# Chapter 5 Diamond Water Paradox Discussion

Description

Prior to beginning work on this discussion, read Farah Mohammeds article, Why Are Diamonds More Expensive Than Water? (Links to an external site.), as well as Chapter 5 in your textbook, especially Sections 5.1 and 5.3, and respond to the following:
Describe the relationship between total utility and marginal utility.
Explain if marginal utility can be negative.
Examine the diamond-water paradox. Why are diamonds more expensive than water?
Evaluate the law of diminishing marginal utility.
Identify some items, explaining your reasoning, that do not follow the law of diminishing marginal utility.

Evaluate how the law of diminishing marginal utility can explain the diamond-water paradox.
The Law of Diminishing Marginal Utility paper

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5
Demand and Consumer Choice
Charles O. Cecil/age fotostock/Superstock
Learning Outcomes
After reading this chapter, you should be able to
 Discuss the importance of utility in explaining consumer choice.
 Derive an individual demand curve for a good based on the equation for maximizing total utility and the
principle of diminishing marginal utility.
 Apply utility theory to explanations of consumer behavior.
 Identify and describe the concept of consumer surplus.
 Describe how advertising attempts to increase utility.
Section 5.1
Choice, Value, and Utility Theory
Introduction
Where you work, where you shop, and all over the world, there are vending machines that
supply everything from soft drinks and snacks to emergency footwear and newspapers. If you
think about it, you will notice a significant difference between the machines that dispense soft
drinks and those that dispense newspapers. After you have deposited the requisite amount
of money, the food and drink machines provide a single can or package through a chute of
some sort, while the newspaper machine allows you to open a door and take one paper from
a stack. Why? Are readers more honest than eaters?
This chapter will help provide an answer to this puzzle. To do this we will look at what determines consumer choice. Since individual demand curves form the bedrock of microeconomic
analysis, we need to consider the factors that underlie them.
The classical approach economists have taken in examining consumer demand involves the
concept of measurable utility. We will use this approach to examine some problems and suggest some applications for demand analysis. Another approach to consumer demand, indifference curve analysis, is more advanced and beyond the scope of this chapter.
5.1 Choice, Value, and Utility Theory
The idea that households and firms must make choices because of scarcity is the fundamental
notion of economic analysis. We now want to expand on that analysis to consider why consumers behave the way they do. Why does a person demand a certain good or service? An
obvious answer is that the good or service is expected to satisfy some need or desire of the
consumer.
Economists view of consumer choice is based on five assumptions about the psychology of
consumer behavior:
1. Consumers (or households) must make choices because they have limited income
and are forced to choose which of their many wants to satisfy.
2. Consumers make rational choices when they make these consumption decisions.
That is, they weigh costs and benefits and make the decision that gives them the
most satisfaction.
3. Consumers make these choices with imperfect information. In other words, they
dont know (with certainty) all the attributes of the goods they are choosing to
consume.
4. As increasing amounts of a good are consumed, the additional satisfaction gained
from an additional unit becomes smaller.
5. Many goods have qualities that make them satisfactory substitutes for other goods.
All of these statements may seem simple and obvious, but they will enable us to draw some
powerful conclusions about the nature of demand.
Section 5.1
Choice, Value, and Utility Theory
Economics in Action: Crunch Into Utility Theory
Using the classic cookie, this video bites straight into utility theory to help us understand
the total amount of satisfaction one gains from a product despite the diminishing marginal
utility. Check out the following clip. https://www.youtube.com/watch?v=KOUJEyy48qY
The History of Utility Theory: The DiamondWater Paradox
In the early development of economic theory, economists often posed questions that they
then debated. One of the popular debate topics was what determined value. Adam Smith
wrote that value could mean either value in use or value in exchange. He posed (in 1776)
what became known as the diamondwater paradox:
The things that have the greatest value in use have frequently little or no
value in exchange; and on the contrary, those which have the greatest value
in exchange have frequently little value in use. Nothing is more valuable than
water, but it will purchase scarce anything; scarce anything can be had in
exchange for it. A diamond, on the contrary, has scarce any value in use; but a
very great quantity of other goods may frequently be had in exchange for it.
(Smith)
The diamondwater paradox was the problem that classical economists used when they
argued that value in use could not determine price (value in exchange). Diamonds, although
less useful than water, are more expensive than water. The dialogue about the diamondwater
paradox went on for a long time. Many famous mathematicians, economists, and philosophers took part in the debate. The confusion over the diamondwater paradox arose in part
over disagreement as to what the term useful meant. In the 1870s William Stanley Jevons,
Carl Menger, and Léon Walras, all writing
separately, solved the paradox by developing
a theory of value in which demand and utility
came to the forefront. Their solution played
a major role in developing the theory of consumer demand.
Another part of the debate underlying the
over whether value (or price) was determined by supply or demand. In a famous
analogy, Alfred Marshall, the great British
economist, said that one could no more say
whether supply or demand determined value
than one could say which blade of a pair of
scissors did the cutting. That is, value (or
price) is determined by the interaction of
supply and demand.
Ingram Publishing/Thinkstock
value in use cannot determine price.
Diamonds, for example, are arguably less
useful than water but are more expensive
than water.
Section 5.1
Choice, Value, and Utility Theory
Well consider the influence of demand on value first and leave supply for later chapters.
Demand theorists use the notion of utility. If a consumer wants a good or service, then that
good or service has utility for that person. Utility is the satisfaction a consumer receives from
consuming a good or service The same good may have a great deal of utility for one person
and none or very little for some other person. Note that in economics, the word utility does
not necessarily mean useful. There are a number of items in the real world that are not useful that give great satisfaction.
Total Utility and Marginal Utility
A good unit for the measurement of utility, like the pound or gallon or mile, does not exist.
Since utility is unique to the individual, however, an arbitrary (and imaginary) unit called the
util can be employed. As long as no attempt is made to compare the number of utils of different people, this is a satisfactory measuring device. Such comparisons between people are
inappropriate because the number of utils is a subjective measure of a certain individuals
satisfaction and as such is not subject to meaningful comparisons. (Some people prefer the
beach to the mountains!)
A relationship that expresses a persons desire to consume differing amounts of a good is
called a utility function. For example, suppose you try to construct your utility function for
a certain brand of soft drink. First, choose a convenient time period, such as a day. Then, for
one unit (one can) of soda per day, assign an arbitrary number of utils, say 20. (You can choose
any number at all: 1, or 1,000, or 47½.) Ask yourself, if I get 20 utils from one can, how many
would I get if I consumed two cans per day? Suppose, after much reflection, you say 38. Ask
yourself the same question about three cans per day, four, five, six, and so on. You use these
figures to construct a utility schedule, as shown in Table 5.1.
Table 5.1: Utility schedule for soda
Cans of soda per day
Total utility (utils)
Marginal utility (utils)
1
20
20
3
54
16
2
4
5
6
7
8
9
10
38
67
77
84
88
89
87
82
18
13
10
7
4
1
2
5
Section 5.1
Choice, Value, and Utility Theory
Marginal utility (MU) is the amount of utility that one more or one less unit consumed adds
to or subtracts from total utility. It is the change in satisfaction provided by one more or one
less unit of consumption. The formula for marginal utility is
MU =
change in total utility
one-unit change in quantity consumed
In Table 5.1 the marginal utility is determined by calculating how much each additional can
of soda adds to total utility. For example, the first can of soda adds 20 utils to total utility. The
fourth can of soda adds 13 utils to total utility. Marginal utility is found by subtracting the
total utility of consuming three sodas from the total utility of consuming that number plus
one (67  54 = 13).
The Principle of Diminishing Marginal Utility
The important feature of the schedule shown in Table 5.1 is that, although the total utility
becomes larger the more you consume per day (up to a point), the increases to total utility
from each additional unit consumed become smaller. The fact that additional, or marginal,
utility declines as consumption increases is called diminishing marginal utility.
The principle of diminishing marginal utility states that the greater the level of consumption of a particular good in a given time period, the lower the marginal utility of an additional
unit. As you consume more units of a good, the later units yield less of an addition to total
utility than the preceding units did. For instance, the seventh soda is expected to provide less
additional pleasure than the sixth. This principle is reflected in Table 5.1. Marginal utility falls
from 7 utils for the sixth soda to 4 utils for the seventh.
Figure 5.1(a) shows the total utility curve plotted from Table 5.1. Figure 5.1(b) shows the
marginal utility curve that corresponds to the table. Note that when the total utility curve
reaches its maximum, marginal utility is zero. Thereafter, each additional unit contributes a
negative marginal utility; thus, total utility will be decreased. In Table 5.1 total utility reaches
a maximum at eight sodas per day because the ninth soda has a negative marginal utility.
Section 5.2
Utility and Consumer Behavior
Figure 5.1: Total and marginal utility
Total utility increases as consumption increases to a certain level, in this case eight sodas per day, and
then it declines. When total utility is increasing, marginal utility is declining, illustrating the principle
of diminishing marginal utility. At the point that total utility begins to decline, marginal utility becomes
negative.
(a)
Total
utility (utils)
100
90
80
70
60
50
40
30
20
10
0
Total
utility
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
(b)
Marginal
utility (utils)
20
18
16
14
12
10
8
6
4
2
0
2
4
6
9 10
Sodas/day
9
Marginal utility
10
Sodas/
day
5.2 Utility and Consumer Behavior
The concepts of utility and price can be combined to show how consumers make choices in
the marketplace. Consumers are confronted with a range of items and also a range of prices.
A consumer may not necessarily choose based solely on which item has the greatest utility;
price and the consumers income are also important factors. In other words, consumers dont
always buy their first choice. You may prefer a Tesla to a Toyota but decide to purchase the
Toyota. The explanation for this behavior lies in the relationship between price and utility.
Section 5.2
Utility and Consumer Behavior
Suppose, for example, you are considering purchasing a six-pack of soft drinks. You are presented with the three possibilities shown in Table 5.2. Coca-Cola is your first choice because
to you it yields the most utility. But the relevant question is not which soft drink has the most
utility but rather which has the most utility per dollar. Therefore, you choose to buy a six-pack
of Pepsi. This choice implies that the extra satisfaction of Coca-Cola over Pepsi is not worth
\$0.75, but the extra satisfaction of Pepsi over RC Cola is worth \$0.25. There are other things
you can do with the extra \$0.75. You are saying that \$0.75 spent on something other than
soda will yield more additional utils than the difference between the utility of Coke and the
utility of Pepsi, but that \$0.25 spent on other goods will not yield more utils than spending it
on Pepsi instead of RC Cola.
Table 5.2: Hypothetical utility-per-dollar comparison
Choice
Marginal utility (utils)
Price (dollars)
Marginal utility per
dollar (utils)
Coca-Cola
30.0
3.75
10
RC Cola
20.0
2.75
10
Pepsi
27.0
3.00
12
Thus, in deciding how to spend your money, you look at marginal utility per dollar rather than
marginal utility alone. You do this because money is the common measure of what you have to
give up. Dollars can be used to buy any available good. So for each dollar you spend, you want
to choose the item with the highest utility per dollar. In doing so, you economize by getting
the most satisfaction per dollar.
Maximizing Total Utility
The self-interest assumption maintains that individuals will act to maximize their total utility. To see how marginal utility and price influence how a consumer maximizes total utility,
consider an example with only two goods, cola and pizza. A unit of cola costs \$0.50, and a
unit of pizza costs \$1.00. The consumers utility schedules for the two goods are presented in
Table 5.3. The consumer has a given amount of income, called a budget constraint. A budget
constraint is a given level of income that determines the maximum amount of goods that
may be purchased by a consumer. Lets allow this consumer a budget constraint of \$13 and
see how that amount will be allocated between the two goods to achieve maximum utility.
Section 5.2
Utility and Consumer Behavior
Table 5.3: Utility for a consumer of two goods
Cola
MU/P (P
= \$0.50)
Total
utility,
TU
(utils)
Quantity
per week
(pieces)
Marginal
utility,
MU
(utils)
MU/P (P
= \$1.00)
Total
utility,
TU
(utils)
15
30
15
1
32
32
32
13
26
42
3
28
28
91
Quantity
per week
(cans)
Marginal
utility,
MU
(utils)
1
3
2
4
5
6
7
8
9
10
11
12
Pizza
14
12
11
10.75
10.25
10
9
8
7
6.5
28
24
22
21.5
20.5
20
18
16
14
13
29
2
54
4
65
5
75.75
6
86
7
96
8
105
9
113
10
120
11
126.5
12
31
24.75
20.25
18
17
16
14
12
11
9
31
24.75
20.25
18
17
16
14
12
11
9
63
115.75
136
154
171
187
201
213
224
233
The first dollar will be allocated to pizza because a dollars worth of pizza (one piece) yields
32 utils of satisfaction compared with 29 utils for a dollars worth of cola (two cans). The
next dollar will also be spent on pizza because it yields 31 utils, which is still greater than the
first dollars worth of cola, the alternative purchase. In other words, the consumer buys two
pieces of pizza before buying any cola. The third dollar is spent on cola because the 29 utils of
satisfaction gained from purchasing two cans are greater than the 28 utils that are yielded by
a third piece of pizza. The process continues until the entire income of \$13 is spent. In maximizing total utility, the consumer will spend \$5 on 10 cans of cola and \$8 on eight pieces of
pizza. This allocation produces 300 utils of satisfactionthe maximum total utility that can
be purchased with \$13 of income. You cannot find a different combination of cola and pizza
that will produce more satisfaction (try reducing cola consumption by two cans and increasing pizza consumption by one piece, or vice versa).
The consumers choices are based on a maximization rule that says that total utility is maximized when the last dollar spent on good A yields the same utility as the last dollar spent on
good B. In algebraic form, total utility is maximized when
This can be written
Marginal utility of good A
Price of good A
MUA
PA
=
=
Marginal utility of good B
MUB
Price of good B
PB
Section 5.2
Utility and Consumer Behavior
The marginal utility of a can of cola, when 10 cans per week are consumed, is 8 utils, and the
price of a can is \$0.50. Thus,
MUcola
Pcola
=
8
\$0.50
= 16 utils per dollar
For pizza, at the optimum consumption rate, the marginal utility is 16, and the price is \$1.
Thus,
MUpizza
Ppizza
=
16
\$1.00
= 16 utils per dollar
Of course, individuals dont spend all their income on goods. Sometimes individuals hold
money as they do any other commodity. Including money (symbolized by \$), the equation for
maximization of utility is
MUA
PA
=
MUB
PB
=
MU\$
P\$
Utility maximization is the process by which a consumer adjusts consumption, given a budget constraint and a set of prices, in order to attain the highest total amount of satisfaction.
The equation above is an expression for utility maximization. It includes all commodities,
even money. This equation says that in order to maximize total utility, the marginal utilities
per dollar of all goods consumed have to be equal and also have to equal the marginal utility
of money. If this is not the case, a change in the consumption pattern can produce more satisfaction for a given budget constraint. This equation is just a formal way of saying that people
allocate their income so as to yield the most satisfaction possible. When utility is being maximized, the additional satisfaction from any use of a dollar will equal the additional satisfaction from any other use of that dollar. When this is not the case, the consumer can reallocate
personal income from one good to another and gain more satisfaction.
To see how a given consumption pattern can be adjusted to achieve maximum utility, look
again at Table 5.3. Lets give Shandra an income of \$9 and say that she uses it to buy \$3 worth
of cola and \$6 worth of pizza. The expression
MUcola
doesnt hold because
Pcola
=
10.75
0.50
MUpizza
Ppizza
>
18
1
Shandra isnt maximizing her utility, because the last dollar she spent on cola yielded more
utils than the last dollar she spent on pizza. Shandra should reallocate her consumption outlays. By giving up a dollars worth of pizza, she will lose 18 utils. But she will gain 20.25 utils
by spending that dollar on more cola. Her total utility will thus rise by 2 (rounded off), and
10
0.50