The relationship between price and marginal utility is important not because it explains issues like the jade–bread 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 the price mechanism is working as a device to secure the efficient 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. 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.

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 (consumer surplus). Virtually every purchase yields such a surplus to the buyer.

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.

The consumer may in fact not care whether he receives A or D—that is, he may be indifferent (indifference) (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.

and with y-intercept

.

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 to purchase; 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 highest indifference 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 problem—it explains, in principle, the consumer's 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 the slope 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 spent on X or on Y. If this is not so—as at point R in Figure 4-->, where the consumer gets more for his money by spending a dollar on Y rather than on X—it will pay him to reallocate his expenditures between the two commodities accordingly, moving toward S from R.

The diagram becomes more illuminating when one investigates how the consumer's decision is affected by a change in his income or in the price of a commodity. Equation (2) indicates that a change in income, M, does not affect the slope of the price line, only its intercept. Thus, as the person's income increases, the price line undergoes a sequence of parallel shifts (Figure 5-->). For each such line there will be a point of tangency, T, with an indifference curve, showing the consumer's optimal bundle of purchases with the corresponding income. The locus of these points (T₁, T₂, T₃ . . .) may be called the income–consumption curve; it shows how the consumer's 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 P_X rises, the price line shifts from PP′ to PR′ in Figure 6-->. This means that, as P_X 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 P_X, one contains a locus UU′, τηε price–consumption curve, showing how the consumer's purchases vary with P_X.

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 consumer's overall purchasing power. The effect on purchases of this reduction of purchasing power is called the income effect of the price change. Its effect via the relative price change is called the substitution effect. The division can be carried out graphically as follows: let the price of X increase so that the price line in 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 income effect, 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.

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 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. Hüsler and R.-D. Reiss (eds.), Extreme Value Theory (1989), containing conference proceedings. 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 d'économie politique, 2 vol. (1896–97); J.R. Hicks and R.D.G. Allen, “A Reconsideration of the Theory of Value,” Economica, New Series, 2 parts, 1:52–76,196–219 (1934); R.G.D. Allen, “Professor Slutsky's Theory of Consumers' Choice,” The Review of Economic Studies, 3:120–129 (1936); Carl Menger, Principles of Economics (1950, reissued 1981; originally published in German, 1871); Léon Walras, Elements of Pure Economics; or, The Theory of Social Wealth (1954, reprinted 1984; originally published in French, 1874); W. Stanley Jevons, The Theory of Political Economy, 5th ed. (1957); Alfred Marshall, Principles of Economics, 9th ed., 2 vol. (1961), also discussing price; John Weeks, Capital and Exploitation (1981), a study of Marx's labour theory of value; Hermann Heinrich Gossen, The Laws of Human Relations and the Rules of Human Action Derived Therefrom (1983; originally published in German, 1854); and K.K. Valtukh, Marx's 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 advanced readership; and Hal R. Varian, Microeconomic Analysis, 3rd ed. (1992), and Intermediate Microeconomics, 3rd ed. (1993), both at an advanced level.William J. Baumol Ed.