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Austrian and Neoclassical Concepts of Marginal Ulitity

September 28, 2012
A recent comment by Bryan Caplan provides a good opportunity to discuss differences between Austrian and neoclassical concepts of marginal utility. In response to Steve Horwitz, who claimed that the law of diminishing marginal utility and the downward-sloping demand curve can be known a prior, Bryan asks:
Mainstream micro textbooks often have counterintuitive examples with increasing marginal utility. Are you really saying that the premise of these problems is somehow logically impossible? Or are you using a heterodox conception of marginal utility?
As Chesterton said, heterodoxy is your doxy and orthodoxy is my doxy, but I think I know what he means. Indeed, the modern, neoclassical concept of marginal utility is quite different from the causal-realist version offered by Menger and developed by Menger, Böhm-Bawerk, Fetter, Rothbard, and others. Both the Austrian and neoclassical approaches to demand begin with an ordinal preference ranking. But the understandings of marginal and total utility are completely different. For Menger, marginal utility applies only to discrete units of a homogenous stock of a good. The fourth apple is allocated to a lower-valued use than the third apple, and so on. The law of demand follows from the fact that additional units of a homogenous good are used to satisfy lower-ranked ends.Note that for the Austrians, the term “marginal” applies to the units, not the utilities. “Marginal utility” is the total utility of the marginal unit, not the marginal utility of a unit. There is no larger concept of “total utility,” of which marginal utility is a little slice. Note also that if an agent possesses a set of unique goods—one apple, a piece of candy, a dollar bill, an iPod, etc.—he can rank them ordinally, but cannot assign marginal utilities to specific goods, since there are no “supplies”—multiple, homogeneous units—of apples, candy, money, and iPods. The neoclassical approach begins with consumers who rank not discrete units of goods, but n-tuples or “bundles” of all goods in existence. Bundle A represents one apple, one piece of candy, and one iPod. Bundle B represents two apples, one piece of candy, and one iPod. Bundle C includes one apple, two pieces of candy, and one iPod, and so on. For all possible bundles i and j (and the set of feasible bundles depends on assumptions about divisibility) the consumer is assumed to prefer i to j, to prefer j to i, or to prefer neither i nor j. Hence the concept of indifference: if Bundle D is neither preferred nor dis-preferred to Bundle E, then the consumer is indifferent between D and E (and, if we assume a continuous space of bundles, they lie on the same indifference curve). In this model, prices are expressed as exchange ratios between elements of the bundles. Given an amount of “income,” which when combined with a given ratio of relative prices gives a set of bundles that the consumer can afford, we can identify which bundle or bundles yield the greatest benefit (i.e., no other bundle is both affordable and preferred to the optimal bundle). This notion of ranking bundles is necessary to decompose the effects of relative-price changes into the familiar substitution and income effects. The notion of a substitution effect assumes that relative-prices changes combined with Hicksian income transfers can be represented by a movement along an indifference curve. Note that if the consumer is ranking bundles, not individual units of goods, and the bundles are heterogeneous, then Menger’s concept of marginal utility does not apply. The consumer attaches a total utility to each ranked good— i.e., to each bundle—but there are no marginal utilities of individual units of goods, because we have no ordinal rankings of individual goods, only bundles. Hicks of course abandoned the concept of marginal utility altogether in favor of the marginal rate of substitution (the rate at which the consumer would substitute i for good j or the slope of the indifference curve). But Mengerian analysis concerns preferences that can be demonstrated in action. Because indifference among ranked goods (bundles) cannot be demonstrated in action, there is no place for a marginal rate of substitution, and no such thing as a substitution effect that can be analyzed independently of an income effect. In short, in causal-realist analysis we go from an ordinal preference ranking among homogenous goods (gallons of water, bushels of wheat, whatever) to the law of diminishing marginal utility to the individual’s downward-sloping demand curve to the downward-sloping market demand curve to the conclusion that an increase in the supply of a good on the market leads to a reduction in price and an increase in quantity demanded. The neoclassical approach starts with rankings of heterogeneous bundles of goods, leading to an indifference map in which marginal rates of substitution could be increasing, decreasing, constant, or undefined (as with L-shaped indifference curves) and a conditional law of demand in which a decrease in price may or may not lead to an increase in the quantity demanded, depending on the sign of the income effect and the relative magnitudes of the income and substitution effect. For Mises, the law of diminishing marginal utility is not only knowable a priori but "apodictically certain," not conjectural, historically contingent, or subject to validation in a clever (freaky?) laboratory experiment.

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