Brian's: downward-sloping, balanced.
5. Suppose that Bridget and Erin spend their incomes on two goods,
food (F) and clothing (C). Bridget’s preferences are represented by
the utility function U(F,C) 10FC, while Erin’s preferences are
represented by the utility function U(F,C) .20F2 C2 . a. With food on
the horizontal axis and clothing on the vertical axis, identify on a
graph the set of points that give Bridget the same level of utility as
the bundle (10, 5). Do the same for Erin on a separate graph. b. On
the same two graphs, identify the set of bundles that give Bridget
and Erin the same level of utility as the bundle (15, 8). c. Do you
think Bridget and Erin have the same preferences or different
preferences? Explain.
Bridget vs Erin – Utility Functions
 Bridget: U = 10FC → smooth, convex curves.
 Erin: U = 0.2F²C² → curves more bowed, shaped by squared terms.
Graph: Plot (10,5) and (15,8) bundles.
Preferences differ: Erin values both goods together more (due to
squared effect), while Bridget’s are more linear.

6. Suppose that Jones and Smith have each decided to allocate $1000
per year to an entertainment budget in the form of hockey games or
rock concerts. They both like hockey games and rock concerts and
will choose to consume positive quantities of both goods. However,
they differ substantially in their preferences for these two forms of
entertainment. Jones prefers hockey games to rock concerts, while
Smith prefers rock concerts to hockey games. a. Draw a set of
indifference curves for Jones and a second set for Smith. b. Using
the concept of marginal rate of substitution, explain why the two
sets of curves are different from each other.
Jones and Smith – Entertainment Budget
 Jones prefers hockey → curves flatter toward hockey.
 Smith prefers concerts → curves flatter toward concerts.
MRS: Slope is different. Each gives up less of their favorite for more
of the other.

7. The price of DVDs (D) is $20 and the price of CDs (C) is $10. Philip
has a budget of $100 to spend on the two goods. Suppose that he
has already bought one DVD and one CD. In addition, there are 3
more DVDs and 5 more CDs that he would really like to buy. a. Given
the above prices and income, draw his budget line on a graph with
CDs on the horizontal axis. b. Considering what he has already
purchased and what he still wants to purchase, identify the three
different bundles of CDs and DVDs that he could choose. For this
 part of the question, assume that he cannot purchase fractional
units.
Philip’s DVD/CD Purchase
 Budget = $100
 DVD = $20, CD = $10
→ Budget line: max 5 CDs (if only CDs), or 5 DVDs (if only DVDs),
combinations must satisfy:
20D+10C≤10020D + 10C \leq 10020D+10C≤100
Already bought: 1 DVD + 1 CD → $30 spent → $70 left.
Three bundles might be:
 2 DVDs + 3 CDs
 3 DVDs + 1 CD
 1 DVD + 5 CDs

8. Anne has a job that requires her to travel three out of every four
weeks. She has an annual travel budget and can travel either by
train or by plane. The airline on which she typically flies has a
frequent-traveler program that reduces the cost of her tickets
according to the number of miles she has flown in a given year.
When she reaches 25,000 miles, the airline will reduce the price of
her tickets by 25 percent for the remainder of the year. When she
reaches 50,000 miles, the airline will reduce the price by 50 percent
for the remainder of the year. Graph Anne’s budget line, with train
miles on the vertical axis and plane miles on the horizontal axis.
Anne’s Travel Budget (Train vs Plane)
 Before 25,000 miles: Constant slope.
 After 25,000 miles: Plane tickets cheaper → budget line bends
outward (flatter slope).
 After 50,000 miles: Flattens again.
→ Budget line has kinks at 25,000 and 50,000 plane miles.

9. Debra usually buys a soft drink when she goes to a movie theater,
where she has a choice of three sizes: the 8-ounce drink costs
$1.50, the 12-ounce drink $2.00, and the 16-ounce drink $2.25.
Describe the budget constraint that Debra faces when deciding how
many ounces of the drink to purchase. (Assume that Debra can
costlessly dispose of any of the soft drink that she does not want.)
Debra’s Soft Drink Budget Constraint
 Choices:
o 8 oz = $1.50
o 12 oz = $2.00
 o 16 oz = $2.25
→ Price per ounce drops as she buys bigger drinks.
→ Budget constraint has step-like shape, not smooth.

10. Antonio buys five new college textbooks during his first year
at school at a cost of $80 each. Used books cost only $50 each.
When the bookstore announces that there will be a 10 percent
increase in the price of new books and a 5 percent increase in the
price of used books, Antonio’s father offers him $40 extra. a. What
happens to Antonio’s budget line? Illustrate the change with new
books on the vertical axis. b. Is Antonio worse or better off after the
price change? Explain.
Antonio’s Textbooks
 Before:
o New = $80
o Used = $50
→ 5 new = $400 budget
 After price change:
o New = $88
o Used = $52.50
→ Budget increases to $440
a. Budget line shifts slightly outward.
b. Worse off: Prices rose more than income adjustment → fewer
books for same money.

11. consumers in Georgia pay twice as much for avocados as they

do for peaches. However, avocados and peaches are the same price
in California. If consumers in both states maximize utility, will the
marginal rate of substitution of peaches for avocados be the same
for consumers in both states? If not, which will be higher?
Avocado vs Peach Prices
In Georgia: Avocados cost twice as much as peaches.
In California: Same price.
Conclusion:
 In Georgia, MRS (of peaches for avocados) = 2 → you must give
up 2 peaches for 1 avocado.
 In California, MRS = 1
→ Not the same across states, since prices differ.

12. Ben allocates his lunch budget between two goods, pizza and
burritos. a. Illustrate Ben’s optimal bundle on a graph with pizza on
the horizontal axis. b. Suppose now that pizza is taxed, causing the
price to increase by 20 percent. Illustrate Ben’s new optimal bundle.
 c. Suppose instead that pizza is rationed at a quantity less than
Ben’s desired quantity. Illustrate Ben’s new optimal bundle

🔵 12a. Initial Optimal Bundle

Budget: $20

Pizza: $2 each

Burritos: $2 each

Budget line: A straight line between max 10 pizzas and 10 burritos.

Ben’s optimal bundle: Where an indifference curve is tangent to this

line (not shown here but it's on the line).

🟠 12b. Pizza Price Increases by 20%

New Pizza Price: $2.40

Now, Ben can afford fewer pizzas for the same budget.

Budget line shifts inward, getting flatter.

His new optimal point will likely have fewer pizzas and more burritos.

🔴 12c. Pizza Is Rationed (Max 5 Allowed)

Even if Ben wants more, he can't buy more than 5 pizzas.

This creates a kink in the budget constraint: horizontal up to 5 pizzas,

then vertical.

His optimal bundle is likely at the kink or on the horizontal line,

depending on preferences.

13. Brenda wants to buy a new car and has a budget of $25,000.
She has just found a magazine that assigns each car an index for
styling and an index for gas mileage. Each index runs from 1 to 10,
with 10 representing either the most styling or the best gas mileage.
While looking at the list of cars, Brenda observes that on average,
as the style index increases by one unit, the price of the car
increases by $5000. She also observes that as the gas-mileage
index rises by one unit, the price of the car increases by $2500. a.
Illustrate the various combinations of style (S) and gas mileage (G)
that Brenda could select with her $25,000 budget. Place gas
mileage on the horizontal axis. b. Suppose Brenda’s preferences are
such that she always receives three times as much satisfaction from
 an extra unit of styling as she does from gas mileage. What type of
car will Brenda choose? c. Suppose that Brenda’s marginal rate of
substitution (of gas mileage for styling) is equal to S/(4G). What
value of each index would she like to have in her car? d. Suppose
that Brenda’s marginal rate of substitution (of gas mileage for
styling) is equal to (3S)/G. What value of each index would she like
to have in her car?
14. Connie has a monthly income of $200 that she allocates
between two goods: meat and potatoes. a. Suppose meat costs $4
per pound and potatoes $2 per pound. Draw her budget constraint.
b. Suppose also that her utility function is given by the equation
U(M, P) 2M P. What combination of meat and potatoes should she
buy to maximize her utility? (Hint: Meat and potatoes are perfect
substitutes.) c. Connie’s supermarket has a special promotion. If she
buys 20 pounds of potatoes (at $2 per pound), she gets the next 10
pounds for free. This offer applies only to the first 20 pounds she
buys. All potatoes in excess of the first 20 pounds (excluding bonus
potatoes) are still $2 per pound. Draw her budget constraint. d. An
outbreak of potato rot raises the price of potatoes to $4 per pound.
The supermarket ends its promotion. What does her budget
constraint look like now? What combination of meat and potatoes
maximizes her utility?
15. jane receives utility from days spent traveling on vacation
domestically (D) and days spent traveling on vacation in a foreign
country (F), as given by the utility function U(D,F) 10DF. In addition,
the price of a day spent traveling domestically is $100, the price of
a day spent traveling in a foreign country is $400, and Jane’s annual
travel budget is $4000. a. Illustrate the indifference curve
associated with a utility of 800 and the indifference curve associated
with a utility of 1200. b. Graph Jane’s budget line on the same
graph. c. Can Jane afford any of the bundles that give her a utility of
800? What about a utility of 1200? *d. Find Jane’s utility-maximizing
choice of days spent traveling domestically and days spent in a
foreign country
16. Julio receives utility from consuming food (F) and clothing (C)
as given by the utility
In addition, the price of food is $2 per unit, the price of clothing is
$10 per unit, and Julio’s weekly income is $50. a. What is Julio’s
marginal rate of substitution of food for clothing when utility is
maximized? Explain. b. Suppose instead that Julio is consuming a
bundle with more food and less clothing than his utility maximizing
bundle. Would his marginal rate of substitution of food for clothing
be greater than or less than your answer in part a? Explain.
17. The utility that Meredith receives by consuming food F and
clothing C is given by U(F,C) FC. Suppose that Meredith’s income in
1990 is $1200 and that the prices of food and clothing are $1 per
unit for each. By 2000, however, the price of food has increased to
$2 and the price of clothing to $3. Let 100 represent the cost of
living index for 1990. Calculate the ideal and the Laspeyres cost-of-
living index for Meredith for 2000. (Hint: Meredith will spend equal
amounts on food and clothing with these preferences.