McConnell Campbell R., Brue Stanley L., Barbiero Thomas P. Microeconomics. Ninth Edition

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chapter summary

terms and concepts

170 Part Two • Microeconomics of Product Markets

1. The income and substitution effects and the

law of diminishing marginal utility help ex-

plain why consumers buy more of a product

when its price drops and less of a product

when its price increases.

2. The income effect implies that a decline in the

price of a product increases the consumer’s

real income and enables the consumer to buy

more of that product with a ﬁxed money

income. The substitution effect implies that a

lower price makes a product relatively more

attractive and, therefore, increases the con-

sumer’s willingness to substitute it for other

products.

3. The law of diminishing marginal utility states

that, beyond a certain quantity, additional

units of a speciﬁc good will yield declining

amounts of extra satisfaction to a consumer.

4. We assume that the typical consumer is

rational and acts based on well-deﬁned pref-

erences. Because income is limited and goods

have prices, consumers cannot purchase all

the goods and services they might want. Con-

sumers therefore select the attainable combi-

nation of goods that maximizes their utility or

satisfaction.

5. A consumer’s utility is maximized when in-

come is allocated so that the last dollar spent

on each product purchased yields the same

amount of extra satisfaction. Algebraically,

the utility-maximizing rule is fulﬁlled when

and the consumer’s total income is spent.

6. The utility-maximizing rule and the demand

curve are logically consistent. Because mar-

ginal utility declines, a lower price is needed

to induce the consumer to buy more of a par-

ticular product.

MU of product B

ᎏᎏᎏ

Price of B

MU of product A

ᎏᎏᎏ

Price of A

income effect, p. 156

substitution effect, p. 156

utility, p. 157

total utility, p. 157

marginal utility, p. 157

law of diminishing marginal

utility, p. 159

rational behaviour, p. 160

budget contraint, p. 160

utility-maximizing rule, p. 160

study questions

1. Explain the law of demand through the in-

come and substitution effects, using a price

increase as a point of departure. Explain the

law of demand in terms of diminishing mar-

ginal utility.

KEY QUESTION Complete the follow-

ing table and answer the questions below.

Units consumed Total utility Marginal utility

11010

2—8

325—

430—

5—3

634—

a. At which rate is total utility increasing: a

constant rate, a decreasing rate, or an in-

creasing rate? How do you know?

b. “A rational consumer will purchase only

one unit of the product represented by

these data, since that amount maximizes

marginal utility.” Do you agree? Explain

why or why not.

c. “It is possible that a rational consumer

will not purchase any units of the product

represented by these data.” Do you agree?

Explain why or why not.

3. Mrs. Wilson buys loaves of bread and litres

of milk each week at prices of $1 and $.80,

respectively. At present she is buying these

two products in amounts such that the mar-

ginal utilities from the last units purchased

of the two products are 80 and 70 utils,

respectively. Is she buying the utility-

maximizing combination of bread and milk?

If not, how should she reallocate her expen-

ditures between the two goods?

KEY QUESTION Columns 1 through 4

in the table below show the marginal utility,

chapter seven • the theory of consumer choice 171

measured in utils, that Ricardo would get by

purchasing various amounts of products A,

B, C, and D. Column 5 shows the marginal

utility Ricardo gets from saving. Assume that

the prices of A, B, C, and D are $18, $6, $4,

and $24, respectively, and that Ricardo has

an income of $106.

a. What quantities of A, B, C, and D will

Ricardo purchase in maximizing his utility?

b. How many dollars will Ricardo choose to

save?

c. Check your answers by substituting them

into the algebraic statement of the utility-

maximizing rule.

Column 1 Column 2 Column 3 Column 4 Column 5

Units Units Units Units Number of

of A MU of B MU of C MU of D MU dollars saved MU

172 124 115 136 1 5

254 215 212 230 2 4

345 312 3 8 324 3 3

43649474184 2

52757555135 1

6186564676

⁄2

715 7 2 7 3

⁄2 74 7

⁄4

8128183828

⁄8

5. KEY QUESTION You are choosing

between two goods, X and Y, and your mar-

ginal utility from each is as shown below. If

your income is $9 and the prices of X and Y

are $2 and $1, respectively, what quantities

of each will you purchase to maximize utility?

What total utility will you realize? Assume

that, other things remaining unchanged, the

price of X falls to $1. What quantities of X and

Y will you now purchase? Using the two prices

and quantities for X, derive a demand sched-

ule (price–quantity demanded table) for X.

Units of X MU

Units of Y MU

11018

2827

3636

4445

5354

6263

6. How can time be incorporated into the the-

ory of consumer behaviour? Explain the fol-

lowing comment: “Want to make millions of

dollars? Devise a product that saves Canadi-

ans lots of time.”

7. Explain:

a. “Before economic growth, there were too

few goods; after growth, there is too little

time.”

b. “It is irrational for an individual to take

the time to be completely rational in eco-

nomic decision making.”

c. “Telling Santa what you want for Christ-

mas makes sense in terms of utility max-

imization.”

8. In the past decade or so there has been a

dramatic expansion of small retail conven-

ience stores (such as Mac’s, 7-Elevens, Beck-

ers), although their prices are generally

much higher than prices in large supermar-

kets. What explains the success of the con-

venience stores?

9. Many apartment-complex owners are in-

stalling water meters for each apartment and

billing the occupants according to the amount

of water they use, in contrast to the former

procedure of having a central meter for the

entire complex and dividing up the water

expense as part of the rent. Where individual

meters have been installed, water usage has

declined 10 to 40 percent. Explain that drop,

referring to price and marginal utility.

10. Advanced analysis: A mathematically fair

bet is one in which a gambler bets, say, $100,

for a 10 percent chance to win $1000 dollars

($100 = .10 × 1000). Assuming diminishing

marginal utility of dollars, explain why this is

not a fair bet in terms of utility. Why is it even

a less fair bet when the house takes a cut of

each dollar bet? So is gambling irrational?

172 Part Two • Microeconomics of Product Markets

11. Advanced analysis: Let MU

= z = 10 – x and

= z = 21 – 2y, where z is marginal utility

per dollar measured in utils, x is the amount

spent on product A, and y is the amount

spent on product B. Assume that the con-

sumer has $10 to spend on A and B—that is,

x + y = 10. How is the $10 best allocated

between A and B? How much utility will the

marginal dollar yield?

12. (The Last Word) In what way is criminal

behaviour similar to consumer behaviour?

Why do most people obtain goods via legal

behaviour as opposed to illegal behaviour?

What are society’s main options for reducing

illegal behaviour?

internet application questions

The ESPN Sportszone, <wspn.sportzone.com>

is a major sports information site. Most of the

content is free, but ESPN has a premium

membership (articles marked with IN are only

available through it) for a monthly or an

annual fee. Similar but free sports content

can be found at CNN/Sports Illustrated at

<www.cnnsi.com> and CBS Sports Line at

<cbs.sportsline.com>. Since ESPN has put a

price tag on some of its sports content, it

implies that the utility of a premium member-

ship cannot be found at a free site and is,

therefore, worth the price. Is this the case?

Use the utility maximization rule to justify

subscribing or not subscribing to the pre-

mium membership.

2. Assume that you and several classmates

each receive a $300 credit voucher (good

for today only) from Wal-Mart Online. Go to

<www.wal-mart.com> and select $300 worth

of merchandise. Use Add to Cart to keep a

running total, and use Review Cart to print

your ﬁnal selection. Compare your list with

your classmates’ lists. What explains the dif-

ferences? Would you have purchased your

items if you had received $300 in cash to be

spent whenever and wherever you pleased?

chapter seven • the theory of consumer choice 173

Appendix to

Chapter 7

A more advanced explanation of consumer behaviour and equilibrium is based on

(1) budget lines and (2) so-called indifference curves.

The Budget Line: What Is Attainable

A budget line (or, more technically, a budget constraint) is a schedule or curve that

shows various combinations of two products a consumer can purchase with a spe-

ciﬁc money income. If the price of product A is $1.50 and the price of product B is

$1.00, a consumer could purchase all the combinations of A and B shown in Table

A7-1 with $12 of money income. At one extreme, the consumer might spend all the

income on eight units of A and have nothing left to spend on B. Or, by giving up two

units of A and thereby freeing $3, the consumer could have six units of A and three

of B. At the other extreme, the consumer could buy 12 units of B at $1.00 each,

spending his or her entire money income on B with nothing left to spend on A.

Figure A7-1 shows the same budget line graphically. Note that the graph is not

restricted to whole units of A and B as is the table. Every point on the graph repre-

sents a possible combination of A and B, including fractional quantities. The slope

of the graphed budget line measures the ratio of the price of B to the price of A;

more precisely, the absolute value of the slope is

= $1.00/$1.50 = 2/3. This is the mathe-

matical way of saying that the consumer must

forgo two units of A (measured on the vertical

axis) to buy three units of B (measured on the

horizontal axis). In moving down the budget

or price line, two units of A (at $1.50 each) must

be given up to obtain three more units of B (at

$1.00 each). This yields a slope of 2/3.

The budget line has two other signiﬁcant

characteristics:

1. Income changes The location of the

budget line varies with money income.

An increase in money income shifts the

budget line to the right; a decrease in

money income shifts it to the left. To verify

this, recalculate Table A7-1, assuming that

money income is (a) $24 and (b) $6 and

plot the new budget lines in Figure A7-1.

budget line

A line that shows

various combina-

tions of two prod-

ucts a consumer

can purchase with

a speciﬁc money

income, given the

products’ prices.

TABLE A7-1 THE BUDGET

LINE: WHOLE-UNIT

COMBINATIONS

OF A AND B

ATTAINABLE

WITH AN INCOME

OF $12

Units of A Units of B

(price = $1.50) (price = $1.00) Total expenditure

8 0 $12 (= $12 + $0)

6 3 $12 (= $9 + $3)

4 6 $12 (= $6 + $6)

2 9 $12 (= $3 + $9)

0 12 $12 (= $0 + $12)

Indifference Curve Analysis

174 Part Two • Microeconomics of Product Markets

2. Price changes A change in product

prices also shifts the budget line. A decline

in the prices of both products—the equiv-

alent of an increase in real income—shifts

the curve to the right. (You can verify this

by recalculating Table A7-1 and replotting

Figure A7-1 assuming that P

= $.75 and

= $.50.) Conversely, an increase in the

prices of A and B shifts the curve to the

left. (Assume P

= $3 and P

= $2 and re-

work Table A7-1 and Figure A7-1 to sub-

stantiate this statement.)

Note what happens if P

changes while P

and

money income remain constant. In particular, if

drops, say, from $1.00 to $.50, the lower end

of the budget line fans outward to the right.

Conversely, if P

increases, say, from $1.00 to

$1.50, the lower end of the line fans inward

to the left. In both instances the line remains

anchored at eight units on the vertical axis

because P

has not changed.

Indifference Curves: What Is Preferred

Budget lines reﬂect objective market data, speciﬁcally income and prices. They

reveal combinations of products A and B that can be purchased given current

money income and prices.

Indifference curves, however, reﬂect subjective information about consumer

preferences for A and B. An indifference curve shows all the combinations of two

products A and B that will yield the same total satisfaction or total utility to a con-

sumer. Table A7-2 and Figure A7-2 present a hypothetical indifference curve for

products A and B. The consumer’s subjective preferences are such that he or she will

realize the same total utility from each combination of A and B shown in the table

or on the curve. The consumer will be indifferent (will not care) as to which combi-

nation is actually obtained.

Indifference curves have several important characteristics.

INDIFFERENCE CURVES ARE DOWNSLOPING

An indifference curve slopes downward because

more of one product means less of the other, if

total utility is to remain unchanged. Suppose the

consumer moves from one combination of A and

B to another, say, from j to k in Figure A7-2. In so

doing, the consumer obtains more of product B,

increasing total utility. But because total utility is

the same everywhere on the curve, the consumer

must give up some of the other product, A,

to reduce total utility by a precisely offsetting

amount. Thus more of B necessitates less of A,

and the quantities of A and B are inversely

TABLE A7-2 AN INDIFFERENCE

SCHEDULE

(WHOLE UNITS)

Combination Units of A Units of B

j 12 2

k 64

l 46

m 38

FIGURE A7-1 A CONSUMER’S

BUDGET LINE

Income = $12

= $1.50

2 4 6 8 10 12

Quantity of B

Quantity of A

Income = $12

= $1.00

(Attainable)

(Unattainable)

The budget line shows all the combinations of any two prod-

ucts that can be purchased given the prices of the products

and the consumer’s money income.

indifference

curves

Curves

showing the differ-

ent combinations of

two products that

yield the same

satisfaction or utility

to a consumer.

chapter seven • the theory of consumer choice 175

related. A curve that reﬂects inversely related

variables is downward sloping.

INDIFFERENCE CURVES ARE CONVEX

TO THE ORIGIN

A downward-sloping curve can be concave

(bowed outward) or convex (bowed inward) to

the origin. A concave curve has an increasing

(steeper) slope as one moves down the curve,

while a convex curve has a diminishing (ﬂatter)

slope as one moves down the curve. Note in

Figure A7-2 that the indifference curve is con-

vex to the origin. Its slope diminishes or

becomes ﬂatter as we move from j to k to l, and

so on down the curve. Technically, the slope of

the indifference curve at each point measures

the marginal rate of substitution (MRS) of the

combination represented by that point. The

slope or MRS shows the rate at which the con-

sumer who possesses that combination will

substitute one good for the other (say, B for A)

to remain equally satisﬁed. The diminishing

slope of the indifference curve means the will-

ingness to substitute B for A diminishes as we

move down the curve.

The rationale for this convexity—that is, for a diminishing MRS—is that con-

sumers’ subjective willingness to substitute B for A (or A for B) will depend on the

amounts of B and A they have to begin with. Consider Table A7-2 and Figure A7-2

again, beginning at point j. Here, in relative terms, the consumer has a substantial

amount of A and very little of B. Within this combination, a unit of B is very valu-

able (that is, its marginal utility is high), while a unit of A is less valuable (its mar-

ginal utility is low). The consumer will then be willing to give up a substantial

amount of A to get, say, two more units of B. In this case, the consumer is willing to

forgo six units of A to get two more units of B; the MRS is 6/2 or 3.

But at point k the consumer has less A and more B. Here A is somewhat more valu-

able and B less valuable at the margin. In a move from point k to point l, the consumer

is willing to give up only two units of A to get two more units of B, so the MRS is only

2/2 or 1. Having still less of A and more of B at point l, the consumer is willing to give

up only one unit of A in return for two more units of B and the MRS falls to 1/2.

Generally, as the amount of B increases, the marginal utility of additional units of

B decreases. Similarly, as the quantity of A decreases, its marginal utility increases. In

Figure A7-2 we see that in moving down the curve, the consumer will be willing to

give up smaller and smaller amounts of A to offset acquiring each additional unit

of B. The result is a curve with a diminishing slope, a curve that is convex to the ori-

gin. The MRS declines as one moves southeast along the indifference curve.

The Indifference Map

The single indifference curve of Figure A7-2 reﬂects some constant (but unspeciﬁed)

level of total utility or satisfaction. It is possible and useful to sketch a whole series

FIGURE A7-2 A CONSUMER’S

INDIFFERENCE

CURVE

24681012

Quantity of B

Quantity of A

Every point on indifference curve I represents some combina-

tion of products A and B, and all those combinations are

equally satisfactory to the consumer. That is, each combina-

tion of A and B on the curve yields the same total utility.

<ingrimayne.saintjoe.edu/

econ/MaximizingBeha/

Indifference.html>

Another look at

indifference curves

marginal

rate of

substitu-

tion (mrs)

The rate at which a

consumer is pre-

pared to substitute

one good for

another (from a

given combination

of goods) and

remain equally satis-

ﬁed (have the same

total utility); equal to

the slope of a con-

sumer’s indifference

curve at each point

on the curve.

176 Part Two • Microeconomics of Product Markets

of indifference curves or an indifference map,

as shown in Figure A7-3. Each curve reﬂects a

different level of total utility. Speciﬁcally, each

curve to the right of our original curve (labelled

in Figure A7-3) reﬂects combinations of A and

B that yield more utility than I

. Each curve to

the left of I

reﬂects less total utility than I

. As

we move out from the origin, each successive

indifference curve represents a higher level of

utility. To demonstrate this fact, draw a line in a

northeasterly direction from the origin; note

that its points of intersection with successive

curves entail larger amounts of both A and B

and, therefore, higher levels of total utility.

Equilibrium at Tangency

Since the axes in Figures A7-1 and A7-3 are

identical, we can superimpose a budget line on

the consumer’s indifference map, as shown in

Figure A7-4. By deﬁnition, the budget line indi-

cates all the combinations of A and B that the

consumer can attain with his or her money

income given the prices of A and B. Of these

attainable combinations, the consumer will

prefer that combination that yields the greatest

satisfaction or utility. Speciﬁcally, the utility-

maximizing combination will be the combina-

tion lying on the highest attainable indifference curve, which is called the

consumer’s equilibrium position.

In Figure A7-4 the consumer’s equilibrium position is at point X, where the

budget line is tangent to I

. Why not point Y? Because Y is on a lower indifference

curve, I

. By moving down the budget line—by shifting dollars from purchases of

A to purchases of B—the consumer can attain an indifference curve farther from the

origin and thereby increase the total utility derived from the same income. Why not

point Z? For the same reason as for Y: point Z is on a lower indifference curve, I

By moving up the budget line—by reallocating dollars from B to A—the consumer

can get on the higher indifference curve I

and increase total utility.

How about point W on indifference curve I

? While it is true that W would yield

a greater total utility than X, point W is beyond (outside) the budget line and, hence,

is not attainable by the consumer. Point X represents the optimal attainable combi-

nation of products A and B. Note that, according to the deﬁnition of tangency, the

slope of the highest attainable indifference curve equals the slope of the budget line.

Because the slope of the indifference curve reﬂects the MRS (marginal rate of sub-

stitution) and the slope of the budget line is P

, the consumer’s optimal or equi-

librium position is the point where

MRS =

(You may beneﬁt by trying to answer Appendix Key Question 3 at this time.)

ᎏ

indifference

map

A series of

indifference curves,

each of which rep-

resents a different

level of total utility

and together show

the preferences of

the consumer.

equilibrium

position

The

combination of

products that yields

the greatest satis-

faction or utility.

FIGURE A7-3 AN INDIFFERENCE

MAP

24681012

Quantity of B

Quantity of A

An indifference map is a set of indifference curves. Curves

farther from the origin indicate higher levels of total utility.

Thus, any combination of products A and B represented by a

point on I

has greater total utility than any combination of A

and B represented by a point on I

, I

, and I

chapter seven • the theory of consumer choice 177

The Measurement of Utility

There is an important difference between the

marginal utility theory of consumer demand

and the indifference curve theory. The marginal

utility theory assumes that utility is numerically

measurable, that is, that the consumer can say

how much extra utility he or she derives from

each extra unit of A or B. The consumer needs

that information to realize the utility-maximiz-

ing (equilibrium) position, as indicated by

The indifference curve approach imposes a less

stringent requirement on the consumer, who

need only specify whether a particular combi-

nation of A and B will yield more, less, or the

same amount of utility than some other combi-

nation of A and B. The consumer need only say,

for example, that six units of A and seven of B

will yield more (or less) satisfaction than four of

A and nine of B. Indifference curve theory does

not require that the consumer specify how much

more (or less) satisfaction will be realized.

When we compare the equilibrium situations

in the two theories, we ﬁnd that in the indiffer-

ence curve analysis, the MRS equals P

equilibrium; however, in the marginal utility

approach, the ratio of marginal utilities equals

. We therefore deduce that at equilibrium, the MRS is equivalent in the mar-

ginal utility approach to the ratio of the marginal utilities of the last purchased units

of the two products.

The Derivation of the Demand Curve

We noted earlier that with a ﬁxed price for A, an increase in the price of B will

cause the bottom of the budget line to fan inward to the left. We can use that fact

to derive a demand curve for product B. In Figure A7-5(a) we reproduce the part

of Figure A7-4 that shows our initial consumer equilibrium at point X. The budget

line determining this equilibrium position assumes that money income is $12 and

that P

= $1.50 and P

= $1.00. Let’s see what happens to the equilibrium posi-

tion when we increase P

to $1.50 and hold both money income and the price

of A constant.

Marginal utility of B

ᎏᎏᎏ

Price of B

Marginal utility of A

ᎏᎏᎏ

Price of A

FIGURE A7-4 THE CONSUMER’S

EQUILIBRIUM

POSITION

24681012

Quantity of B

Quantity of A

The consumer’s equilibrium position is represented by point X,

where the black budget line is tangent to indifference curve I

The consumer buys four units of A at $1.50 per unit and six of B

at $1.00 per unit with a $12 money income. Points Z and Y rep-

resent attainable combinations of A and B that yield less total

utility, as is evidenced by the fact that they are on lower indif-

ference curves. Point W would entail more utility than X, but

it requires a greater income than the $12 represented by the

budget line.

If we begin with the utility-maximizing rule, MU

= MU

, and then multiply through by

and divide through by MU

, we obtain P

= MU

/MU

. In indifference curve analysis we

know that at the equilibrium position MRS = P

. Hence, at equilibrium, MRS also equals

/MU

178 Part Two • Microeconomics of Product Markets

The result is shown in Figure A7-5(a). The

budget line fans to the left, yielding a new equi-

librium point X⬘ where it is tangent to lower

indifference curve I

. At X⬘ the consumer buys

three units of B and ﬁve of A compared with

four of A and six of B at X. Our interest is in B,

and we now have sufficient information to

locate two points on the demand curve for

product B. We know that at equilibrium point

X, the price of B is $1.00 and six units are pur-

chased; at equilibrium point X⬘, the price of B is

$1.50 and three units are purchased.

These data are shown graphically in Figure

A7-5(b) as points on the consumer’s demand

curve for B. Note that the horizontal axes of Fig-

ure A7-5(a) and (b) are identical; both measure

the quantity demanded of B. We can there-

fore drop vertical reference lines from Figure

A7-5(a) down to the horizontal axis of Figure

A7-5(b). On the vertical axis of Figure A7-5(b)

we locate the two chosen prices of B. Knowing

that these prices yield the relevant quantities

demanded, we locate two points on the

demand curve for B. By simple manipulation of

the price of B in an indifference curve–budget

line context, we have obtained a downward-

sloping demand curve for B. We have thus

again derived the law of demand assuming

other things are equal, since only the price of B

was changed (the price of A and the consumer’s

money income and tastes remained constant).

In this case, we have derived the demand curve

without resorting to the questionable assump-

tion that consumers can measure utility in units

called utils. In this indifference curve approach,

consumers simply compare combinations of

products A and B and determine which combi-

nation they prefer given their incomes and the

prices of the two products.

FIGURE A7-5 DERIVING THE

DEMAND CURVE

= $1.00

= $1.50

24681012

Quantity of B

(a) Two equilibrium positions

24681012

Quantity of B

(b) The demand curve for product B

1357911

Quantity of A

Price of B

$1.50

1.00

.50

⬘

Panel (a): When the price of product B is increased from $1.00

to $1.50, the equilibrium position moves from X to X⬘, decreas-

ing the quantity of product B demanded from six to three units.

Panel (b): The demand curve for product B is determined by

plotting the $1.00–six-unit and $1.50–three-unit price–

quantity combinations for product B.

chapter seven • the theory of consumer choice 179

appendix summary

appendix study questions

1. The indifference curve approach to consumer

behaviour is based on the consumer’s budget

line and indifference curves.

2. The budget line shows all combinations of

two products that the consumer can purchase

given product prices and money income.

3. A change in either product prices or money

income moves the budget line.

4. An indifference curve shows all combina-

tions of two products that will yield the same

total utility to a consumer. Indifference curves

are downward sloping and convex from the

origin.

5. An indifference map consists of a number of

indifference curves; the farther from the ori-

gin, the higher the total utility associated with

a curve.

6. The consumer is in equilibrium (utility is max-

imized) at the point on the budget line that

lies on the highest attainable indifference

curve. At that point the budget line and indif-

ference curve are tangent.

7. Changing the price of one product shifts the

budget line and determines a new equilibrium

point. A downsloping demand curve can be

determined by plotting the price–quantity

combinations associated with two or more

equilibrium points.

1. What information is embodied in a budget

line? What shifts occur in the budget line

when money income (a) increases and (b) de-

creases? What shifts occur in the budget line

when the price of the product shown on the

vertical axis (a) increases and (b) decreases?

2. What information is contained in an indiffer-

ence curve? Why are such curves (a) down-

ward sloping and (b) convex from the origin?

Why does total utility increase as the consumer

moves to indifference curves farther from the

origin? Why can’t indifference curves intersect?

APPENDIX KEY QUESTION Using

Figure A7-4, explain why the point of tan-

gency of the budget line with an indifference

curve is the consumer’s equilibrium position.

Explain why any point where the budget line

intersects an indifference curve is not equilib-

rium. Explain: “The consumer is in equilib-

rium where MRS = P

.”

4. Assume that the data in the accompanying

table give an indifference curve for Mr. Chen.

Graph this curve, putting A on the vertical

axis and B on the horizontal axis. Assuming

that the prices of A and B are $1.50 and $1.00,

respectively, and that Mr. Chen has $24 to

spend, add his budget line to your graph.

What combination of A and B will Mr. Chen

purchase? Does your answer meet the MRS =

rule for equilibrium?

Units of A Units of B

16 6

12 8

424

5. Explain graphically how indifference analysis

can be used to derive a demand curve.

6. Advanced analysis: Demonstrate mathemati-

cally that the equilibrium condition MRS =

is the equivalent of the utility-maximiz-

ing rule MU

= MU

appendix terms and concepts

budget line, p. 173

indifference curves, p. 174

marginal rate of substitution

(MRS), p. 175

indifference map, p. 176

equilibrium position, p. 177