Karl Heinrich Rau
Rau’s textbook was not only a paragon for other works, it also contained a number of ideas and concepts, often wrongly attributed to other authors, which foreshadowed and even anticipated in full later developments.
In the second edition of volume I Rau put forward a distinction that paralleled Soden’s: while “species value” (Gattungswerth) refers to a class or type of commodities and is not related to the quantity consumed, “concrete (use) value” (konkreter Wert) of a unit of the commodity, alternatively also called “quantitative value,” is seen to depend on the quantity consumed of it and thus points in the direction of marginal utility. A first clear formulation of the principle of diminishing marginal utility is to be found in the third edition of volume I. The concept of concrete value established for the first time the idea of use value depending on quantity. By means of his two concepts of value Rau sought to solve the “paradox of value”: while Smith’s value in use corresponds to Rau’s “species value”, Smith’s value in exchange corresponds to Rau’s concrete value. Comparing water and diamond involves, on the one hand, comparing two incommensurables - two species values - but, on the other, it involves comparing two commensurables - two concrete values - in terms of the fact that their consumption or use generates utility for the consumer, the magnitude of which is taken to depend on the quantity consumed of each of the two goods.In his reflections, Rau started from separable utilities derived from the consumption of different goods. He originally retained the assumption of satiability with regard to each need and want. Later he weakened this assumption, at first explicitly with regard to luxury goods “for which no limit of requirement can be specified”, then also implicitly with regard to all goods, provided we are willing to follow Chipman’s translation of what Rau stated into “a total utility function... which is strictly increasing, concave, continuous, and once-differentiable; thus satiable preferences have become insatiable.” (Chipman 2013: 15) Interestingly, Rau also pointed out that commodities are typically possessed of different characteristics, or of the same characteristics in different proportions, thus foreshadowing Kevin Lancaster’s (1971) view that what consumers seek to acquire are not commodities themselves, but the characteristics they contain.
To the extent to which commodities have some characteristics in common (for example, caloric content in the case of food) they are substitutes and belong to the same species. While Rau does not use the term, it is clear that he has this concept in mind.While on the one hand Rau was keen to solve the “paradox of value”, he was also concerned with another Smithian problem: the estimation of the size of the wealth of a nation. He rejected Jean-Baptiste Say’s proposal to measure utility by value, and he was also critical of the idea to measure it in terms of the sum total of quantities multiplied by current prices. He was on the lookout for some invariant measure of value, a search that had plagued Ricardo until the end of his life, and after some deliberation opted for using an average of prices over a period of time. Interestingly, he also advocated the idea of a diminishing marginal utility of income, which hints, of course, in the direction of finite satiation levels of goods.
In an appendix to the fourth edition of his Lehrbuch, published in 1841, Rau introduced intersecting demand and supply curves - only three years after and independently of the first use of demand curves in Cournot (1838). Rau’s analysis was the starting point of Mangoldt’s investigation (1863).