utility and value

8/4/2019 Utility and Value

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utility and valuePrimary Contributor:William J. Baumol

utility andvalue, ineconomics, the determination of the prices of goods and services.

The modern industrial economy is characterized by a high degree of interdependence of its parts.

The supplier of components orraw 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 throughtheprice 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 examinesthe efficiency of the resultingallocation of resources. Value theory is also applied by business

firms and government agencies in their decisions that relate to pricing and the allocation ofresources.

Theories of value

Cost-of-production analysis

Modern value theory began withAdam Smith(1776),David Ricardo(1817), and a number of

other writers, who are generally lumped together as the classical school. These writers sought toexplain pricing primarily on the basis ofcostofproduction. That is, if commodity A costs twice

as much to produce as commodity B, the price of A will be pushed toward a level twice as high

as that of B. If this were not the caseif, for example, A sold for three times the price of B

then the greater profitability of investment in A would cause its production to increase and drivedown its price, while the production of B would decline, thus raising its price. Prices would

finally be driven to the 2:1 ratio of the costs of production.

The classical economists were well aware of the oversimplification in this explanation, but, as

with most theoretical analysis, its strength lay in the amount it was able to explain with a verysimple model. (It is highly misleading to interpret theclassical analysisliterally, as a picture of

its authors views of the complex world of reality.) It was soon recognized, however, that the

cost-of-production analysis considered only part of the relevant problem. Since cost depends on

the quantity produced (e.g., costs per unit may decline as production of an item increases), the

analysis must take into account the demand for the product. The analysis of demand was madepossible by the theory of utility, developed by H.H. Gossen in Germany (1854),Karl Mengerin

Austria (1871),Lon Walrasin France (187477), andW.S. Jevonsin England (1871).

The role of utility analysis in value theory will be discussed later. It need only be added at this

point that modern value theory, following the lead of the English economist Alfred Marshall

(Principles of Economics, 8th ed., 1920), considers prices to be determined simultaneously by
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cost and demand considerations. The analysis also recognizes the complex interdependencies in

the system, withdemands and suppliesof various commodities affecting one another.

Resource limitations and allocation

The fact that goods have value can be ascribed ultimately to the limitations in the worldsmaterial 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 inunlimited supply they would be free. Price usually serves as therationingdevice whereby their

use is kept down to the available supply.

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 ofresourcesin 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 inone manufacturing process must cause it to become scarcer in other uses.

The cost of a product in terms of money may not measure its true cost to society. The true costof, 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 societys available resources;

it means the foregoing of an opportunity to produce something else. In deciding how to useresources most effectively to satisfy the wants of the community, thisopportunity costmust

ultimately be taken into account.

In amarket economythe 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 ofnotmaking 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 producingthem. But the price of these inputs, in turn, depends on what they can produce elsewhereif the

handbags that can be produced with the leather are valued very highly by consumers, the price of

leather will be bid up correspondingly.

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 reflectconsumertastes andpreferences. 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 senseon its utility to purchasers as it affects their bids.

Marginal utility
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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 consumersessential 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 todays analysis of

demand. Marginal utility was defined as the value to the consumer of an additional unit of somecommodity. 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 ofthe 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 foreveryone to fill his stomach, a 32nd slice may be worth very little. Moreover, the difference in

value between 122 and 123 slices may be negativea 123rd slice may just add to the familysdisposal 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 32slices 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 anincrement 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 goodwill 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 additionalunit costshim 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

consumers self-interest will lead him (without conscious calculation) to purchase an amountsuch 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 isapproximately equal to its price.

It now becomes easy to explain the paradox underlying the relationship between the prices ofjade 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 familys bread may be very valuable to it, but, if it has enough, themarginal utility of the bread will besmall, and this will be reflected in its low price.

The relationship between price and marginal utility is important not because it explains issueslike the jadebread paradox but because it enables one to analyze the relationship between prices

and quantities demanded. It also, as a practical matter, permits one to judge how well any portion

of theprice mechanismis working as a device to secure the efficient satisfaction of the wants ofthe public, within the limits set by available resources. The conclusion that at any price the
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consumer will purchase the quantity at which marginal utility is equal to price makes it possible

to draw ademand curveshowingto a reasonable degree of

approximationhow the amount demanded will vary with price. A curve based on the previousexample 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 questionand ask how much the family would purchase at any particular price, say three cents. The graphindicates 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.

Consumers surplus

Figure 1 leads to an important conclusion about the consumers gains from his purchases. The

diagram shows that the difference between 10 and 11 slices of bread is worth nine cents to theconsumer (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 theareas 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
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rectangle 0CBD90 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 andabove 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 calledconsumers surplus.Virtually every purchase yields such a surplus to the buyer.

The concept of consumers surplus is important forpublicpolicy, because it offers at least a

crude measure of the public benefits of various types of economic activity. In deciding whether a

governmentagency should build a dam, for example, one may estimate the consumers surplusfrom 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.

Utility measurement and ordinal utility

As originally conceived, utility was taken to be a subjective measure of strength of feeling. Anitem 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 wasquestioned. 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) andVilfredo Paretoin Italy (189697), 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 atrivial observation, but it is not as simple as it sounds.
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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, Xand 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 toA. 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.


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The consumer may in fact not care whether he receives A or Dthat is, he may beindifferent

(see Figure 3). Assuming that there is some continuity in his preferences, there will be a locusconnecting A and D, any point on which (E or A or D) represents bundles of commodities of

equal interest to this consumer. This locus (II in Figure 3) is called anindifference curve. It

represents the consumers subjective trade off between the two commoditieshow much more

of one he will have to get to make up for the loss of a given amount of another. That is, one maytreat 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 toexchange the two commodities. In mathematical terms, FE divided by FD represents the average

slope of the indifference curve over arc ED; it is called themarginal rateof 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 ispreferred. 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 diagramthere is an indifference curve. Figure 3, with its family of indifference curves, is called anindifference map. This map obviously does no more than rank the available possibilities; itindicates 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 gainsFD of X, a gain worth FD multiplied by the marginal utility of X. Relative marginal utilitiescan

be measured in this way because their ratio does not measure subjective quantitiesrather, it

represents a rate of exchange of two commodities. The marginal utility of X measured in moneyterms 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.

Prices and incomes

One other type of information is needed to complete the analysis of consumer choice: the prices

of X and Y and the amount the consumer has available to spend. In what follows, it will beassumed that the consumer spends all his money on the available commodities (savings bonds

being among the commodities). If PX and PY are the prices of commodities X and Y,

respectively, and M represents the amount of money available for spending, the condition that all

of the money is spent yields the equation

or, solving for Y in terms of X,
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(2)This is obviously the equation of a straight line with slope and with y-intercept .

The line, called the budget line, or price line, represents all the combinations of X and Y that the

consumer can afford to buy with income M at the given prices.

Equilibrium of the consumer

Figure 4 combines this price line and the indifference curves, permitting direct analysis of the

consumer purchase decision. Line PP is the price line corresponding to equation (2) above. Any

point R on that line represents a combination of X and Y that a given consumer can afford topurchase; however, R is not an optimal choice. This can be seen by comparing R with S on the

same price line. Since S lies on a higher indifference curve than R, the former is the preferred

position, and, since S costs no more than R (they are on the same price line, so each costs M

dollars), S gives the consumer more for his money. It is at T, however, the point of tangency

between the price line and an indifference curve, that the consumer reaches his highestindifference curve; this is, therefore, the optimal point for him, given his pattern of tastes as

shown by the shapes of his indifference curves. This is the solution of the choice problemit

explains, in principle, the consumers purchase decision on the basis of his given preferences,with no assumptions as to degrees of measurable utility.

The tangency at the solution point has a significant interpretation. It was noted above that theslope of the indifference curve is the ratio of the marginal utilities of the two commodities. It

follows that, at the optimal point T, a dollar of expenditure must offer the same utility whether


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spent on X or on Y. If this is not soas at point R in Figure 4, where the consumer gets more for

his money by spending a dollar on Y rather than on Xit will pay him to reallocate hisexpenditures between the two commodities accordingly, moving toward S from R.

Changes in prices and incomes

The diagram becomes more illuminating when one investigates how the consumers decision is

affected by a change in his income or in the price of a commodity. Equation (2) indicates that achange in income, M, does

not affect the slope of the price line, only its intercept. Thus, as the persons income increases,

the price line undergoes a sequence of parallel shifts (Figure 5). For each such line there will be apoint of tangency, T, with an indifference curve, showing the consumers optimal bundle ofpurchases with the corresponding income. The locus of these points (T1, T2, T3 . . .) may be

called the incomeconsumption curve; it shows how the consumers purchases vary with his

income. Normally the curve will have a positive slope, as EE does in Figure 5A, meaning that as

a person grows wealthier he will buy more of each commodity. But the slope can be negative for

some stretches (GG in Figure 5B). In that case, X is said to be an inferior good of which the

consumer buys less as his income rises.

The diagram can also be used to show what happens as the price of X varies. From equation (2)

it can be seen that the Y-intercept is not affected by an increase in the price of X but that the

slope of the price line grows. Thus, as PX rises, the price line shifts from PP to PR in


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Figure 6. This means that, as PX rises, M dollars will buy as much of good Y as before (the

position of point P at which all M dollars are spent on commodity Y does not change), but that M

dollars will now buy less of good X, so that the position of point P must move toward the left.Once again, by following the points of tangency between indifference curves and the price lines

for various values of PX, one contains a locus UU, priceconsumption curve, showing how

the consumers purchases vary with PX.

Income and substitution effects

It is useful to divide the effects of the price change conceptually into two parts. An increase in

the price of X obviously affects the relative cost of X and Y. But it also decreases the consumersoverallpurchasing power. The effect on purchases of this reduction of purchasing power is

called theincome effectof the price change. Its effect via the relative price change is called thesubstitution effect. The division can be carried out graphically as follows: let the price of X

increase so that the price line in
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Figure 7 moves from PP to PR, and assume an imaginary intermediate price line,LL, with the

slope of PR but tangent to the indifference curve that was attained with the old price line PP.

The imaginary price line has the following properties: (1) it involves the same real income as PP(tangency points T and S are the same indifference curve), and (2) it involves the same relative

prices as the new price line since their slopes are the same. The rise in price has, in the figure,

caused the demand for X to fall from C to A (the quantities of X corresponding to tangency

points T and U). It has been possible to divide the total effect, CA, into two parts, the incomeeffect, BA, and the substitution effect, CB. This breakdown is important, because a number of

interesting and important theorems can be proved about the substitution effect. Two of these

theorems will illustrate the point.

Under the normal assumptions of demand theory it can be proved that a rise in the price of Xmust, via the substitution effect, work to reduce the demand for X; the second theorem states the

surprising result that, considering onlysubstitution effects, a dollar rise in the price of X must

change the demand for Y by precisely the same amount as a dollar rise in the price of Y changes

the demand for X. Similar relationships have been shown to hold when there are more than twocommodities involved.

William J. BaumolARTICLE

Additional Reading

Two good introductory discussions of the nature of value theory and its application to the

economy as a whole are Robert Dorfman, The Price System (1964), and Prices and Markets, 3rd

ed. (1978). The classic work on the history of economic theory, particularly of value theory, is
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Joseph Schumpeter,History of Economic Analysis, ed. by Elizabeth Boody Schumpeter (1954,

reissued 1986). An excellent brief discussion can be found in George J. Stigler,Essays in the

History of Economics (1965, reprinted 1987), especially essays 5, 6, and 12. Three rather

advanced works on modern value theory are J.R. Hicks, Value and Capital, 2nd ed. (1950,

reissued 1974); Paul A. Samuelson, Foundations of Economic Analysis, enlarged ed. (1983); and

J. Hsler and R.-D. Reiss (eds.),Extreme Value Theory (1989), containing conferenceproceedings. Marc R. Tool,Essays in Social Value Theory: A Neo-Institutionalist Contribution

(1986), provides very insightful views.

Seminal works in the history of value theory include David Ricardo, On the Principles of

Political Economy and Taxation (1817, reissued 1981); F.Y. Edgeworth,Mathematical Psychics(1881, reprinted 1967); Vilfredo Pareto, Cours dconomie politique, 2 vol. (189697); J.R.

Hicks and R.D.G. Allen, A Reconsideration of the Theory of Value,Economica, New Series, 2

parts, 1:5276,196219 (1934); R.G.D. Allen, Professor Slutskys Theory of Consumers

Choice, The Review of Economic Studies, 3:120129 (1936); Carl Menger, Principles of

Economics (1950, reissued 1981; originally published in German, 1871); Lon Walras,Elements

of Pure Economics; or, The Theory of Social Wealth (1954, reprinted 1984; originally publishedin French, 1874); W. Stanley Jevons, The Theory of Political Economy, 5th ed. (1957); AlfredMarshall, Principles of Economics, 9th ed., 2 vol. (1961), also discussing price; John Weeks,Capital and Exploitation(1981), a study of Marxs labour theory of value; Hermann HeinrichGossen, The Laws of Human Relations and the Rules of Human Action Derived Therefrom

(1983; originally published in German, 1854); and K.K. Valtukh, Marxs Theory of Commodity

and Surplus-Value: Formalised Exposition, trans. from Russian (1987). Two good discussions of

the more recently popular theories of utility are David M. Kreps,Notes on the Theory of Choice

(1988); and Bill Gerrard (ed.), The Economics of

Rationality (1993).

Among the best modern textbooks in microeconomics are David D. Friedman, Price Theory, 2nd

ed. (1990), an introductory text which includes nonconventional applications of price theory;

David M. Kreps,A Course in Microeconomic Theory (1990), for intermediate and advancedreadership; and Hal R. Varian,Microeconomic Analysis, 3rd ed. (1992), andIntermediate

Microeconomics, 3rd ed. (1993), both at an advanced level.

William J. BaumolEd.

utility and value

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