CHAPTER 8 Consumer Choice and Demand in Traditional and Network Markets

Changes in Price and the Law of Demand Suppose your marginal utility for Coke and hot dogs is as shown in the table below.. Demand is elastic: • if total consumer expenditures rise whe

Consumer Choice and Demand in

Traditional and Network Markets

It is not the province of economics to determine the value of life in “hedonic units” or any other units, but to work out, on the basis of the general principles of conduct and the fundamental facts of social situation, the laws which determine prices of commodities and the direction of the social economic process It is therefore not quantities, not even intensities, of satisfaction with which we are concerned .or any other absolute

magnitude whatever, but the purely relative judgment of comparative significance of alternatives open to choice

Frank Knight

eople adjust to changes in some economic conditions with a reasonable degree of predictability When department stores announce lower prices, customers will pour through the doors The lower the prices go, the larger the crowd will be When the price of gasoline goes up, drivers will make fewer and shorter trips If the price stays up, drivers will buy smaller, more economical cars Even the Defense Department will

reduce its planned purchases when prices rise

Behavior that is not measured in dollars and cents is also predictable in some

respects Students who stray from the sidewalks to dirt paths on sunny days stick to

concrete when the weather is damp Professors who raise their course requirements and grading standards find their classes are shrinking in size Small children shy away from

doing things for which they have recently been punished When lines for movie tickets

become long, some people go elsewhere for entertainment

On an intuitive level you find these examples reasonable Going one step beyond intuition, the economist would say that such responses are the predictable consequences

of rational behavior That is, people who desire to maximize their utility can be expected

to respond in these ways Their responses are governed by the law of demand, a concept

we first introduced in Chapter 3 and now take up in greater detail

Predicting Consumer Demand

The assumptions about rational behavior described early in the book provide a good

general basis for explaining behavior People will do those things whose expected

benefits exceed their expected costs They will avoid doing things for which the opposite

is true By themselves, however, such assumptions do not allow us to predict future

P

behavior The law of demand, which is a logical consequence of the assumption of

rational behavior, does allow us to make predictions

The alert reader may sense an inconsistency in logic Rational behavior is based on the existence of choice, but a true choice must be free—it cannot be predetermined or

predicted If we can predict a person’s behavior, can that individual be free to choose?

Choice is not completely free, nor is complete freedom required by the concept of

rationality As discussed earlier, the individual’s choices are constrained by time and by

physical and social factors that restrict his or her opportunities There are limits to a

person’s range of choice Freedom exists within those limits

Our ability to predict is also limited We cannot specify with precision every choice the individual will make For instance, we cannot say anything about what Judy

Schwartz wants or how much she wants the things she does Before we can employ the

law of demand, we must be told what she wants Even given that knowledge, we can

only indicate the general direction of her behavior Theory does not allow us to

determine how fast or how much her behavior will change

To see how consumer behavior can be predicted, we will derive the law of demand from the behavior of an individual consumer

Rational Consumption: The Concept of Marginal Utility

The essence of the economist’s notion of rational behavior can be summed up this way:

more goods and services are preferable to less (assuming that the goods and services are desired) This statement implies that the individual will use his entire income, in

consumption or in saving or in some combination of the two, to maximize his

satisfaction It also implies that the individual will use some method of comparing the

value of various goods

Generally speaking, the value the individual places on any one unit of a good

depends on the number of units already consumed For example, you may be planning to consume two hot dogs and two Cokes for your next meal Although you may pay the

same price for each unit of both goods, there is no reason to assume that you will place

the same value on each The value of the second hot dog—its marginal utility—will

depend on the fact that you have already eaten one The formula for marginal utility is

change in total utility

MU = change in quantity consumed

Achieving Consumer Equilibrium

Marginal utility determines the variety of a quantity of goods and services you consume

The rule is simple If the two goods, Cokes and hot dogs, both have the same price, you will allocate your income so that the marginal utility of the last unit of each will be equal

Mathematically, the formula can be stated as

MU c = MU h

Where MU c equals the marginal utility of a Coke and MU h equals the marginal utility of a hot dog

If you are rational, and if the price of a Coke is the same as the price of a hot

dog, the last Coke you drink will give you the same amount of enjoyment as the

last hot dog you eat When the marginal utilities of goods purchased by the

consumer are equal, the resulting state is called consumer equilibrium

Consumer equilibrium is a state of stability in consumer purchasing patterns in

which the individual has maximized his or her utility Unless conditions—income,

taste, or prices—change, the consumer’s buying patterns will tend to remain the

same

An example will illustrate how equilibrium is reached Suppose for the sake of

simplicity that you can buy only two goods, Cokes and hot dogs Suppose further that

one of each cost the same price, $1, and you are going to spend your whole income

(How much your total income is and how many units of Coke or hot dogs you will

purchase is unimportant We simply assume that you purchase some combination of

those two goods.) We will also assume that utility (joy, satisfaction) can be measured As you remember from an earlier chapter, a unit of satisfaction is called a util Finally,

suppose that the marginal utility of the last Coke you consume is equal to 20 utils, and the marginal utility of the hot dog is 10 utils Obviously you have not maximized your

utility, for the marginal utility of your last Coke is greater than (>) the marginal utility of

your last hot dog:

MU c > MU h

You could have purchased one less hot dog and used the dollar saved the to buy an additional Coke In doing so, you would have given up 10 utils of satisfaction (the

marginal utility of the last hot dog purchased), but you would have acquired an additional

20 utils from the new Coke On balance, your total utility would have risen by 10 utils

(20 – 10) If you are rational, you will continue to adjust your purchases of Coke and hot dogs until their marginal utilities are equal

Even if you would prefer to spend your first dollar on a hot dog, after eating

several you might wish to spend your next dollar on a Coke Purchases can be

adjusted until they reach equilibrium because as more of a good is purchased, its

relative marginal utility decreases—a phenomenon known as the law of

diminishing marginal utility According to the law of diminishing marginal

utility, as more of a good is consumed, its marginal utility or value relative to the

marginal value of the good or goods given up eventually diminishes Thus, if

MU h > MU c , and MU h falls relative to MU c as more hot dogs and fewer Cokes are

consumed, sooner or later the result will be MU h = MU c

Adjusting for Differences in Price and Unit Size

Cokes and hot dogs are not usually sold at exactly the same price To that extent, our

analysis has been unrealistic If we drop the assumption of equal prices, the formula for

maximization of utility becomes:

MUc = MUh

Pc Ph

Where MUc equals the marginal utility of a Coke, MUh the marginal utility of a hot dog,

Pc the price of a Coke, a Ph the price of a hot dog This is the same formula we used

before, but because the price of the goods was the same in that example, the

denominators canceled out When prices differ, the denominator must be retained The

consumer must allocate his or her money so that the last penny spent on each commodity yields the same amount of satisfaction

Suppose a Coke costs $0.50 and the price of a hot dog is $1 If you buy hot dogs and Cokes for lunch and the marginal utility of the last Coke and hot dog you consume

are the same, say 15 utils, you will not be maximizing your satisfaction In relation to

price, you will value your Coke more than your hot dog That is, MU c /P c (or 15

utils/$0.50) exceeds MU h /P h (or 15 utils/$1) You can improve your welfare by eating

fewer hot dogs and drinking more Cokes By giving up a hot dog, you can save a dollar, which you can use to buy two Cokes You will lose 15 utils by giving up the hot dog,

something you would probably prefer not to do You will regain that loss with the next

Coke purchased, however, and the one after that will permit you to go beyond your

previous level of satisfaction

Therefore, if you are rational, you will adjust your purchases until the utility-price

ratios of the two goods are equal As you consume more Coke, the relative value of each additional Coke will diminish If you reach a point where the next Coke gives you 10

utils and the next hot dog yields 20 utils, you will no longer be able to increase your

satisfaction by readjusting your purchases By giving up the next hot dog, you save $1

and lose 20 utils of satisfaction Now the most you can accomplish by using that $1 to

buy two Coke instead is to recoup your loss of 20 utils In fact, the value of the second

new Coke may be less than 10 utils, so you may actually lose by giving up the hot dog

So far we have been talking in terms of buying whole units of Cokes and hot dogs, but the same principles apply to other kinds of choices as well Marginal utility is

involved when a consumer chooses a 12-ounce rather than a 16-ounce can of Coke, or a regular-size hot dog rather than a foot-long hot dog The concept could also be applied to the decision whether to add cole slaw and chili to the hot dog The pivotal question the

consumer faces in all these situations is whether the marginal utility of the additional

quantity consumed is greater or less than the marginal utility of other goods that can be

purchased for the same price

Most consumers do not think in terms of utils when they are buying their lunch, but

in a casual way, they do weigh the alternatives Suppose you walk into a snack bar If

your income is unlimited, you have no problem If you can only spend $3 for lunch,

however, your first reaction may be to look at the menu and weigh the marginal values of the various things you can eat If you have twenty cents to spare, do you not find

yourself mentally asking whether the difference between a large Coke and a small one is

worth more to you than lettuce and tomato on your hamburger? (If not, why do you

choose a small Coke instead of a large one?) You are probably so accustomed to making decisions of this sort that you are almost unaware of the act of weighing the marginal

values of the alternatives

Consumers do not usually make choices with conscious precision Nor can they

achieve a perfect equilibrium—the prices, unit sizes, and values of the various products

available may not permit it They are trying to come as close to equality as possible, The economist’s assumption is that the individual will move toward equality, not that he will

always achieve it

Changes in Price and the Law of Demand

Suppose your marginal utility for Coke and hot dogs is as shown in the table below

Marginal Utility of Marginal Utility of

Unit Consumed Cokes (at $0.50) Hot Dogs (at $1)

If a Coke is priced at $0.50 and a hot dog at $1, $3 will buy you two hot dogs and two

Cokes—the best you can do with $3 at those prices Now suppose the price of Coke rises

to $0.75 and the price of hot dogs falls to $0.75 With a budget of $3 you can still buy

two hot dogs and two Cokes, but you will no longer be maximizing your utility Instead

you will be inclined to reduce your consumption of Coke and increase your consumption

of hot dogs

At the old prices, the original combination (two Cokes and two hot dogs) gave you

a total utility of only 64 utils (45 from hot dogs and 19 from Coke) If you cut back to

one Coke and three hot dogs now, your total utility will rise to 67 utils (57 from hot dogs and 10 from Coke) Your new utility-maximizing combination—the one that best

satisfies your preferences—will therefore be one Coke and three hot dogs No other

combination of Coke and hot dogs will give you greater satisfaction (Try to find one.)

To sum up, if the price of hot dogs goes down relative to the price of Coke, the

rational person will buy more hot dogs If the price of Coke rises relative to the price of

hot dogs, the rational person will buy less Coke This principle will hold true for any

good or service and is commonly known as the law of demand The law of demand

states the assumed inverse relationship between product price and quantity demanded,

everything else held constant If the relative price of a good falls, the individual will buy

more of the good If the relative price rises, the individual will buy less

Figure 8.1 shows the demand curve for Coke—that is, the quantity of Coke

purchased at different prices The inverse relationship between price and quantity is

reflected in the curve’s downward slope If the price falls from $1 to $0.75, the quantity

the consumer will buy increases from two Cokes to three The opposite will occur if the

price goes up

Thus the assumption of rational behavior, coupled with the consumer’s willingness

and ability to substitute less costly goods when prices go up, leads to the law of demand

We cannot say how many Cokes and hot dogs a particular person will buy to maximize

his or her satisfaction That depends on the individual’s income and preferences, which

depend in turn on other factors (how much he likes hot dogs, whether he is on a diet, and how much he worries about the nutritional deficiencies of such a lunch) We can predict

the general response, whether positive or negative, to a change in prices

FIGURE 8.1 The Law of Demand

Price varies inversely with the quantity consumed,

producing a downward-sloping curve like this one

If the price of Coke falls from $1 to $0.75, the

consumer will buy three Cokes instead of two.

Price is whatever a person must give up in exchange for a unit of goods or services

purchased, obtained, or consumed It is a rate of exchange and is typically expressed in

dollars per unit Note that price is not necessarily the same as cost In an exchange

between two people—a buyer and a seller—the price at which a good sells can be above

or below the cost of producing the good What the buyer gives up to obtain the good

does not have to match what the seller-producer gives up in order to provide the good

Nor is price always stated in dollars and cents Some people have a desire to watch sunsets—a want characterized by the same downward-sloping demand curve as the one for Coke The price of the sunset experience is not money Instead it may be the lost

opportunity to do something else, or the added cost and trouble of finding a home that

will offer a view of the sunset (In that case, price and cost are the same because the

buyer and the producer are one and the same.) The law of demand will apply

nevertheless The individual will spend some optimum number of minutes per day

watching the sunset and will vary that number of minutes inversely with the price of

watching

From Individual Demand to Market Demand

Thus far we have discussed demand solely in terms of the individual’s behavior The

concept is most useful, however, when applied to whole markets or segments of the

population Market demand is the summation of the quantities demanded by all

consumers of a good or service at each and every price during some specified time

period To obtain the market demand for a product, we need to find some way of adding

up the wants of the individuals who collectively make up the market

The market demand can be shown graphically as the horizontal summation of the

quantity of a product each individual will buy at each price Assume that the market for

Coke is composed of two individuals, Anna and Betty, who differ in their demand for

Coke, as shown in Figure 8.2 The demand of Anna is DA and the demand of Betty is DB

Then to determine the number of Cokes both of them will demand at any price, we

simply add together the quantities each will purchase, at each price (see Table 8.1) At a price of $11, neither person is willing to buy any Coke; consequently, the market demand must begin below $11 At $9, Anna is still unwilling to buy any Coke, but Betty will buy

two units The market quantity demanded is therefore two If the price falls to $5, Anna wants two Cokes and Betty, given her greater demand, wants much more, six The two

quantities combined equal eight If we continue to drop the price and add the quantities

bought at each new price, we will obtain a series of market quantities demanded When

plotted on a graph they will yield curve DA+B , the market demand for Coke (see Figure

8.2)

_

FIGURE 8.2 Market Demand Curve

The market demand curve for Coke, DA+B , is

obtained by summing the quantities that individuals

A and B are willing to buy at each and every price

(shown by the individual demand curves DA and

DB )

This is, of course, an extremely simple example, since only two individuals are

involved The market demand curves for much larger groups of people, however, are

derived in essentially the same way The demands of Fred, Marsha, Roberta, and others would be added to those of Anna and Betty As more people demand more Coke, the

market demand curve flattens out and extends further to the right

Elasticity: Consumers’ Responsiveness to Price Changes

In the media and in general conversation, we often hear claims that a price change will

have no effect on purchases Someone may predict that an increase in the price of

prescription drugs will not affect people’s use of them The same remark is heard in

connection with many other goods and services, from gasoline and public parks to

medical services and salt What people usually mean by such statements is that a price

change will have only a slight effect on consumption The law of demand states only that

a price change will have an inverse effect on the quantity of a good purchased It does

not specify how much of an effect the price change will have

TABLE 8.1 Market Demand for Coke

In other words, we have established only that the market demand curve for a

good will slope downward The actual demand curve for a product may be relatively flat,

like curve D 1 in Figure 8.3, or relatively steep, like curve D2 Notice that at a price of P1,

the quantity of the good or service consumed is the same in both markets If the price is

raised to P2, however, the response is substantially greater in market D1 than in D2 In

D 1 , consumers will reduce their purchases all the way to Q1 In D 2, consumption will

drop only to Q2

Economists refer to this relative responsiveness of demand curves as the price

elasticity of demand Price elasticity of demand is the responsiveness of consumers, in

terms of the quantity purchased, to a change in price, everything else held constant

Demand is relatively elastic or inelastic, depending on the degree responsiveness to price

change Elastic demand is a relatively sensitive consumer response to price changes If

the price goes up or down, consumers will respond with a strong decrease or increase in

the quantity demanded Demand curve D 1 in Figure 8.3 may be characterized as

relatively elastic Inelastic demand is a relatively insensitive consumer response to price

changes If the price goes up or down, consumers will respond with only a slight

decrease or increase in the quantity demanded Demand curve D2 in Figure 8.3 is

relatively inelastic

The elasticity of demand is a useful concept, but our definition is imprecise

What do we mean by “relatively sensitive” or “relatively insensitive”? Under what

circumstances is consumer response sensitive or insensitive? There are two ways to add precision to our definition One is to calculate the effect of a change in price on total

consumer expenditures (which must equal producer revenues) The other is to develop

mathematically values for various levels of elasticity We will deal with each in turn

FIGURE 8.3 Elastic and Inelastic Demand

Demand curves differ in their relative elasticity

Curve D 1 is more elastic than curve D2 , in the sense

that consumers on curve D 1 are more responsive to

a price change than are consumers on curve D2

Analyzing Total Consumer Expenditures

An increase in the price of a particular product can cause consumers to buy less

Whether total consumer expenditures rise, fall, or stay the same, however, depends on the extent of the consumer response Many people assume that businesses will charge the

highest price possible to maximize profits Although they sometimes do, high prices are

not always the best policy For example, if a firm sells fifty units of a product for $1, its

total revenue (consumers’ total expenditures) for the product will be $50 (50 x $1) If it

raises the price to $1.50 and consumers cut back to forty units, its total revenue could

rise to $60 (40 x $1.50) If consumers are highly sensitive to price changes for this

particular good, however, the fifty-cent increase may lower the quantity sold to thirty

units In that case total consumer expenditures would fall to $45 ($1.50 x 30).1

1

To prove this result, let’s look at marginal revenue MR, or the change in total revenue in response to a

change in quantity Q Taking the derivative of P(Q) • Q with respect to Q, we obtain

Q dQ

dP Q P dQ

Q Q P

= [ ( ) ] ( )MR

Factoring price out of the right-hand side of this equation gives us

, is the same as

The opposite can also happen If a firm establishes a price of $1.50 and then

lowers it to $1, the quantity sold may rise, but the change in total consumer expenditures

will depend on the degree of consumer response In other words, consumer

responsiveness determines whether a firm should raise or lower its price (We will return

to this point later.)

We can define a simple rule of thumb for using total consumer expenditures to

analyze the elasticity of demand Demand is elastic:

• if total consumer expenditures rise when the price falls, or

• if total consumer expenditures fall when the price rises

Demand is inelastic:

• if total consumer expenditures rise when the price rises, or

• if total consumer expenditures fall when the price falls

Determining Elasticity Coefficients

Although we have refined our definition of elasticity, it still does not allow us to

distinguish degrees of elasticity or inelasticity Elasticity coefficients do just that The

elasticity coefficient of demand (Ed) is the ratio of the percentage change in the quantity demanded to the percentage change in price Expressed as a formula,

percentage change in quantity

Ed = percentage change in price The elasticity coefficient will generally be different a different points on the

demand curve Consider the linear demand curve in Figure 8.4 At every point on the

curve, a price reduction of $1 causes quantity demanded by rise by ten units, but a $1

decrease in price at the top of the curve is a much smaller percentage change than a $1

decrease at the bottom of the curve Similarly, an increase of ten units in the quantity

demanded is a much larger percentage change when the quantity is low than when it is

high Therefore the elasticity coefficient falls as consumers move down their demand

curve Generally, a straight-line demand curve has an inelastic range at the bottom, a

unitary elastic point in the center, and an elastic range at the top.2

1 if0

1 if0

1 if0

11MR

P

From this it follows immediately that an increase in Q (a decrease in P) increases total revenue if E > 1, has

no effect on total revenue if E = 1, and reduces total revenue if E < 1

where P represents price, Q is quantity demanded, and A and B are positive constants The total revenue

associated with this demand curve is given by

_

FIGURE 8.4 Changes in the Elasticity Coefficient

The elasticity coefficient decreases as a firm moves

down the demand curve The upper half of a linear

demand curve is elastic, meaning that the elasticity

coefficient is greater than one The lower half is

inelastic, meaning that the elasticity coefficient is

less than one This means that the middle of the

linear demand curve has an elasticity coefficient

equal to one

There are two formulas for elasticity, one for use at specific points on the curve

and one for measuring average elasticity between two points, called arc elasticity The

formula for point elasticity, which is used for very small changes in price, is:

change in quantity demanded change in price

Ed = initial quantity demanded ÷ initial price

From footnote 1, we know that when marginal revenue is equal to 0, elasticity is equal to 1 From Equation

(2) here, this implies that E = 1 when

0B2

A− Q=

or when

B

A2

Q1 Q2 P1 – P2

Ed = ½ (Q1 + Q2) ÷ ½ (P1 P2)

Where the subscripts 1 and 2 represent two distinct points, or prices, on the demand

curve Note that although the calculated elasticity is always negative, economists, by

convention, speak of it as a positive number Economists, in effect, use the absolute

value of elasticity

The change can be illustrated by computing the arc elasticity between two

sets of points, ab and cd Arc elasticity between points a and because:

Elasticity coefficients can tell us much at a glance When the percentage

change in quantity is greater than the percentage change in price, an elasticity

coefficient that is greater than 1.0 results In these cases, demand is said to be elastic

When the percentage change in quantity is less than the percentage change in price,

the elasticity coefficient will be less than 1.0 Demand is said to be inelastic When

the percentage change in the price is equal to the percentage change in quantity, the

elasticity coefficient is 1.0, and demand is unitary elastic.3 In short:

Elastic demand: Ed > 1

Inelastic demand: Ed < 1

Unitary elastic demand: Ed = 1

Elasticity coefficients enable economists to make accurate comparisons A

demand with an elasticity coefficient of 1.75 is more elastic than one with an elasticity

coefficient of 1.55 A demand with a coefficient of 0.25 is more inelastic than one with a coefficient of 0.78

Although elasticity coefficients are useful for some purposes, their accuracy

depends on data that are often less than precise In the real world, there is constant

change in the nonprice variables that influence how much of any product consumers

want It is extremely difficult for economists to separate the effects of a change in price

3

Remember that all elasticity coefficients are negative and are preceded by a minus sign (The demand curve has a negative slope.) economists generally omit the minus sign, as we have seen

from all the other forces operating in the marketplace Small differences in elasticity

coefficients may reflect the imperfections of statistical analysis rather than true

differences in consumer responsiveness to price

Elasticity, Not the Same as Slope

Students often confuse the concept of elasticity of demand with the slope of the demand

curve A comparison of their mathematical formulas, however, shows they are quite

when the price goes down by a given amount Slope is an unreliable indicator of

consumer responsiveness, however, because it varies with the units of measurement for

price and quantity For example, suppose that when the price rises from $10 to $20,

quantity demanded decreases from 100 to 60 The slope is –1/4

-10 -1 slope = 40 = 4

If a price is measured in pennies instead of dollars, however, the slope comes out to –25

-1000 -25 slope = 40 = 1

No matter how the price is measured, the arc elasticity of demand remains –0.75

Furthermore, two parallel demand curves of identical slope will not have the same

elasticity coefficients For example, consider the two curves in Figure 8.5 When the

price falls from $5 to $4, the quantity demanded rises by the same amount for each curve:

ten units Yet the percentage change in quantity is substantially lower for D2 than for D 1 (A rise from seventy to eighty is not nearly as dramatic in percentage terms as a rise from

twenty-five to thirty-five.) Thus the elasticity coefficient is lower for demand curve D2

Be careful not to judge the elasticity of demand by looking at a curve’s slope

Applications of the Concept of Elasticity

Elasticity of demand is particularly important to producers Together with the cost of

production, it determines the prices firms can charge for their products We have seen

that an increase or decrease in price can cause total consumer expenditures to rise, fall, or remain the same, depending on the elasticity of demand Thus if a firm lowers its price

and incurs greater production costs (because it is producing and selling more units), it

may still increase its profits As long as the demand curve is elastic, revenues can (but

will not necessarily) go up more than costs Over the last three decades, the American

Telephone and Telegraph Company has frequently lowered its prices on long-distance

calls To justify those decisions, AT&T had to reason that demand was sufficiently

elastic to produce revenues that would more than cover the cost of servicing the extra

calls During the 1950s a 1960s, many electric power companies requested rate

reductions for the same reason

Producers of concerts and dances estimate the elasticity of demand when they

establish the price of admission If admission costs $10, tickets may be left unsold At a lower price, say $7, attendance and profits may be higher Even if costs rise (for extra

workers and more programs), revenues can still rise more

_

FIGURE 8.5 Two Parallel Curves Do Not Have

the Same Elasticity

Even two parallel demand curves of the same slope

do not have the same elasticity Although a given

change in price—for example, a $1 change—will

produce the same unit change in quantity

demanded, the percentage change will differ

Here, a drop in price from $5 to $4 produces a

ten-unit gain in quantity demanded on both curves

D 1 and D2 A ten-unit increase in sales represents a

lower percentage change at an initial sales level of

seventy (curve D2 )

The difference in the elasticity of the two curves

can be illustrated by computing the arc elasticity

between two sets of points, ab on curve D 1 and cd

on curve D2 Arc elasticity between points a and b:

Government too must consider elasticity of demand, for the consumer’s demand

for taxable items is not inexhaustible If a government raises excise taxes on cars or

jewelry too much, it may end up with lower tax revenues The higher tax, added to the

final price of the product, may cause a negative consumer response It is no accident that

the heaviest excise taxes are usually imposed on goods for which the demand tends to be inelastic, such as cigarettes and liquor

The same reasoning applies to property taxes Many large cities have tended to

underestimate the elasticity of demand for living space Indeed, a major reason for the

recent migration from city to suburbs in many metropolitan areas has been the desire of

residents to escape rising tax rates By moving just outside a city’s boundaries, people

can retain many of the benefits a city provides without actually paying for them This

movement of city dwellers to the suburbs lowers the demand for property within the city, undermining property values and destroying the city’s tax base Thus, if governments

wish to maintain their tax revenues, they have to pay attention to the elasticity of demand

for living in their jurisdictions

Determinants of the Price Elasticity of Demand

So far our analysis of elasticity has presumed that consumers are able to respond to a

price change However, consumers’ ability to respond can be affected by various factors, such as the number of substitutes and the amount of time consumers have to respond to a change in price by shifting to other products or producers

Substitutes

Substitutes allow consumers to respond to a price increase by switching to another good

If the price of orange juice goes up, you are not required to go on buying it You can

substitute a variety of other drinks, including water, wine, and soda

The elasticity of demand for any good depends very much on what substitutes are available The existence of a large number and variety of substitutes means that demand

is likely to be elastic That is, if people can switch easily to another product that will

yield approximately the same value, many will do so when faced with a price increase

The similarity of substitutes—how well they can satisfy the same basic want—also

affects elasticity The closer a substitute is to a product, the more elastic demand for the

product will be If there are no close substitutes, demand will tend to be inelastic What

we call necessities are often things that lack close substitutes

Few goods have no substitutes at all Because there are many substitutes for

orange juice—soda, wine, prune juice, and so on—we would expect the demand for

orange juice to be more elastic than the demand for salt, which has fewer viable

alternatives Yet even salt has synthetic substitutes Furthermore, though human beings

need a certain amount of salt to survive, most of us consume much more than the

minimum and can easily cutback if the price of salt rises The extra flavor that salt adds

is a benefit that can be partially recouped by buying other things

At the other extreme from goods with no substitutes are goods with perfect

substitutes Perfect substitutes exist for goods produced by an individual firm engaged in

perfect competition An individual wheat farmer, for example, is only one among

thousands of producers of essentially the same product The wheat produced by others is

a perfect substitute for the wheat produced by the single farmer Perfect substitutability

can lead to perfect elasticity of demand

The demand curve facing the perfect competitor is horizontal, like the one in

Figure 8.6 If the individual competitor raises his price even a minute percentage above

the going market price, consumers will switch to other sellers The elasticity coefficient

of such a horizontal demand curve is infinite Thus this demand curve is described as

perfectly elastic A perfectly elastic demand is a demand that has an elasticity

coefficient of infinity It is expressed graphically as a curve horizontal to the X-axis

Time

Consumption requires time Accordingly, a demand curve must describe some particular time period Over a very short period of time—say a day—the demand for a good may

not react immediately It takes time to find substitutes With enough time, however,

consumers will respond to a price increase Thus a demand curve that covers a long

period will be more elastic than one for a short period

_

FIGURE 8.6 Perfectly Elastic Demand

A firm that has many competitors may lose all its

sales if it increases its price even slightly Its

customers can simply move to another producer

In that case its demand curve is horizontal, with an

elasticity coefficient of infinity

Oil provides a good example of how the elasticity of demand can change over

time In 1973 Arab oil producers raised the price of their crude oil, and domestic oil

producers followed suit For a time consumers were caught Drivers were stuck with

big, gas-guzzling cars and with suburban homes located far from their work places

Automakers were tooled up to produce big cars, not subcompacts Over the long term,

however, alternative modes of transportation became available and alternative sources of energy were found People altered their lifestyles, walking or riding bicycles to work

The long-term demand curve for oil is much more elastic than the short-term demand

curve

Changes in Demand

The determinants of the elasticity of demand are fewer and easier to identify than the

determinants of demand itself As we saw in Chapter 3, the demand for almost all goods

is affected in one way or another by (1) consumer incomes; (2) the prices of other goods; (3) the number of consumers; (4) expectations concerning future prices and incomes; and (5) that catchall variable, consumer tastes and preferences Additional variables apply in

differing degrees to different goods The amount of ice cream and the number of golf

balls bought both depend on the weather (very few golf balls are sold at the North Pole) The number of cribs demanded depends on the birthrate Together all these variables

determine the position of the demand curve If any variable changes, so will the position

of the demand curve

We saw in Chapter 3 that if consumer preference for a product—say, blue jeans—increases, the change will be reflected in an outward movement of the demand curve (see Figure 8.7) That is what happened during the late 1960s, when college students’ tastes

changed and wearing faded blue jeans became chic By definition, such a change in taste means that consumers are willing to buy more of the good at the going market price If

the price is P1, the quantity demanded will increase from Q2 to Q3 A change in tastes

can also mean that people are willing to buy more jeans at each and every price At P2

they are now willing to buy Q2 instead of Q1 blue jeans We can infer from this pattern

that consumers are willing to pay a higher price for any given quantity In Figure 8.7, the

increase in demand means that consumers are willing to pay as much as P2 for Q2 pairs of jeans, whereas formerly they would pay only P1 (If consumers’ tastes change in the

opposite direction, the demand curve moves downward to the left, as in Figure 8.8, a

quantity demanded at a given price decreases.)

Whether demand increases or decreases, the demand curve will still slope

downward Everything else held constant, people will buy more of the good at a lower

price than a higher one To assume that other variables will remain constant, of course, is unrealistic because markets are generally in a state of flux In the real world, all variables just do not stay put to allow the price of a good to change by itself Even if conditions

change at the same time that price changes, the law of demand tells us that a decrease in

price will lead people to buy more than they would otherwise, and an increase in price

will lead them to buy less

For example, in Figure 8.8, the demand for blue jeans has decreased, because

consumers are less willing to buy the product A price reduction can partially offset the

decline in demand If producers lower their price from P2 to P1, quantity demanded will

fall only to Q2 instead of Q1 Although consumers are buying fewer jeans than they once did (Q2 as opposed to Q3) because of changing tastes, the law of demand still holds

Because of the price change, consumers have increased their consumption over what it

would otherwise have been

A change in consumer incomes will affect demand in more complicated ways

The demand for most goods, called normal goods, increases with income A normal

good or service is any good or service for which demand rises with an increase in

income and falls with a decrease in income The demand for a few luxury goods actually

outstrips increases in income A luxury good or service is any good or service for which

demand rises proportionally faster than income An inferior good or service is any good

or service for which demand falls with an increase in income and rises with a decrease in

income Beans are an example of a good many people would consider inferior People

who rely on beans as a staple or filler food when their incomes are low may substitute

meat and other higher-priced foods when their incomes rise

FIGURE 8.7 Increase in Demand

When consumer demand for blue jeans increases,

the demand curve shifts from D1to D2

Consumers are now willing to buy a larger

quantity of jeans at the same price, or the same

quantity at a higher price At price P1, for

instance, they will buy Q3 instead of Q2 And

they are now willing to pay P2 for Q2 jeans,

whereas before they wold pay only P1

_

_ FIGURE 8.8 Decrease in Demand

A downward shift in demand, from D 1 to D2 , represents a decrease in the quantity of blue jeans consumers are willing to buy at each and every price It also indicates a decrease in the price they are willing to pay for each and every

quantity of jeans At price P2 , for instance,

consumers will now buy only Q1 jeans (not Q3 ,

as before); and they will now pay only P2 for Q1

jeans not P3, as before

Thus, while economists can confidently predict the directional movement of

consumption when prices change, they cannot say what will happen to the demand for a

particular good when income changes, because each individual determines whether a

particular good is a normal, inferior, or luxury good Different people will tend to answer

this question differently in different markets Beans may be an inferior good to most

low-income consumers and a normal good to many others

For example, how do you think a change in income will affect the demand for

low-, medium-, and high-quality liquor? You may have some intuitive notion about the

effect, but you are probably not as confident about it as you are about the effect of a price

decrease In fact, during past recessions, the demand for both low- and high-quality

liquor has increased Some consumers may have switched to high-quality liquor to

impress their friends, and to suggest that they have been unaffected by the economic

malaise Others may have tried to maintain their old level of consumption by switching

to a low-quality brand

The effect of a change in the price of other goods is similarly complicated Here

the important factor is the relationship of one good—say, ice cream—to other

commodities Are the goods in question substitutes for ice cream, like frozen yogurt?

Are they complements, like cones? Are they used independently of ice cream? Demand for ice cream is unlikely to be affected by a drop in the price of baby rattles, but it may

well decline if the price of frozen yogurt drops

Two products are generally considered substitutes if the demand for one goes up when the price of the other rises The price of a product does not have to rise above the price of its substitute before the demand for the substitute is affected Assume that the

price of sirloin steak is $6 per pound and the price of hamburger is $2 per pound The

price difference reflects the fact that consumers believe the two meats are of different

quality If the price of hamburger rises to $4 per pound while the price of sirloin remains

constant at $6, many buyers will increase their demand for steak The perceived

difference in quality now outweighs the difference in price

Because complementary products—razors and razor blades, oil and oil filters,

VCRs and videocassette tapes—are consumed jointly, a change in the price of one will

cause an increase or decrease in the demand for both products at once An increase in the price of razor blades, for instance, will induce some people to switch to electric razors,

causing a decrease in the quantity of razor blades demanded and a decrease in the

demand for safety razors Again, economists cannot predict how many people will

decide the switch is worthwhile, they can merely predict from theory the direction in

which demand for the product will move

Derivation of Demand from Indifference Curves

And the Budget Line

Our discussion of theoretical foundations of demand has, admittedly, been casual Here

we can add greater precision to the analysis Much of the discussion has been founded on the notion of the rational pursuit of individual preferences That is, we assume the

individual knows what he or she wants and will seek to accomplish those goals

Preference, however, is a nebulous concept To lend concreteness to the idea, economists have developed the indifference curve

Individuals face limits in what they can produce and buy, a point of earlier

chapters That fact, together with the existence of indifference curves, can be used to

derive an individual’s demand for a product

Derivation of the Indifference Curve

Consider a student whose wants include only two goods, pens and books Figure 8.9

shows all the possible combinations of pens and books she may choose The student will

prefer a combination far from the origin to one closer in At point b, for instance, she

will have more books and more pens than at point a For the same reason, she will prefer

a to c In fact the student will prefer a to any point in the lower left quadrant of the graph

and will prefer any point in the upper right quadrant to a

We can also reason that the student would prefer a to d, where she gets the same number of pens but fewer books than at a Likewise, she will prefer e to a because it

yields the same number of books and more pens than a If a is preferred to d and e is

preferred to a, then as the student moves from d to e, she must move from a less

preferable to a more preferable position with respect to a At some point along that path, the student will reach a combination of books and pens that equals the value of point a

Assuming that combination is f (it can be any point between d and e), we can say that the individual is indifferent between a and f

Using a similar line of logic, we can locate another point along the line gih that

will be equal in value to a and therefore to f In fact, any number of points in the lower

right-hand and upper left-hand quadrants of the graph are of equal value to a Taken

together, these points form what is called an indifference curve (see curve I1 in Figure

8.10)

_

FIGURE 8.9 Derivation of an Indifference Curve

Because the consumer prefers more of a good to less,

point a is preferable to point c, and point b is

preferable to point a If a is preferable to demand but

e is preferable to a, then when we move from point d

to e, we must move from a combination that is less

preferred the one that is more preferred In doing so

we must cross a point—for example, f—that is equal

in value to a Indifference curves are composed by

connecting all those points —a, f, i, and so on—that

are of equal value to the consumer

Using a similar line of logic, we can locate another point along the line gih that

will be equal in value to a and therefore to f In fact, any number of points in the lower

right-hand and upper left-hand quadrants of the graph are of equal value to a Taken

together, these points form what is called an indifference curve (see curve I1 in Figure

8.10) An indifference curve shows the various combinations of two goods that yield

the same level of total utility

Using the same line of reasoning, we can construct a second indifference curve

through point b Because b is preferable to a, and all points on the new indifference

curve will be equal in value to point b, we can conclude that any point along the new

curve I2 is preferable to any point on I1 Using this same procedure, we can continue to

derive any number of curves, each one higher than, and preferable to, the last

From this line of reasoning, an economist can draw several conclusions about the student’s preference structure (called an “indifference map”):

1 The student’s total utility level rises as she moves up and to the right, from one

indifference curve to the next

2 Indifference curves slope downward to the right

3 Indifference curves cannot intersect (An intersection would imply that all points

on all the intersecting curves are of equal value, contradicting the conclusion that

higher indifference curves represent higher levels of utility)

FIGURE 8.10 Indifference Curves for

Pens and Books

Any combination of pens and books that falls along

curve I1 will yield the same level of utility as any

other combination on that curve The consumer is

indifferent among them By extension, any

combination on curve I2 will be preferable to any

combination on curve I1

The Budget Line and Consumer Equilibrium

From indifference curves we can derive the law of demand First we need to construct

the individual’s budget line, a special form of the production possibilities curve The

budget line shows graphically all the combinations of two goods that a consumer can buy with a given amount of income Assume that our student earns an income of $150, which she uses to buy books and pens Books cost $3 each and pens cost $5 a package The student can spend all $150 on fifty books or thirty pen packs, or she can divide her

expenditures in any number of ways to yield various combinations of books and pens

By plotting all the possible combinations, we obtain the student’s budget line, B1 P1 in

Figure 8.11

All combinations on the budget line are possible for the student She can choose

point a, twenty-five books and fifteen pen packs, or point b, forty-five books and three

pen packs Either combination exhausts her $150 budget The rational individual will

choose that point where the budget line just touches (is tangent to) an indifference

curve—point a in this case.4 Points farther up or down the budget line will put the

student on a lower indifference curve and are therefore less preferable (If, for instance,

the student moves to c on the budget line, she will be on a lower indifference curve, I2

instead of I1.) At point a, the individual’s wants are said to be in equilibrium As long as

her income and preferences and the prices of books and pens remain the same, she has no reason to move from that point.5

4

This tangency condition can be derived mathematically by maximizing the consumer's utility subject to

the budget constraint, or by maximizing the U (X,Y) with respect to X and Y, subject to P x X + P y Y = I

This constrained maximization problem can be carried out by forming the Lagrangian function

)(

)

U

where λ is known as a Lagrangian multiplier, and maximizing it with respect to X and Y and minimizing it

with respect to λ The necessary conditions are

U X

U Y

L

Y X

λ

Equation (1) can be divided by equation (2), which, after simple algebraic manipulation, yields

(Missing equation to be added)

The left-hand side of t his equation is -1 multiplied by the ratio of the marginal utility of good X to the marginal utility of good Y, or the slope of the indifference curve The right-hand side is -1 multiplied by the ratio of the price of good X to the price of good Y, or the slope of the budget constraint

The equality of these two slopes is dependent on the assumption that the consumer will consume positive quantities of both goods Later in this chapter, we will consider the possibility that the consumer may maximize utility subject to the budget constraint by deciding to consume none of one of the goods

5

We can provide another intuitive rationale for the required condition for consumer equilibrium Starting with the tangency requirement

Y X Y

X P

P MU

MU

=

we can obtain the equivalent condition

Y Y X

X P

MU P

MU

=

by simple algebraic manipulation Verbally, this means that the consumer receives the same increase in utility from spending $1 more on good X as would be received from spending more on good Y We can see that this condition is necessary if utility is being maximized subject to the budget constraint by

assuming that the condition is not satisfied Assume for example, that (continued on next page)

Y Y X

X P

MU P

MU

>

_

FIGURE 8.11 The Budget Line and Consumer

Equilibrium

Constrained by her budget, the consumer will

seek to maximize her utility by consuming at the

point where her budget line is tangent to an

indifference curve Here the consumer chooses

point a, where her budget line just touches

indifference curve I 1 All other combinations on

the consumer’s budget line will fall on a lower

indifference curve, providing less utility Point c,

for instance, falls on indifference curve I 2

_

What happens if prices change? Suppose the individual’s wants are in

equilibrium at point a in Figure 8.11 when the price of pens falls from $5 a pack to $3 a

pack (The price of books stays the same.) The budget line will pivot to B1P2 in Figure

8.12, reflecting the greater buying power of the student’s income (She can now buy fifty pen packs with $150.) The new budget line gives the student a chance to move to a

higher indifference curve—for instance, to point c, twenty-two pens and twenty-eight

books

The Law of Demand, Again

The result of the price reduction is that the student buys more pens Thus we derive the

law of demand, that quantity demanded is inversely related to price The

downward-sloping demand curve for pens shown in Figure 8.13 is obtained by plotting the quantities

of pen packs bought from Figure 8.12 against the price paid per pack When the price of pens falls from $5 to $3 a pack in Figure 8.12, the consumer increases the quantity

purchased from fifteen to twenty-two packages

This tells us that if $1 less is spent on good Y, utility will not decline as much as it will increase if $1 more

is spent on good X Therefore, the consumer can increase total utility without increasing expenditures by reducing the consumption of good Y and increasing the consumption of good X This will continue to be true until the equality is restored, which will happen eventually as MUY increases relative to MUX In a similar manner, we can argue that the consumer will move toward the equilibrium condition if we assume that

Y Y X

X P

MU P

MU

<

FIGURE 8.12 Effect of a change in Price on

Consumer Equilibrium

If the price of pens falls, the consumer’s budget

line will pivot outward, from B1P1 to B1P2 As a

result, the consumers can move to a higher

indifference curve, I2 instead of I1 At the new

price the consumer buys more pens, twenty-two

packs as opposed to fifteen

FIGURE 8.13 Derivation of the Demand Curve

for Pens When the price of pens changes, shifting the

consumer’s budget line from I1 to I2 in Figure 8.14, the consumer equilibrium point changes with it The consumer’s demand curve for pens is obtained by plotting her equilibrium quantity of pens at various prices At $5 a pack, the consumer buys fifteen packs

of pens (point a) At $3 a pack, she buys twenty-two packages (point c)

Application: Cash Versus In-Kind Transfers

A cash grant will raise the welfare of the poor more than an in-kind transfer of equal

value Figure 8.14 illustrates a poor family’s budget line for higher education and

housing, H3 E3 Without subsidies, this family can buy as much as E3 units of education

(and no housing) or H3 units of housing (and no education) Because the family wants

both housing and higher education, it will probably divide its income between the two,

choosing some combination like point a, or E1 education and H1 housing

Suppose that the government decides to subsidize the family’s higher education

purchases through reduced university tuition Its action lowers the total price of

education, pivoting the family’s budget line out to H3 E5 The result is that the family can

now consume more of both items, education and housing The family will probably

move to some combination like b, H2 housing and D2 education Its education

consumption has gone up and the additional housing purchased represents an increase in

income equal to the vertical distance between b and c

Suppose the family were given the cash equivalent of bc instead The additional

money would not change the relative prices of higher education and housing, as the

reduced tuition program did It would shift the budget line from H3E3 to a parallel

position, H4E4 (dashed line) The relative price of housing is lower on H 4E4 than on

25

25

H3E5 Thus the family would tend to prefer d to b, both of which are available on line

H4E4, we must presume that they would prefer cash to an in-kind subsidy

This point can be seen even more clearly with the help of indifference curves

Imagine an indifference curve tangent to H3E3 in the absence of government relief,

causing the family to point a Imagine a higher indifference curve that is tangent to H3E5

at point b Now, imagine an even higher indifference curve tangent to H4E4 at point d

FIGURE 8.14 Budget Line: Cash Grants versus

Food Stamps

If the price of education is reduced by an in-kind

subsidy, a family’s budget line will pivot from

H3E3 to H3E5 The family will move from point a

to point b, where it can consume more food and

housing If the family is given the same subsidy in

cash, its budget line will move from H3E3 to H4E4

Since the relative price of housing is lower on H4E4

than on H3E5, the family will choose a point like d

over b Since b was the family’s preferred point on

H3E5, but they prefer d to b, we must presume they

also prefer cash to a food subsidy

_

Application: Capturing the Consumer surplus

The price that a consumer pays for a good reflects the value that he or she places on an

additional unit of the good Since the price normally applies uniformly to all units of the

good purchased and the consumer generally values the last unit consumed less than the

units consumed previously, the consumer values the total consumption of a good at more than the amount paid for its consumption The gap between what a consumer is willing

to pay rather than do without a good (the total value placed on the good) and what the

consumer actually pays is referred to as the consumer surplus Obviously, suppliers

prefer that consumers pay more rather than less for a good and are anxious to capture as much consumer surplus as possible We can employ indifference-curve analysis to show how suppliers use different pricing schemes to encourage consumers to pay more for a

given quantity of a good than they would if the good were uniformly priced

Conceptually, the simplest way for a supplier to capture the total consumer

surplus of an individual would be to charge a different price for each unit consumed and

to price each unit at the maximum amount the consumer is willing to pay for that unit

But such a pricing policy would be enormously difficult to implement The supplier