Utility

Utility and value

One purpose of value theory in economics is to explain

how the prices of goods and services are determined.

This is only a step, however, in the analysis of a

deeper problem. The modern industrial economy is

characterized by a high degree of interdependence of

its parts. The supplier of components or raw materials,

for example, must deliver the desired quantities of his

products at the right moment and in the desired

specifications. In economies such as those of western

Europe, North America, and Japan, the coordination of

these activities is done through the price system. The

relative prices of the various inputs (e.g., labour,

materials, machinery) tend to determine the proportions

in which they will be used. Prices also affect the

relative outputs of the various final products, and

they determine who will consume them. Value theory,

therefore, studies the structure of these decisions,

analyzes the influence of prices, and examines the

efficiency of the resulting allocation of resources.

Value theory is also applied by business firms and

government agencies in their decisions that relate to

pricing and the allocation of resources.

To cite this page:

“Economic Theory: Utility and value” Britannica Online.

<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/0.html&gt;

[Accessed 27 February 1998].

Resource limitations and allocation.

The fact that goods have value can be ascribed

ultimately to the limitations in the world’s material

endowment. Man does not have all the arable land,

petroleum, or platinum that he would like; their use

must be rationed. That is why goods have prices; if

they were available in unlimited supply they would be

free. Price usually serves as the rationing device

whereby their use is kept down to the available supply.

(see also Index: conservation)

Resources can be said to be scarce in both an absolute

and in a relative sense: the surface of the Earth is

finite, imposing absolute scarcity; but the scarcity

that concerns economists is the relative scarcity of

resources in different uses. Materials used for one

purpose cannot at the same time be used for other

purposes; if the quantity of an input is limited, the

increased use of it in one manufacturing process must

cause it to become scarcer in other uses. (see also

Index: resources, allocation of)

The cost of a product in terms of money may not measure

its true cost to society. The true cost of, say, the

construction of a supersonic jet is the value of the

schools and refrigerators that will never be built as a

result. Every act of production uses up some of

society’s available resources; it means the foregoing

of an opportunity to produce something else. In

deciding how to use resources most effectively to

satisfy the wants of the community, this opportunity

cost must ultimately be taken into account.

In a market economy the relationship between the price

of a good and the quantity supplied depends on the cost

of making it, and that cost, ultimately, is the cost of

not making other goods. The market mechanism enforces

this relationship. In the first instance, the cost of,

say, a pair of shoes is the price of the leather, the

labour, the fuel, and other elements used up in

producing them. But the price of these inputs, in turn,

depends on what they can produce elsewhere–if the

handbags that can be produced with the leather are

valued very highly by consumers, the price of leather

will be bid up correspondingly.

To cite this page:

“Economic Theory: Utility and value: THEORIES OF VALUE:

Resource limitations and allocation.” Britannica

Online.

<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/2.html&gt;

[Accessed 27 February 1998].

THEORIES OF UTILITY

There are two sides to the analysis of price and value:

the supply side and the demand side. If cost can be

said to underlie the supply relationship that

determines price, the demand side must be taken to

reflect consumer tastes and preferences. “Utility” is a

concept that has been used to describe these tastes. As

already indicated, the cost-of-production analysis of

value given above is incomplete, because cost itself

depends on the quantity produced. The cost analysis,

moreover, applies only to commodities the production of

which can be expanded and contracted. The price of a

first-folio Shakespeare has no relation to cost of

production; it must depend in some sense on its utility

to purchasers as it affects their bids.

To cite this page:

“Economic Theory: Utility and value: THEORIES OF

UTILITY” Britannica Online.

<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/3.html&gt;

[Accessed 27 February 1998].

Marginal utility.

The classical economists suggested that this leads to a

paradox. They argued that utility could not explain the

relative price of fine jade and bread, because the

latter was for many consumers essential to life, and

hence its utility must surely be greater than that of

jade. Yet the price of bread is far lower than that of

jade. The theory of marginal utility that flowered

toward the end of the 19th century supplied the key to

the paradox and provided the basis for today’s analysis

of demand. Marginal utility was defined as the value to

the consumer of an additional unit of some commodity.

If, for example, the consumer is offered a choice

between 22 and 23 slices of bread for his family,

marginal utility measures how much more valuable 23

slices are than 22. It is clear that the magnitude of

the marginal utility varies with the magnitude of, say,

the smaller of the alternatives. That is, for a family

of four, the difference between seven and eight slices

of bread per day can be substantial, if the family will

still be hungry in either case. But the difference in

value between 31 and 32 slices may be negligible. If 31

slices offer enough for everyone to fill his stomach, a

32nd slice may be worth very little. Moreover, the

difference in value between 122 and 123 slices may be

negative–a 123rd slice may just add to the family’s

disposal problem. These observations lead directly to

the plausible notion that marginal utility in some

sense diminishes with the base from which one starts

the calculation. With only seven or eight slices the

marginal utility (incremental value) of an eighth slice

is high. With 31 or 32 slices it is lower, and so on.

The less scarce a commodity, the lower is its marginal

utility, because its possessor in any case will have

enough to satisfy his most pressing uses for it, and an

increment in his holdings will only permit him to

satisfy, in addition, desires of lower priority.

The consumer will be motivated to adjust his purchases

so that the price of each and every good will be

approximately equal to its marginal utility (that is,

to the amount of money he is willing to pay for an

additional unit). If the price of an item is P dollars,

for example, and the consumer is considering buying,

say, 10 units, at which point the marginal utility of

the good to him is M (which is greater than P), the

consumer will be better off if he purchases 11 rather

than 10 units, since the additional unit costs him P

dollars. He will keep revising his purchase plans

upward until he reaches the point where the marginal

utility of the item falls to P dollars. In sum, the

consumer’s self-interest will lead him (without

conscious calculation) to purchase an amount such that

the marginal utility is as close as possible to market

price. So long as the consumer selects a bundle of

purchases that gives him the most benefit (pleasure,

utility) for his money, he must end up with quantities

such that the marginal utility of each commodity in the

bundle is approximately equal to its price.

It now becomes easy to explain the paradox underlying

the relationship between the prices of jade and bread.

Because a piece of fine jade is scarce, its marginal

utility is high, and consumers are willing to pay

comparatively high prices for it. The explanation is

perfectly consistent with a utility analysis of demand,

so long as one relates price to the marginal utility of

the item rather than to its total utility. A family’s

bread may be very valuable to it, but, if it has

enough, the marginal utility of the bread will be

small, and this will be reflected in its low price.

The relationship between price and marginal utility is

[Image] important not because it explains issues like the

Figure 1: jade-bread paradox but because it enables one to

Relationship analyze the relationship between prices and quantities

between marginal demanded. It also, as a practical matter, permits one

utility and to judge how well any portion of the price mechanism is

quantity (see working as a device to secure the efficient

text). satisfaction of the wants of the public, within the

limits set by available resources. The conclusion that

at any price the consumer will purchase the quantity at

which marginal utility is equal to price makes it

possible to draw a demand curve showing–to a

reasonable degree of approximation–how the amount

demanded will vary with price.

FIGURES ARE NOT REPRODUCED HERE!

A curve based on the

previous example of bread consumption is given in

Figure 1. This shows that if the family gets 10 slices

per day the marginal utility of bread will be nine

cents (point A). One may reverse the question and ask

how much the family would purchase at any particular

price, say three cents. The graph indicates that at

this price the quantity would be 30 slices, because

only at that quantity is marginal utility equal to the

three-cent price (point B). Thus the curve in Figure 1,

to a reasonable degree of approximation, may be able to

do double duty: it may serve as a marginal-utility

curve relating marginal utility to quantity and, at the

same time, as a demand curve relating quantity demanded

to price.

To cite this page:

“Economic Theory: Utility and value: THEORIES OF

UTILITY: Marginal utility.” Britannica Online.

<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/4.html&gt;

[Accessed 27 February 1998].

Consumers’ surplus.

 

Figure 1: Relationship between marginal utility and quantity (see text).
FIGURES ARE NOT REPRODUCED HERE!

Figure 1 leads to an important conclusion about the consumer’s gains from his purchases. The diagram shows that the difference between 10 and 11 slices of bread is worth nine cents to the consumer (marginal utility = nine cents). Similarly, a 12th slice of bread is worth eight cents (see the shaded bars). Thus, the two slices of bread together are worth 17 cents, the area of the two rectangles together. Suppose the price of bread is actually three cents, and the consumer, therefore, purchases 30 slices per day. The total value of his purchases to him is the sum of the areas of all such rectangles for each of the 30 slices; i.e., it is (approximately) equal to all of the area under the demand curve; that is, the area defined by the points 0CBE. The amount the consumer pays, however, is less than this area. His total expenditure is given by the area of rectangle 0CBD–90 cents. The difference between these two areas, the quasi-triangular area DBE, represents how much more the consumer would be willing to spend on the bread over and above the 90 cents he actually pays for it, if he were forced to do so. It represents the absolute maximum that could be extracted from the consumer for the bread by an unscrupulous merchant who had cornered the market. Since, normally, the consumer only pays quantity 0CBD, the area DBE is a net gain derived by the consumer from the transaction. It is called consumers’ surplus. Virtually every purchase yields such a surplus to the buyer.

  The concept of consumers’ surplus is important for public policy, because it offers at least a crude measure of the public benefits of various types of economic activity. In deciding whether a government agency should build a dam, for example, one may estimate the consumers’ surplus from the electricity the dam would generate and seek to compare it with the surplus that could be yielded by alternative uses of the resources needed to construct and operate the dam.
 
   
  To cite this page:
“Economic Theory: Utility and value: THEORIES OF UTILITY: Consumers’ surplus.”
Britannica Online.
<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/5.html>
[Accessed 27 February 1998].

Utility measurement and ordinal utility.

  FIGURES ARE NOT REPRODUCED HERE!

As originally conceived, utility was taken to be a subjective measure of strength of feeling. An item that might be described as worth “40 utils” was to be interpreted to yield “twice as much pleasure” as one valued at 20 utils. It was not long before the usefulness of this concept was questioned. It was criticized for its subjectivity and the difficulty (if not impossibility) of quantifying it. An alternative line of analysis developed that was able to accomplish most of the same purposes but without as many assumptions. First introduced by the economists F.Y. Edgeworth in England (1881) and Vilfredo Pareto in Italy (1896-97), it was brought to fruition by Eugen Slutsky in Russia (1915) and J.R. Hicks and R.D.G. Allen in Great Britain (1934). The idea was that to analyze consumer choice between, say, two bundles of commodities, A and B, given their costs, one need know only that one is preferred to another. This may at first seem a trivial observation, but it is not as simple as it sounds.

 

Figure 2: Commodities X and Y (see text).
In the following discussion, it is assumed for simplicity that there are only two commodities in the world. Figure 2 is a graph in which the axes measure the quantities of two commodities, X and Y. Thus, point A represents a bundle composed of seven units of commodity X and five units of commodity Y. The assumption is made that the consumer prefers to own more of either or both commodities. That means he must prefer bundle C to bundle A, because C lies directly to the right of A and hence contains more of X and no less of Y. Similarly, B must be preferred to A. But one cannot say, in general, whether A is preferred to D or vice versa, since one offers more of X and the other more of Y.
 

Figure 3: Indifference curves (see text).
The consumer may in fact not care whether he receives A or D–that is, he may be indifferent (see Figure 3). Assuming that there is some continuity in his preferences, there will be a locus connecting A and D, any point on which (E or A or D) represents bundles of commodities of equal interest to this consumer. This locus (I-I’ in Figure 3) is called an indifference curve. It represents the consumer’s subjective trade off between the two commodities–how much more of one he will have to get to make up for the loss of a given amount of another. That is, one may treat the choice between bundle D and bundle E as involving the comparison of the gain of quantity FD of X with the loss of FE of Y. If the consumer is indifferent between D and E, the gain and loss just offset one another; hence, they indicate the proportion in which he is willing to exchange the two commodities. In mathematical terms, FE divided by FD represents the average slope of the indifference curve over arc ED; it is called the marginal rate of substitution between X and Y.
   
Figure 3 also contains other indifference curves, some representing combinations preferred to A (curves lying above and to the right of A) and some representing combinations to which A is preferred. These are like contour lines on a map, each such line being a locus of combinations that the consumer considers equally desirable. Conceptually, through every point in the diagram there is an indifference curve. Figure 3, with its family of indifference curves, is called an indifference map. This map obviously does no more than rank the available possibilities; it indicates whether one point is preferred to another but not by how much it is preferred.
  It is easy to show that at any point such as E the slope of the indifference curve, roughly FE divided by ED, equals the ratio of the marginal utility of X to the marginal utility of Y for the corresponding quantities. For in moving from E to D the consumer gives up FE of Y, a loss valued, by definition, at approximately FE multiplied by the marginal utility of Y, and he gains FD of X, a gain worth FD multiplied by the marginal utility of X. Relative marginal utilities can be measured in this way because their ratio does not measure subjective quantities–rather, it represents a rate of exchange of two commodities. The marginal utility of X measured in money terms tells one how much of the commodity used as money the consumer is willing to give for more of the commodity X but not what psychic pleasure the consumer gains.
 
   
  To cite this page:
“Economic Theory: Utility and value: THEORIES OF UTILITY: Utility measurement and ordinal utility.”
Britannica Online.
<http://www.eb.com:180/cgi-bin/g?DocF=macro/5001/98/6.html>
[Accessed 27 February 1998].
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