Hermann Gossen
Anticipates the ideas of Jevons, Menger and Walras. Entwicklung der Gesetze des menschlichen Verkehrs ..., 1854, sells few copies but is rediscovered by Walras and Jevons and re-issued in 1889. Gossen has since been acknowledged as pioneer of marginal utility. He says that the mathematical method is vital otherwise economic process cannot be analysed. Gossen uses a consumption approach, postulating that the aim of human conduct is to maximise enjoyment. He thus develops Gossen's First and Second Law. The first law states the principle of diminishing utility and is illustrated with the example of declining enjoyment of successive bites of food. The second law states that the maximum pleasure arises from a uniform level of want-satisfaction, in other words that enjoyment from the last item of each different good consumed by a consumer is equal. Value depends on the amount of enjoyment a good procures and value can only be conceived of in relative terms between object and consumer. Goods that have value are either those of the first class (capable of supplying immediate enjoyment), those of the second class (those requiring joint use with other goods, i.e.. complimentary goods) and those of the third class (those used in the production of other goods). Labour, which creates the means of enjoyment, is also accompanied by pain (disutility). Here are the main elements of Jevons and the Austrian school.

William Jevons
1835 - 1882. Statistician. The State in Relation to Labour 1882 is his main theoretical statement. Jevons was a free-trader but apart from this one laissez-faire principle he judged each economic question individually on its merits. For example, intervention should be allowed in home policy (thus Jevons furthers Mill's breach with classical ideas). His contribution to pure theory is most important. Theory of Political Economy, 1871, vindicates the mathematical method to define economic relationships. Ultimate laws of economics can rightly be compared with those of the physical sciences and 'have their basis more or less obviously in the general principles of mechanics'. Hence economic laws can be cast in mathematical form. Economics 'must be mathematical simply because it deals with quantities'. Where things are capable of being more or less, the laws or relations must be mathematical in nature. Jevons thus aims at full mathematical exposition of the laws of the market. A central principle is that value depends entirely upon utility (the Labour theory of value was abandoned completely by Jevons). Individuals allot incomes such that the marginal utility of each product consumed is equal. Exchange between two individuals of two commodities continues until the marginal utility per unit price, for each commodity, is equal. He says this theory of isolated exchange (exchange between two individuals) applies to competitive exchange (exchange between a multitude of buyers and sellers), but this approach is unacceptable as an explanation of the price at equilibrium in the market because isolated exchange ignores the impact of competition in determining price (in the absence of competition, a number of different prices can result at equilibrium). Later economists would improve upon Jevon's ideas here.

Carl Menger
1840 - 1921. Founder of the Austrian school. Menger attacks the Historical school in Untersuchungen uber die Methode der Socialwissenschaften und Politischen Oekonomie insbesondere, 1883. He discusses the method of the social sciences in general and adopts a positive approach to economics. He points out the difference between social sciences and physical sciences and says that the conditions required for economic laws to operate are rarely in place in total, and that such conditions are almost impossible to measure anyway. But his point is that the Historical school totally disregarded the method of deduction and logical assumption in favour of pure induction, and that the Classical school was aware that self-interest was not the only form of human motivation. The Classical theorists had simply taken the most powerful motivation, or perhaps the most easily observable motivation, and analysed it. Grundsatze der Volkswirtschaftlehre, 1871, identified two poles of economic activity as being human wants and the means of satisfying them. Goods are ordered according to their ability to satisfy wants. First order goods satisfy want directly (e.g. bread), second order goods satisfy wants indirectly (e.g. flour), and third and subsequent order goods also exist in similar fashion. The value of higher order goods, including factors of production, is determined by the anticipated value of those goods which they serve to produce. Goods can be economic goods, where available supply is less than that required to meet wants (thus defines where scarcity exists), or non-economic goods where supply exceeds quantity required to satisfy want. Goods can move between these two categories. Value is the judgement an individual makes about a good when he realises it is an economic good. Free goods cannot therefore possess value. Menger restates Gossen's first law. He states that the value of a good depends on the intensity of the want satisfied by the last portion of that good. Thus he restates Jevon's final degree of utility and anticipates marginal utility as defined by Marshall and Wieser. The value thus defined subjectively now determines price. Exchange is merely the mechanism whereby individuals supply themselves with the maximum satisfaction with their available means. Exchange arises where two individuals have differing subjective values of the two different goods they hold. At equilibrium the ratio of the marginal utilities of the two goods will be the same for each individual. Subjective values thus determines the ratio in which consumers exchange one good for another, thus determining price. Such a price lies within a range determined by the buyer and seller's maximum and minimum exchange ratios, though price itself is indeterminate as it depends upon the relative bargaining power of each counterparty. Menger analysed supply and demand in relation to subjective values for situations ranging from isolated exchange to perfect competition, and this remains a largely accepted analysis. He wrote articles in connection with the Austrian currency reform (one such article is Geld, 1892). Menger applied his subjective theory of value to the field of money, and provided an explanation of the role of money in exchange and setting of prices (he deals with this subject further in Grundsatze). He states that money fulfills the function of a universal medium of exchange that measures subjective values.

Leon Walras
1834 - 1910. Like the other marginal utility theorists, Walras based himself on hedonism as the motivating force behind human economic activity, and used the mathematical approach most thoroughly of all. He avoided Jevon's errors in the translation of subjective values into prices under competitive marketplace assumptions. Instead, he abandons the search for the origin of value in favour of building a formal model of the functional interdependence of supply, demand and price. Influenced by Cournot, Walras combined the utility theory of value into a mathematically precise theory of market equilibrium. Elements d'Economie Politique Pure, 1874. Two part work, theory of exchange 1874 and theory of production 1877. Exchange value is based on utility and scarcity, and the desire to equalise marginal utilities leads to exchange. This desire together with stocks held by each individual, determines demand and supply and the situation can be represented by functional equations or graphically. Equilibrium is established where the price is such that demand and supply are equal. Walras invented a device called the 'prix crie' (the auctioneer's price) that is called out. If demand and supply are not equal at this price, the auctioneer calls out another price until demand and supply are equal. Walras did not make clear whether deals are done at each successive prix crie. If deals aren't done, then Walras's equilibrium price will result. If deals are done, then marginal utilities will change and the equilibrium price established will be different to the Walrasian equilibrium price. Walras's equilibrium can be assumed to arise where there is recontracting (due to Edgeworth) if the prix crie changes.

Walras also invents the 'numeraire', the one good used as a standard of reckoning (not money in the ordinary sense because Walras assumes it is only a unit of account), in order to show how a general exchange equilibrium will arise between n goods. There will be n - 1 equations of supply and demand, and n - 1 prices to determine, thus a determinate solution for general equilibrium prices is available. But Walras achieves this determinate solution, where others have only identified an indeterminate solution, by ignoring how price arises from subjective value and making price the independent variable in his general equilibrium (independent since it is an auctioneer who calls out the prix crie). Given this series of prices, he then builds up the picture of how individuals will exchange to the point at which the ratio of marginal utilities equals the ratio of the quantities exchanged. No longer are quantities exchanged the independent variable in this system.

(In the 1950's, Kenneth Arrow and Gerard Debreu won the Nobel Prize by showing that there will always be a set of prices at which supply and demand in all markets clears. Their theorem required complete flexibility of wages and prices, no uncertainties which cannot be insured against, no externalities or increasing returns, no monopolies or oligopolies. For practical purposes their theory is of course most unrealistic.)

Further criticism was directed at Walras' conclusion that competition will result in maximisation of utility. Trades (and decisions not to trade) at prices other than the one set by competition cannot be proved to result in less satisfaction than that arising at the competitive price. And if changes in the distribution of property are of benefit to a majority of individuals, then why not allow interference in the competitive market in order to bring about a price at which such changes in ownership will proceed and thus benefit the majority?

Alfred Marshall
1842 -1924. Second generation marginal utility theorist according to some, first generation according to others, neo-classical economist according to some, classical according to others. Mathematician, believes in appliance of mathematical techniques to economic analysis but that such an analysis cannot be a comprehensive one due to difficulty of describing reality with sets of formulae. Marshall attempted to preserve the link between theory and policy, accepting marginal utility theories and developing them. Principles of Economics, 1890, was his standard work.

According to Marshall, demand is determined by marginal utility and is reflected in the prices at which given quantities of a good will be demanded. Supply is determined by the marginal disutility reflected in the prices at which given quantities will be supplied. Supply and demand are two blades of a pair of scissors and it is useless to talk of which does the cutting. He defined consumer surplus as the surplus satisfaction that a consumer derives from buying a good at a lower price than that at which he would have chosen to go without the good. This notion follows directly from the difference between total and marginal utility and contrasts with normal approach of examining the producer's surplus. (Professor Pigou's welfare economics was based on Marshall's consumer surplus.)

Marshall analysed the relationship between supply and demand through an analysis of equilibrium of supply and demand. He identified market values determined in the short run when supply is fixed, normal values determined over longer periods when supply can be increased using existing factor inputs, or thirdly when factor inputs can themselves be increased, and fourthly he identified long term changes in normal values determined by shifts in taste population technology and so on. Thus Marshall identified various stages of equilibrium analysis, each stage being a partial equilibrium. Exchange, production, distribution become closely interlinked and an equilibrium analysis must state which period of time is being considered in order to determine which factors are variable and which are fixed. In a long run general equilibrium, the marginal real cost of each factor of production equals the earnings of each factor of production, thus interest equals the marginal disutility of saving and wages equal the marginal disutility of working. In reality such a 'stationary state' equilibrium never arises.

Marshall distinguished between the real cost of production (disutility of labour and sacrifice of capital) and expenses of production (money cost of goods produced). The money cost was not necessarily equal to the real cost: for example, £1 bought a doctor's disutility for an hour, and an agricultural worker's disutility for a day. He developed the ideas of 'elasticity of demand' and 'principle of substitution' and defined 'quasi-rent' being the incomes of the various factors of production in the short run (which are akin to rent).

According to Marshall, the interest rate is established by the intersection of schedules for the supply of and demand for money capital. Demand for money capital depends upon its marginal productivity. Interest is a reward for 'waiting' thus attracting a supply of money capital from savers. Thus, Marshall replaced Nassau Senior's idea of abstinence as the cause of interest by the idea of 'waiting' (anyone who lends money waits for its return, even the rich lender whose receipt of interest could not be justified under Senior's idea of abstinence). But this idea presumes that savings are determined by the rate of interest, so would people save nothing if interest rates were zero? (Keynes later proposed that savings are determined in the long run by the level of income not the rate of interest, and that the level of income depends on the level of employment and hence on the level of investment ... thus the initiative lies with the entrepreneurs to invest, not with the savers to save.)

Vilfredo Pareto
1848 - 1923. Twenty years as an engineer after training in mathematics and physical sciences. Pareto was interested in the application of mathematical techniques and statistics to economics. Walras chose him as his successor at Lausanne. Cours d'Economie Politique 1896 - 1897 is based on his lectures at Lausanne. A second generation utility theorist, he continued Walras' work by repeating general equilibrium analysis and stating its mathematical conditions. He hopes that statistics will one day be available to give quantitative values to the variables in his formulae. (Pareto was criticised by his contemporaries for a reliance on statistics.) He was against socialist planning since he opposed 'coercive forces' in society, arguing that history shows the direction of development to be towards greater 'automatic forces' (laissez-faire) to regulate society. Therefore socialism is a retrograde step in human development.

Pareto's Law of Income Distribution takes statistical evidence to show that the distribution of income to individuals within a nation bears a relationship across a number of nations analysed and for different times. Here, the logarithm of the income bracket against the numbers receiving the specified income plots as a straight line of negative slope. Pareto says that this reflects inequality in human ability. He argues that inequality is natural and cannot be reformed. However his theory was criticised on the basis of statistical inaccuracy, and on the basis that Pareto would have to show that income distribution coincided with ability distribution through the populations.

Pareto's Manuale di Economia Politica 1906, was less liberal economically, and shows that he had altered some of his earlier philosophy. Now he says that utility is not measurable, but that an ordinal conception of utility suffices for formulating a theory of choice. In other words relative preference between two goods is all that is required to be known for development of such a theory, the actual utility derived from each good when consumed in different quantities being irrelevant. Thus determinate utility functions do not come into this analysis. Pareto thus adopts indifference curve analysis, first used by F. Edgeworth in Mathematical Physics, 1881, to write equations for equilibrium arising from indifference functions rather than utility functions.

Pareto defined the collective maximum utility of all individuals (his term for utility is 'ophelimite') as that at which no departure from the current distribution of goods can increase the collective utility. But he cannot propose laissez-faire or a socialist system as better at achieving this desired Pareto maximum of utility.

In Traite de Sociologie Generale, 1917-1919, he develops earlier social and psychological theorems but keeps them separate from his economic theories. It is said that Pareto was later to become an intellectual ally of the fascist movement.