158 CHAI1ER 7 UTILITY AND DEMAND

HouseholdConsumption Choices

Suppose that a household has a certain amountof money to spend and that it cannot influencethe prices of the goods and services that it buys.

How does the household choose the consumptiongoods on which to spend its income? In ahswer tothis question you’re about to study the marginal utility theory. It was invented almost 100 years ago byAlfred Marshall (see Our Advancing Knowledge onpp. 84-85).

To study the marginal utility theory, we’ll exam-inc Lisa’s consumption choices. Lisa has a monthlyincome of $30 and spends all of it on only twogoods — movies and pop. Movies cost $6 each andpop costs 50 cents a can or $3 for a six-pack. Howdoes Lisa divide her $30 between these two goods?The answer depends on her likes and dislikes — onwhat economists call prefrrences. The marginal utilitytheory of consumption choice has a particular wayof describing preferences — it uses the concept ofutility.

The benefit or satisfaction that a person gets fromthe consumption of a good or service is called utility.What exactly is utility and in what units can we measure it? Utility is an abstract theoretical concept andunits of utility are chosen arbitrarily, just like theunits in which we measure temperature.

Temperature — An Analogy Temperature is a conceptwith which you are familiar. Thu know when you feelhot and you know when you feel caM. But you can’tobserve temperature. You can observe water turningto steam if it is hot enough or turning to ice if it iscold enough. You can construct an instrument, calleda thermometer, that will enable you to predict whensuch changes of state will occur. The scale on thethermometer is what we call temperature. But theunits in which we measure temperature are arbitrary.For example, we can accurately predict that when aCelsius thermometer shows a temperature of 0’,water will turn to ice. But the units of measurementdo not matter because this same event will also occurwhen a Fahrenheit thermometer shows a temperatureof 32’.

The concept of utility’ heLps us make predictions about consumption choices in much the same

way that the concept of temperature helps us makepredictions about physical phenomena. It has to beadmitted, thoLigh, that the marginal uti it>’ theory isnot as precise as the theory that enables us to predictwhen water will turn to ice or steam.

Let’s now see how we can use the concept ofutility to describe preferences.

Total Utility and Consumption

Total utility is the total benefit or satisfaction that aperson gets from the consumption of goods and services. The amount of total utility that a person getsdepends on the person’s level of consumption —

more consumption gives more total utility. Table 7.1gives an example of Lisa’s total utility derived fromconsuming different quantities of movies and pop. Ifshe sees no movies, she gets no utility from movies. Ifshe sees I movie in a month, she gets 50 units of utilin As the number of movies she sees in a month increases, her total utility increases so that if she sees10 movies a month, she gets 250 units of total utilityThe other part of the table shows Lisa’s total utilityfrom pop. If she drinks no pop, she gers no utility. Asthe amount of pop she drinks rises, her total utilityincreases.

Movies Pop

Quantity Total Six-packs Totalper month utility per month utiflty

I

UtilityR

F

Toble il Lisos Total Utility from Movies and Pop

0

2

a

4c

6

7

8

c

10

0

50

88

121

1 50

1 75

1 96

214

229

241

250

0

2

3

4

5

6

7

8

9

10

0

75

117

153

181

206

225

243

260

276

291

250a

D

12 ç —

—I 2 3 4 5 6 7 0 9 lOQuantity (movies per month(

The tab!e shows that as Usa’s consumption of movies increases, so does the total utility she derives frommovies. For example, 4 movies give 150 units of utility while 5 movies give 175 units. The table olsoshows her marginal utility — the change in total utility resulting from the last ,cvie seen. Morginol util.ity declines os consumption increoses. For example, the marginal utility from the fourth movie is 29 unitswhile that from the fifth movie is 25 units. Liso’s total utility ond marginal utility from movies aregraphed in the figure. Port (a) shows the extra total utility gained from each odditional movie as a bar.Part (b) shows the marginol utility of each new movie as a declining series of steps.

WL-—--

Such a calculation is shown in the table in Fig 7 2‘When Lisa’s consumption of movies increases from4 to 5 movies a month, her total utility’ from moviesincreases from 150 units to 175 units. Thus Lisa’smarginal utility of the fifth movie each month is25 units. The table displays calculations of marginal

HOUSEHOLD CONSUMPTION CHOICES 159.r___rE_-:W’ , E2Figure 7.2 Total Utility ond Marginal Utility

Total

200

150

100

50

total MarginalQuantity utility utility

0 0 501 50 -

2 8333

3 12129

4 15025

5 17521

6 19618

7 21415

8 22912

9 241

9

10 250

za

D

5Q

—0

Quantity (movies per manth(0

(a) Total Utility (b) Marginal utility

4

IIi

Marginal Utility

Marginal utility is the additional total utility’ derivedfrom the last unit of a good consumed. We calculatemarginal utility as the change in total utility that occurs when one more unit of a good is consumed.

F

160 CHAPTER 7 UTILITY AND DEMAND

utility for each level of movie consumption. Noticethat the units of marginal util tv appear midway’ be—nveen the quantities of consumption. It is the changeih consumption from 4 to 5 movies that producesthe marginal utility of 25 units.

Lisa’s total utility and marginal utility can be illustrated in a graph. Figure 7.2(a) illustrates the totalutility that lisa gets from movies. As you can see, themore movies Lisa sees in a month, the more total utility she gets. Part (b) illustrates her marginal utility’.This graph tells us that as Lisa sees more movies, themarginal utility that she gets from watching moviesfalls. For example, her marginal utility from the firstmovie is 50 units, from the second. 38 units, andfrom the third, 33 units. We call this decline in marginal utilin as the consumption ofa goad increasesthe principle of diminishing masgin jji.

Marginal utility hpositiVe but diminishes asthe consumption of a good increases. Why does marginal utility have these two features? In Lisa’s case,she Likes movies, and the more she sees the better.That’s why marginal utility is positive. The benefitthat Lisa gets from the last movie seen is its marginalutility. To see why’ marginal utility diminishes, thinkabout how you’d feel in the following two situations.In one, you’ve just been studying for 29 evenings in arow. An opportunity arises to see a movie. The utilitythat you get from that movie is the marginal utilityfrom seeing one movie in a month. In the second situation, you’ve been on a movie binge. For the past29 nights, you have not even seen an assignment ortest. You are up to your eyeballs in movies. You arehappy enough to go to a movie on yet one morenight. But the kick that you get out of that thirtiethmovie in 30 days is not very large. It is the marginalutility of the thirtieth movie in a month.

R E V I E W

Lisa divides her income of $30 a month betweenmovies that cost $6 each and pop that costs $3 a six-pack. Lisa’s preferences are described by using theconcept of utility: the more movies Lisa sees in agiven month, the more total utility she gets; the morecans of pop she drinks in a month, the more totalutility she gets. The increase in total utility that results from the last unit ofa good consumed is calledmarginal utility. As the quantity of a good consumedincreases, marginal utility decreases. •

Utlly Maximization

Utility maximization is the at:ai oment of the greatest possible total utility. But a households incomeand the prices that it Ewes limit the utilIty that it canobtain. \Ve assume that a household consumes in away’ that maximizes its total utility taking into consideration its income and the prices that it faces. InLisa’s case, we examine how she allocates her spending between movies and pop to maximize her utility,assuming that movies cost 56 each, pop costs $3 a six-pack, and Lisa has only $30 a month to spend. Wewill now discover a rule that always works to producethe highest attainable level of total utility’.

The Utility-Maximizing Choice Let’s calculate how Lisaspends her money to maximize her utility by constructing a table. Table 7.2 has nvo parts. Part (a) records Lisa’s expenditure and part (b), her total utility.Part (a) shows six ways in which Lisa can allocate her530 ofincome between movies and pop. For example, she can buy 2 movies at a cost ofSl2, in whichcase she will be able to buy 6 six-packs for a cost ofSI S. Each row in part (a) shows the combinations ofmovies and pop that exhaust her income.

Part (b) considers the same affordable combinations of movies and pop that are set out in part (a).Part (b) records three things: firs:, the number ofmovies consumed and the total utility derived fromthem (the left side of the table); second, the numberof six-packs of pop consumed and the total utility derived from them (the right side of the table); andthird, the total utility derived from both movies andpop (the middle column of the table).

Consider, for example, the first row. It showsLisa watching no movies, getting no utihn’ fromthem but getting 291 units of total utility from drinking 10 six-packs of pop. Her total utility from moviesand pop, in this case, is 291 units.

Now consider the second row. Lisa watches 1movie, getting 50 units of total utility’ from it, anddrinks $ six-packs of pop, getting another 260 unitsof total utilinc In this case, her total utility’ from movies and pop is the sum of 50 units from movies and260 units from pop, or 310 units. The rest of part (b)is constructed in exactly the same way.

Notice that Table 7.2 does not consider allocations in which Lisa constunes odd numbers of six-packs of pop (1,3,5,7, or 9). The reason is that shecannot buy haifa movie. She has to buy movies inwhole numbers, and since movies cost $6, twice asmuch as a six-pack of pop, she can consume only 0,

FTable 7.2 Lisa’s Utility Maximizing Combinations of Movies and Pop

HOUSEHOLD CONSUMPTION CHOICES 161

2,4, 6, 8, or 10 six-packs of pop if she spends all herincome on these two goods.

The consumption of movies and pop thatmaximizes Lisa’s total utility’ is highlighted inTable 7.2(b). When Lisa consumes 2 movies and6 six-packs of pop, she gets 313 units of total utility. This is the best Lisa can do given that she hasonly $30 to spend and given the prices of moviesand six-packs. lfshe buys 8 six-packs of pop. shecan see only I movie and gets 310 units of totalutility, 3 less than the maximum attainable. If shesees 3 movies and drinks only 4 six-packs, she gets302 units of total utility, 11 less than the maximum attainable. Thus Lisa can do no better thanconsume 2 movies and 6 six-packs — the allocation of her $30 that maximizes her utility, giventhe prices of movies and pop.

The situation that we’ve just described is a con-

equilibrium. A consumer equilibrium is a/situation in which a consumer has allocated his orher income in a manner that maximizes total utility.In calculating Lisa’s consumer equilibrium, we havemeasured her total utility from the consitmption ofmovies and pop. There is another, better way of determining a consumer equilibrium that does not involvemeasuring total utility at all. Let’s look at this alternathe.

Equalizing Marginal Utility perDollar Spent

We can find out the allocation that maximizes aconsumer’s utility by making the marginal utility perdollar spent on each good equal for all goods. Themarginal utility per dollar spent is the marginal

(a) Expenditure

Movies Pop

Total• Expenditure expenditure Expendiftire

Quantity (dollars) (dollars) (dollars) Six-packs

0 0 30 30 101 6 30 24 82 12 30 18 63 18 30 12 44 24 30 6 25 30 30 0 0

(b) Total utiflty

Movies Pop

Total utilityfrom movies

Quantity Total utility and pop Tatal utility Six-packs

0 0 291 291 101 50 310 260 82 88 313 225 a3 121 302 181 44 150 267 117 25 175 175 0 0

I-i

162 CHAPTER 7 UTILITY AND DEMAND

utili iined from the last unit ofa good consumccLdM _ye prtce of the goo or example,Lisa’s marginal utilityliom onsuming the Firstmovie is 50 units of utility. The price ofa movie is$6, which means that the marginal utility per dollarspent on movies is 50 units divided by S6, or8.33 units of utility per dollar.Lisa maximizes utility when she spends all herincome and consumes movies and pop such that

Let’s do some calculations to see how this formula delivers the utility-maximizing allocation ofLisa’s income.Table 7.3 sets out Lisa’s marginal utilities perdollar spent for both movies and pop. Each row ofthe table represents an allocation of her income thatuses up her $30. You can see that Lisa’s marginal utility per dollar spent on either good, like marginal utility’ itself, declines as consumption of the good rises.The marginal utility per dollar spent on movies fallsfrom 8.33 for the first movie to 6.33 for the secondto 4.16 for the fifth. The marginal utility per dollarspent on pop is 14.00 for 2 six-packs, 9.33 for 4 six-packs, 6.33 for 6 six-packs, and 5.00 for 10 six-packs.Notice that when Lisa consumes 2 movies and6 six-packs of pop, she gets the same marginal utilityper dollar spent from movies as she does from pop.

This allocation of her income maximizes her utilircIt is the same allocation as we calculated in Table 7.2.

Utility is maximized when the marginal utility ncrdot tar spent is cqti al tor all goods.

In calculating the utility-maximizing allocationof income in Table 7.3, we have not used the conceptof total utility at all. All the calculations have beenperformed using marginal utility’ and price. By making the marginal utility per dollar spent equal forboth goods, we know that Lisa has maximized herutilirt but we have not calculated what the maximum level of total utility is. As a matter of fact, wedo not need to know what the level of total utility is.We only need to know that maximum total utilityhas been obtained. This way of viewing maximumutilin’ is important; it means that the units in whichutility is measured do not matter. We could doubleor halve all the numbers measuring utility’, or multiply them by any other positive number, or squarethem, or take their square roots. None of these ttansformations of the units used to measure utility wouldchange the utility-maximizing allocation of theconsumers income. Total utility’ is maximized whenthe marginal utility per dollar spent is equal for allgoods. It is in this respect that utility is analogous totemperature. Our prediction about the freezing ofwater does not depend on the temperature scale; ourprediction about maximizing utility does not dependon the units of utility

Marginal utilityfrom movies -

Price of movies

Marginal utility— from pop— Price of pop

j

Table 7.3 Maximizing Utility by Equalizing Marginal Utilities per Dollar Spent

Movies ($6 each)Pop ($3 per six-pock)

MarginalMarginalutilityutilityMarginal per dollar Marginal per dollarQuantity utility spent Six-packs utility spent

0 010 15 5.001 50 8.33 8 17 5.672 38 6.33 6 19 6.333 33 5.50 4 28 9.334 29 4.83 2 42 14.005 25 4.16 0 0

You can see why the rule “equalize marginalutility per dollar spent on all goods” works by considering what happens if Lisa spends differenclSuppose that instead of consuming 2 movies and6 six-packs of pop, Lisa consumes I movie and 8 six-packs of pop (the second row of Table 7.3). She willthen get 8.33 units of utility from the last dollarspent on movies and 5.67 units of utility from thelast dollar spent on pop. It will pay Lisa to spend lesson pop and more on movies. If she spends a dollarless on pop and a dollar more on movies, her totalutility from pop falls by 5.67 units and her total utiliw from movies rises by 8.33 units. Lisa’s total utilityrises if she spends less on pop and more on movies.

Or suppose that Lisa consumes 3 movies andonly 4 six-packs of pop (the fourth row of the table).In this situation, she gets 5.50 units ofutilin’ fromthe last dollar spent on movies and 9.33 units of utilit>’ from the last dollar spent on pop. Lisa can nowget more total utility by cutting her spending onmovies, at a cost of 5.50 units of utility per dollar,and raising her spending on pop, where she gets9.33 units of utility per dollar. ‘When Lisa’s marginalutility per dollar spent on both goods is equal, shecannot get more total utility by spending differently.Her utility is maximized.

R E V I E W

Consumers maximize total utilinc A consumerspends his or her income in order to make the marginal utility per dollar spent on each good equal.Once the marginal utilities per dollar spent are equal,the consumer cannot reallocate spending to get moretotal utility. The absolute level of utility is irrelevant — all that matters is its maximization. Theunits in which utility is measured are irrelevant — allthat matters is that the marginal utility per dollar isequal for all goods. •

PRWIIoNs OF MARGINAL UTILITY THEORY 163

The Effects of Changes in Prices

First, we’ll work out what happens to Lisa’s consumption if the price of a movie is halved to S3 but theprice of pop is unchanged. Next, we’ll work out whathappens if the price ofa movie stays at $3 and theprice of pop doubles to $6 per six-pack.

A Fall in the Price of Movies Table 7.4 shows va’s ofconsuming movies at $3 each and pop at S3 a six-pack. Once again, each row of the table showsquantities consumed that exactly use up the $30 ofincome available. The marginal utility per dollarspent is the marginal utility of the good divided byits price. Marginal utility, which was shown in thetable in Fig. 7.2, describes Lisa’s preferences. Her preferences do not change when prices change, so hermarginal utilin’ schedule remains the same as that inFig. 7.2. But now we divide her marginal utility frommovies by 53, the new price of a movie, to get themarginal utility per dollar spent on movies. You cansee that Lisa’s marginal utility per dollar spent onmovies declines from 16.67 at 1 movie all the waydown to 3.00 at 10 movies.

SL5TwTable 7.4 How a Chonge in the Price of Movies

Affects Lisa’s Choices

Movies cast $3.00 eachPop costs $3.00 a six-pock

Movies Pop

Marginal Marginalutility utilityper dollar per dollar

Quantity spent Six-pock spent

0 10 5.00

1 16.67 9 5.33

2 12.67 8 5.67

3 11.00 7 &C04 9.67 6 6.33

5 833 5 8.33

6 7.00 4 9.33

7 6.00 3 1 2.00

8 5.00 2 14.00

9 4.00 1 25.00

10 3.00 0

— .

.

.2.

Pt

IS.

h

n

0

at

nd

Predictions of MarginalUtility Theory

Now let’s go on to use marginal utility theoryto make some predictions. In particular, let’ssee what happens to Lisa’s consumption of

movies and pop when their prices change and alsowhen her income changes.

(a) Movies(b) Pop

When rho price ci movies 10fl5 and the price of pop remains constant, Lisa moves along her demandcurve for movies (port a) and there isa shift in her demand For pop (port b).

— —

Lisa’s marginal utility per dollar spent on popdeclines from 25.00 at I six-pack to 5.00 at 10 six-packs. The marginal utilities per dollar spent on movies and on pop are each equal to 8.33 when Lisawatches 5 movies and drinks 5 six-packs.What has been the effect of the fall in the priceof a movie on Lisa’s consumption? You can find theanswer by comparing Lisa’s utility-maximizing allocation shown in Table 7.4 with her allocation inTable 7.3. As a result of the fall in the price of amovie, Lisa watches more movies (up From 2 to 5 amonth) and she drinks less pop (down from 6 six-packs to 5 six-packs a month). That is, Lisa substitutes movies For pop when the price of a movie falls.The effects that we’ve just analysed are illustrated in Fig. 7.3. In part (a) you can see the effect asa movement along Lisa’s demand curve for moviesand in part (b) as a shift in her demand curve for pop.To determine the effects of changes in prices onconsumprion requires three steps. First, we need todetermine the combinations of movies and pop thatcan be bought at the new prices. Second, we need tocalculate the new marginal utiliries per dollar spent.Third, we need to determine the consumption OFeach good that makes the marginal utility per dollarspent on each good equal and that just exhausts themoney available for spending.

Movies cost $3.00 eachPap costs $6.00 a six-pack

Movies PopMarginal Marginalutility utilityper dollar per dollarGuantity spent Sixpock spent

0 5 4.172 12.67 4 4.674 9.67 3 6.006 700 2 7.008 5.00 1 1 2.50

10 3.00 0n

164 CHAPTER 7 UTILITY AND DEMAND

-—. ‘-7..- r- r---r’—’ ‘m’n

flgure7.3AHekeofM& 6CV0.

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o-a=

—

0

0.a

Lisa’s demandfor movies

Lisa’s demand

1

lina’s demand For popwhen movies cast $3

2 5Oucntiy fmavie, per monthj

05 6

CJzr.ity six—packs per month)

\HCt

it

A Rise in the Price of Pop Let us now work out Lisa’sconsumption when the price of a movie stats at 53, butthe price oFpop doubles to $6 a six-pack. The rowsoFTable 7.5 show the possible ways of consuming

Table 7.5 How a Change in Price of PopAffects Usa’s Choices

pREDlaloNs OF MARGINAL UTILITY THEORY 165

Co

x

a0.

C

0-vaU

03

4,0-

0

00

The effects that we’ve just analysed are illustrated in Fig. 7.4. In part (a) you can see the effect asa movement along Lisa’s demand cane for pop andin part (b) as a shift in her demand curve for movies.

R E V I E W

When the price ofa movie falls but the price of popstays constant, Lisa increases her consumption ofmovies and reduces her consumption of pop. Thereis a movement along her demand cun’e for moviesand a shift in her demand curve for pop. When theprice ofa movie stays constant but the price of popincreases, Lisa reduces her consumption of pop andincreases her consumption of movies. There is amovement along her demand curve for pop and ashift in her demand curve for movies. If the price ofamovie falls or the price of pop rises and Lisa does notchange her consumption of movies and pop, her marginal utility’ per dollar spent on movies exceeds thatof pop. To restore the equality of the marginal utilityper dollar spent on each good, she must increase herconsumption of movies and decrease her consumption of pop. •

Figure 7.4 A Rise in the Price of Pop

43

C

0Lisa’s demandlo’ movies w:-.enCp costs $6

aU

a-Lisa’s demand fo, movieswhen pop costs $3

0

3

0Quantity six—packs per month(

(a) Pop (b) Movies

When the price of pap rises and the price of movies remains ccr.stant, Lisa moves a(cng her demandcurve for pop and there is a shift in her demand curve for movies.

5 6Quantity (movies per mcnth(

v’•

I

I

I

pop and movies at these new prices. Because popnow costs $6, Lisa cannot consume more than 5 six-packs. Five six-packs of pop cost S30, exactly theamount that she has available. Since we are assumingthat a six-pack cannot be split into single cans, Lisacan consume only 0,2,4,6, 8, or 10 movies. Because movies cost the same as in Table 7.4 the marginal utility’ per dollar spent on them remains thesame. You can see thar if Lisa sees 2 movies, her marginal utility per dollar spent on movies is 12.67 inboth cases. If Lisa sees 10 movies, her marginal utilityper dollar spent on movies is 3.00.

Lisa’s marginal utility per dollar spent on pop isthe marginal utility of pop divided by the new priceof pop ($6). These marginal utilities per dollar spentare set out in Tahle 7.5. As you can see, the marginalutility per dollar spent on movies and on pop areequal when Lisa watches 6 movies and drinks 2 six-packs a month. You can calculate the effects of therise in the price of pop on Lisa’s consumption bycomparing her choice in Table 7.5 with that inTable 7.4. Lisa’s consumption of pop has fallen from5 six-packs to 2 six-packs, and her consumption ofmovies has increased from 5 to 6 a month. For Lisa,pop and movies are substitutes. When there is a risein the price of pop, Lisa substitutes movies for pop.She sees more movies and drinks less pop.

i66 CHAPTER? UTIUTY AND DEMAND

Marginal utility’ theory predicts these two resuits: if the price of a good rises, the quantity demanded of that good falls; if the price of one goodrises, the demand for another good that can serve as asubstitute increases. Does thk sound familiar? Itshould. These predictions of marginal utility theorycorrespond to the assumptions that we made aboutconsumer demand in Chapter 4. There we assumedthat the demand curve for a good sloped downward,and we assumed that a rise in the price of a substituteincreased demand. Marginal utility- theory predictsthese responses to price changes. In doing so it makesthree assumptions. First, that consumets maximizeutility. Second, that they get more utility as they consume more of a good. Third, as consumption increases, marginal utility’ declines.Thus the assumption of diminishing marginalutility implies the law of demand. But this is not theonly implication of diminishing marginal utility Italso has implications for the response of consump

The Effects of a Rise in IncomeLet’s suppose that Lisa gets a raise ofSl2 a month,which means that she now has 342 a month to spendon movies and pop. Let’s also suppose that moviescost $3 each and a six-pack costs $3 (as in Table 7.4).We now want to compare Lisa’s consumption of movies and pop at her original income of 530 with her consumption at her new income of $42. The calculationsfor such a comparison are presented in Table 7.6.Case 1 (which is identical to Table 7.4) shows Lisa’sutility-maximizing consumption of movies and popwhen she earns $30. Case 2 shows what happenswhen Lisa’s income goes up to 542. With $42, Lisacan buy 14 movies a month and no pop or 14 six-packs a month and no movies or any combination ofthe two goods shown in the rows of Table 7.6.

don to a change in income. Let’s see the effects ofachange in Lisa’s income on her consumption.

HI i.

IF

LzZzrEEEZEzzzliZZ .rZZZEZZEZTable 7.6 How o Chonge in Income Affects Usa’s Choices

Case I: Income $30Case 2; Income $42

Movies Pop Movies Pop($3 each) $3 per six.pack) ($3 each) (53 per six-pock)Marginal Marginal Marginal Marginalutility utility utility utilityper dollar per dollar per dollar per dollarQuantity spent Six-pack spent Quantity spent Sixpock spent

0 10 5.00 0 141 16.67 9 5.33 1 16.67 132 12.67 8 5.67 2 12.67 123 11.00 7 6.00 3 11.00 114 967 6 6.33 4 9.67 10 5.005 8.33 5 8.33 5 8.33 9 5.336 7.00 4 9.33 6 7.00 8 5.677 6.00 3 12.00 7 6.00 7 6.308 5.00 2 14.00 8 5.00 6 6.339 4.00 1 25.00 9 4.00 5 8.3310 3.00 0 10 3.00 4 9.3311 3 12.0012 2 14.0013

I 25.0014

0L.-

PREDICTIONS OF MARGINAL UTILITY THEORY 167

We can calculate the marginal utility per dollarspent on movies and pop in exactly the same way aswe did before. Only now, because Lisa has more income, she can consume more pop for any given consumption of movies or, equivalenrl> more movies forany given consumption of pop. For example, Lisacan watch 1 movie and drink 13 six-packs of popwhen she earns $42. When her income is $30, how-ever, she can buy only 9 six-packs of pop if she seesI movie. Lisa maximizes her utility when the marginal utilities per dollar spent on movies and on popare equal. At an income of $42 such a situation occurs when the marginal utility per dollar spent oneach good is 6.00 units. Lisa watches 7 movies amonth and drinks 7 six-packs of pop.

By comparing Case 2 with Case 1, we can seeanother important prediction of the marginal utilitytheory of consumption. When Lisa earns more income, she increases her consumption of both goods.In this particular example, Lisa increases her consumption of both goods by the same amount —

2 more six-packs and 2 more movies. This responsearises from Lisa’s preferences, as described by her marginal utilities. Different preferences produce differentquantitative responses, but for normal goods, a higherincome always brings a larger consumption of all goods.

For Lisa, pop and movies are normal goods.When her income rises, Lisa buys more of bothgoods. This prediction of the marginal utility theorycorresponds to another assumption that we madewhen studying the theory of demand in Chapter 4.There we assumed that demand for a normal goodrises when income rises. Here we have obtained thatresult as a prediction of marginal utility theory.

The marginal utility theory of consumption issummarized in Table 7.7. We can use the marginalutility theory of consumer behaviour to make senseof some of the features of the world described at thebeginning of this chapter. For example, it explainswhy the demand for some goods, such as audio headsets, is elastic and for others, such as oil, is inelastic.It also explains why, as income increases, the proportion of income spent on some goods, such as automobiles, increases, while the proportion spent on othergoods, such as food, decreases. These effects occur because of our preferences. The speed with which ourmarginal utility for each good diminishes as we increase our consumption of the good affects the wayin which we reallocate our income in response toprice changes and the way in which our spending responds to a change in income. The calculations thatwe’ve performed for Lisa illustrate these effects.

Assumptions

{al A consumer derives utility From the goods consumed.

lb) Each additional unit of consumption yie!ds additional total utility; marginal utility is pasitive.

Implication

The consumer’s total utility is maximized when the morginol utilityper dollar spent is equal for all goads.

Predictions

(a) Other things being equal, the higher the price oF a goad, thelower is the quantity baught (the law of demond).

(bI Other things being equal, the higher the price of a goad, thehigher is the consumption of substitutes far that goad.

(c) Other things being equal, the higher the consumer’s income,the greater is the quantity demanded of normal goads.

Criticisms of MarginalUtility Theory

atginal utility theory helps us to understand the choices people make, but thereare some criticisms of this theory. Let’s

Utility Can’t Be Observedor Measured

Agreed — we can’t observe utility. But we do notneed to observe it to use it. We can and do observethe quantities of goods and services that people consume, the prices of those goods and services, andpeople’s incomes. Our goal is to understand the consumption choices that people make and to predictthe effects of changes in prices and incomes on thesechoices. To make such predictions, we assume thatpeople derive utility from their consumption, thatmore consumption yields more total utilins and thatmarginal utility diminishes. Given these assumptions,we can make predictions about the directions of changein consumption when prices and incomes change. As

—..

7.!E ‘Y•W’i. .‘ .:: -,• ‘ .cn

Table 7.7 Marginal Utility Theory

I

II

Mlook at them.

168 CHAPTER 7 UflLHV AND DEMAND

we’ve already seen, the actual numbers we use to express utility do not matter. Consumers maximizetotal utility by making the marginal utility per dollar spent on each good equal. As long as we use thesame scale to express utility for all goods, we’ll getthe same answer regardless of the units on ourscale. In this regard, utility is similar to temperature — water freezes when it’s cold enough, andthat occurs independently of the temperature scaleused.

People Aren’I’ That SmartSome critics maintain that marginal utility theory assumes that people are supercomputers. It requirespeople to look at the marginal utility of every good atevery different quantity they might consume, dividethose numbers by the prices of the goods, and thencalculate the quantities so as to equalize the marginalutility of each good divided by its price.

Such criticism of marginal utility theory confuses the actions of people in the real world withthose of people in a model economy. A model economy is no more an actual economy than a model railway is an actual railway. The people in the modeleconomy perform the calculations that we have justdescribed. People in the real world just consume. Weobserve their consumption choices, not their mentalgymnastics. The marginal utility theory proposes thatthe consumption patterns ‘ye observe in the realworld are similar to those implied by the model economy in which people do compute the quantities ofgoods that maximize total utility. We test how closelythe marginal utility model resembles reality’ by checking the predictions of the model against observedconsumption choices.Marginal utility’ theory also has some broaderimplications that provide an interesting way of testing its usefulness. Let’s examine two of them.

Some lmp)ications ofMarginal Utility Theory

Wcall love bargains — paying less for something than its usual price. One implication of the marginal utility theoty is thatwe almost always get a bargain when we buy some-

thing. That is, we place a higher total value on thethings we buy than the amount that they cost us.Let’s see wh

Consumer Surplus and the Gainsfrom Trade

In Chapter 3, we saw how people can gain by specializing in producing the goods in which they have acomparative advantage and then trading with eachother. Marginal utility theory provides a precise wayof measuring the gains from trade.When Lisa buys movies and pop, she exchangesher income for them. Does Lisa profit from this exchange? Are the dollars she has to give up worthmore or less than the movies and pop are worth toher? As we are about to discover, the principle of diminishing marginal utility guarantees that Lisa getsmore value from the goods she buys than the amountof money she gives up in exchange.

Calculating Consumer SurplusThe value a consumer places on a good is the maximum amount that person would be willing to payfor it. The amount actually paid for a good is itsprice. Consumer surplus is the difference betweenthe value of a good and its price. The principle of diminishing marginal utility guarantees that there always is a consumer surplus. To understand why, let’slook again at Lisa’s consumption choices.

As before, let’s assume that Lisa has $30 amonth to spend, that movies cost 53 each, and thatshe watches 5 movies each month. Now Jet’s look atLisa’s demand curve for movies, shown in Fig. 7.5.We can see from Lisa’s demand curve that if she wereable to watch only I movie a month, she would bewilling to pays? to see it. She would be willing topay $6 to see a second movie, $5 to see a third, andsoon.Luckily for Lisa, she has to pay only $3 for eachmovie she sees—the market price ofa movie. Although she values the first movie she sees in a monthat $7, she pays only S3, which is 54 less than shewould be willing to pay. The second movie she seesin a month is worth 56 to her. The difference between the value she places on this movie and whatshe has to pay is S3. The third movie she sees in amonth is worth S5 to her, which is $2 more than shehas to pay for it, and the fourth movie is worth $4,which is $1 more than she has to pay for it. You can

Lisa is willing to pay $7 to watch her first movie, $6 to watchher second, $5 to watch her third, and $4 to watch her fourth.She actually has to pay only $3 For each movie. At that price,she sees 5 movies. She has a consumer surplus an the Firstfour movies equo1 to $ 0— the difference between he highestprice she is willing to poy ond the price she actually pays($4 + $3 + $2 + $1).

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sec this progression in Fig. 7.5, which highlights thedifference between the price she pays ($3) and thehigher value she places on the first, second, third,and fourth movies. These differences are a gain toLisa. Let’s calculate her total gain.

The total amount that Lisa is willing to pay forthe 5 movies that she sees is $25 (the sum of $7, $6,$5, $4, and $3). She actually pays $15 (5 movies at$3 each). The extra value she receives from the movies is therefore $10. This amount is Lisa’s consumersurplus. From watching 5 movies a month, she gets$10 worth of value in excess of what she has to spendto see them.

Let’s now look at another implication of themarginal utility theory.

The Paradox of Value

More than 200 years ago, Adam Smith posed the paradox that we raised at the start of this chapter. \Vater,which is essential to life itself, costs little, but diamonds, which arc useless compared to water, are expensive. Why? Adam Smith could not solve theparadox. Not until the theory of marginal utility hadbeen invented could anyone give a satisfactory answer.

You can solve Adam Smith’s puzzle by distinguishing between total utility and marginal utility.The total utility that we get from water is enormous,But remember, the more we consume of something,the smaller is its marginal utility. We use so muchwater that the marginal utility — the benefit we getfrom one more glass of water — diminishes to a tinyvalue. Diamonds, on the other hand, have a smalltotal utility relative to water, but because we buy fewdiamonds, they have a high marginal utility.

Our theory also tells us that consumers spendin a way that makes the marginal utility from eachgood divided by its price equal for all goods. Thisalso holds true for their spending on diamonds andwater: diamonds have a high marginal utility dividedby a high price, while water has a low marginal utility divided by a low price. In each case, the marginalutility per dollar spent is the same.

We’ve now completed our study of the marginalutility theory of consumption. We’ve used that theory to examine how Lisa allocates her income between the two goods that she consumes — moviesand pop. We’ve also seen how the theory can be usedto resolve the paradox of value. Furthermore, we’veseen how the theory can be used to explain our real-world consumption choices.

In the next chapter, we’re going to study an alternative theory of household behaviour. To help yousee the connection between the marginal utility theory of this chapter and the more modern theory ofconsumer behaviour of the next chapter, we’ll continue with the same example. We’ll meet Lisa againand discover another way of understanding how shegets the most out of her 530 a month.

S U M M A R Y

Individual Demand and Market Demand

Individual demand represents the relationship between the price of a good and the quantity de

manded by a single individual, other things beingequal. Market demand is the sum of all individual demands. (pp. 157)

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SuMMARY 169

Figure 75 Consumer Surplus

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