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From the studies of the history of economic thought, we can learn that many theorems of the modern general equilibrium theory were well anticipated in the classical economics and the economics of the marginal revolution. For example, first, what Johann Heinrich von Thunen (1783–1850) did, in his strange theory of natural wage, can be interpreted as an early, pioneering attempt to use the so-called Negishi method (1960), which is now intensively used for the proof of the existence theorem and the numerical calculation of a general equilibrium. Second, as is well known, no exchanged transactions are permitted out of equilibria in the famous Walrasian tatonnement adjustment process towards market equilibria. Against this, the importance of transactions carried out at disequilibria is emphasized in the studies of the so-called Hahn–Negishi non-tatonnement process (1962). As a matter of fact, in the classical economics, this is exactly what William Thomas Thornton (1813–1380) insisted against the authority of John Stuart Mill (1800–1873). Finally, subjectively perceived (often kinked) demand curves are considered in my proof of the existence of a general equilibrium in the case of monopolistic competition (1961). To my surprise, however, I found later that such demand curves were already hidden in Adam Smith's (1723–1790) consideration of markets and the division of labor, and that the increase of demand never fails to lower the price of goods.

In Negishi (1986), I developed my view on the so-called Mill's recantation of the wages fund doctrine, the short-run theory of wages in the classical school of the economics. According to a survey article on the recent John Stuart Mill interpretations, “a further twist to the debate has been given by Negishi (1986). He reminds us that Mill, in the 1871 edition of the Principles, retracted some of his earlier enthusiasm for Thornton. There he in effect rejected the idea that disequilibrium trades in any way undermine the importance of the principle of the equality of supply and demand, and cautioned that it was too early to adduce any firm conclusions from the discussion engendered by Thornton's book”(De Marchi, 1988).I have three purposes in this present article. The first one is to offer a Japanese version of Negishi (1986), which I think it worthwhile, since there are still no Japanese translation available of the related literature referred and quoted there, i. e., Thornton (1869), Mill (1869) and Thornton (1870). Secondly, I wish to record the appearance of some related literature published in 1990's, like Ekelund (1997), Forget (1991), Fukagai (1995), Mawatari (1997), Mirowsky (1990), Negishi (1998), Vint (1994), and White (1994). Particularly, I wish to make some detailed rejoinders to comments given by Mawatari (1997).The final one is to consider, from the point of view of the modern economic theory (Arrow and Hahn (1971), pp. 324-346, and Negishi (1972), pp. 207-227), how Mill should have replied to Thornton, who asked the significance of a small amount of trade at equilibrium prices, which are arrived after a great bulk of goods were already sold at disequilibrium prices (Thornton, 1869, pp. 53-54; 1870, p. 65). As is easily seen at a glance at Figures 6, 7 and 8 in the text of the present article, i. e., those of box diagram and of utility frontier, the importance of the final small amount of trade at equilibrium prices is that the Pareto optimality is assured.

Alfred Marshall has been wrongly accused by many modern economic theorists that he forgot to take producers' surplus into consideration in Figure 31 in his Principles (Marshall, 1890, 1961, p.468, Ellis and Fellner, 1943, Samuelson, 1967), where he proposed the tax and bounty plan. Elsewhere we defended Marshall that Figure 31 can be interpreted as the case of no producers' surplus, in view of his distinction between the supply curve and the particular expenses curve. In other words, Marshall did not forget to consider producers' surplus, but merely considered the case of no producers' surplus (Negishi, 1999).

Marx insists that the richer country exploits the poorer one through an unequal exchange of labour quantities. Elsewhere I have confirmed that the unequal exchange of labour quantities is possible, but I failed to consider carefully whether this implies an unequal exchange of values, i.e. international exploitation. This paper argues that Marx is wrong to insist on it, in that he does not consider properly the comparison of values differently dated, and points out that a similar failure can be found in the theory of Bauer and Grossmann. Finally, I state my own theory, which is free from the difficulties found in Marxian theories. JEL Classification Numbers: B1, F0.

J. S. Mill (1806–1873)s Principles of Political Economy (1848) was written as “a work similar in its object and general conception to that of Adam Smith, but adapted to the more extended knowledge and improved ideas of the present age” (Mill 1909, p. xxviii). It was highly successful as the last of the great books of the classical economics founded by A. Smith. From the point of view of the history of international trade theory, it is, in general, to be remembered by its extension of Ricardo’s theory of comparative costs to take account of the effects of reciprocal demand on the terms of trade. We must emphasize, however, that Mill seems to start the so-called modern interpretation of Ricardo, which we criticized in Chap. 4.

In the classical theory of international trade, the comparative advantage in the sense of the comparative costs is simply given exogenously. In other words, it is presupposed that different countries have different technology of production, which includes the difference in natural conditions for the production like the climate. In the modern theory of international trade, however, it is assumed that different countries have the identical technology which is given in the form of the identical production function. The comparative advantage of the different countries is explained, then, not by the difference in technology, but by the difference in the factor endowments. Such a modern theory is generally known as Heckscher–Ohlin theory, because the groundwork for substantial developments in the theory is laid by Eli Heckscher (1919) and Bertil Ohlin (1933).

In his Capital (1867–94) and Theories of Surplus Value (1905–10), K. Marx insisted two different types of exploitation. The first one is, of course, the exploitation of labor by capital in the case of equal labor quantity exchange, while the second is the exploitation of poor countries by rich ones through unequal labor quantity exchanges. The exploitation theory of interest, i.e., the exploitation of labor by capital, was criticized by Boehm-Bawerk from the point of view of the comparison of values differently dated. Marx’s own consideration of the international exploitation was fragmentary, but it was succeeded and developed by modern Marxian economists. The same criticism seems to be applicable to this Marxian theory of international trade, however, as the one used by Boehm-Bawerk against the exploitation theory of interest (profit).

A great classic often has many different aspects that permit many different and mutually inconsistent interpretations by later scholars. The Wealth of Nations (WN) of Adam Smith is a good example of such a classic. Smith’s theory of natural prices has been interpreted and developed as an equilibrium theory by modern economic theorists. We shall try, however, to interpret Smith’s economic theory as disequilibrium theory. Of course, there already exist some disequilibrium approaches to Smith on the dynamic process of growth involving increasing returns to scale. We shall rather be concerned, however, with a disequilibrium approach to the problems of markets, that is, international trade, competition and division of labor, and a disequilibrium interpretation of what economists now refer to as “increasing returns to scale.” We shall start this disequilibrium analysis from a study of Smith’s theory of international trade. Smith explained international trade by the existence of disequilibrium, that is, surplus, and was criticized by Ricardo from the point of view of the equilibrium theory.

David Ricardo (1772–1823) was the representative theorist of the classical school of economics which was initiated by Adam Smith. Ricardo’s theory of comparative advantage developed in Chap. 7 of his Principles (1817) has been one of the few theories that economists of all the different schools understand and agree with. Although the current mainstream economics, the neo-classical school, has been developed from the marginal revolution against the classical school, it cannot be denied that Ricardo’s theory of comparative advantage is still an important cornerstone of the modern theory of international trade and has been studied intensively by many leading scholars of the neo-classical economics. Such modern interpretations of Ricardo are, however, sometimes very much different from what Ricardo really meant, as will be seen below.

The standard interpretations of Ricardo's theory of foreign trade assume that money ˙is neutral and conclude that the terms of trade cannot be determined since reciprocal demands are not taken into consideration. In Japan, however, Kojima and Morita emphasized the role of non-neutral metallic money and insisted that Ricardo can determine the terms of trade without introducing the reciprocal demands. A model is constructed to show that their arguments using numerical examples are. justified and that Ricardo's theory has conditional determinacy of the terms of trade without explicitly considering reciprocal demands.

In 1935 the Japanese economist Shibata criticized Bohm-Bawerk's discussion to deny the role of power on market and argued that the validity of Bohm-Bawerk's conclusion depends crucially on his special assumptions on the structure of production in his theory of interest. Unfortunately, both Bohm-Bawerk and Shibata used in their discussions an untenable supposition that the value of heterogeneous capital, which depends on values of endogenous variables, can be given exogenously. Our aim is to reconsider the problem in the light of a new interpretation of Bohm-Bawerk's theory of interest, which is free from this supposition.

We demonstrated elsewhere that the natural rate of profit falls as the rate of growth is increased by a higher rate of saving in our Smithian growth model. This confirms Smith's theory of the falling rate of profit, which was criticized by Ricardo but defended by Malthus's regulating principle of profit. Malthus went further, however, to argue that the saving, if it is pushed to excess, implies the discouragement to an increase of wealth in his theory of the optimal rate of saving. To deal with this problem, with which Malthus distinguished himself from Smith, we have to modify our Smithian growth model so as to consider the effects of the motives to produce, which Malthus considered to be a function of the rate of profit. The aggregate level of production is considered to be an increasing function of the rate of profit through its effects on labour productivity, while aggregate saving, which is for Malthus identical to investment, is shown to be independent of the rate of profit.

Following the appearance of John Barton Condition of the Labouring Classes of Society (1817), David Ricardo admitted, in the third edition (1821) of his Principles, that the process of mechanization may prove injurious to the working class.1 Michio Morishima claims, however, that he carefully investigates Ricardos chapter on machinery and shows that the introduction of machinery does not create unemployment (Morishima 1989, p. 14). In view of the importance of Ricardos machinery problemin the history of economic thought,2 aS well as its applicability in past and current cases of rapid industrialization,3 it is worthwhile to scrutinize Morishimas criticism of Ricardo carefully.

Samuelson’s work on stability (collected in Samuelson 1947, pp. 257–349) contains the first rigorous attempt to analyze the dynamic stability of Walrasian tâtonnement. It is interesting, however, to see that a recent trend in microeconomics called non-Walrasian economics has developed, via the stability analysis of the so-called non-tâtonnement process, from this study of the most typically Walrasian problem.

This chapter discusses the significance of Gossen's work. Gossen anticipated not only the theory of marginal utility of which Jevons shared the fame with Walras and Menger, but also Jevons's theory of exchange in the market, which was based on a view of the market quite different from that of Cournot and Walras, and was succeeded and developed by Edgeworth. Gossen's theory of exchange can be considered as the predecessor of the theory of Jevons, and also of Edgeworth. Gossen considered the case of a two-individual two-good exchange, with highly special assumptions on the shape of the marginal utility curves and on the initially available quantities of goods to each individual. It clearly shows, however, a view of markets which is different from that of Cournot and Walras and is similar to those of Jevons and Edgeworth.

Adam Smith was the founder of the classical school of economics. Although Ricardo later developed classical economics and Marx insisted that he was the sole successor to it, Smith's economic theory was not strictly succeeded by the labor theory of value of Ricardo and Marx and it is much more similar to modern neo-classical economics. This chapter discusses the formation of classical economics. It presents a brief description of the life and early writings of Adam Smith and explains the content of The Wealth of Nations . The chapter also reviews Samuelson's mathematical model of Smith's economic theory. In section 3, Smith's theory of value and that of natural price, particularly his theory of the natural rate of wage, will be considered from the point of view of modern theories of economic growth and human capital, from which it will be concluded that Smith's theory is not properly developed by the Ricardo-Marx theory of embodied labor value. The last two sections are devoted to discussing Smith's two theorems on the division of labor, firstly that the division of labor is limited by the extent of the market, and secondly that capital accumulation is necessary for the division of labor.

This chapter focuses on Marx's Economics. As a part of the recent Renaissance of Marxism, Marx's economics have been intensively analyzed by the use of linear economic models, with the result that it at present attracts the interest of many mathematical-minded, non-Marxian economists. The chapter presents a few linear models of Marx's economics to explain the Fundamental Marxian Theorem and the transformation problem of values into prices of production. It discusses the structure of Das Kapital as the dichotomy between the exploitation of labor by the representative industrial capitalist and the redistribution of the exploited values among many different industrial capitalists, landowners, and money-capitalists. The assumption of linear input–output relations cannot always be relied on for the success of Marx's dichotomy.

This chapter discusses Alfred Marshall's Economics. His theory could be said to be dominantly influential to the development of economics in England after the marginal revolution. Unlike Jevons, who openly attacked classical economics, Marshall did not deny the significance of classical economics, but tried to make it more generalized. J.R. Hicks tried to combine Walrasian and Marshallian traditions in his Value and Capital . Hicks insists that Walras and Marshall differ in interest, the former in principles and the latter in practical applications. Even if one is interested in principles only, however, Marshall's contributions are necessary complements to Walrasian ones. Firstly, the time structure of Marshallian equilibria—market day, short-run, and long-run—clarifies the economic significance of time elements, and gives useful suggestions on how to generalize the static and timeless Walrasian general equilibrium theory dynamically. The chapter also presents a problem related to a Marshallian dynamic equilibrium of the industry which is based on the biological analogy.

This chapter focuses on the Austrian School founded by Carl Menger and developed by, among others, Friedrich von Wieser and Eugen von Bohm–Bawerk. Its contributions to the development of economic science are substitutes for, as well as, complements to neo-classical orthodoxy, or Walrasian economics. As some recent neo-Austrians argue, the Austrian school differentiates itself by its emphasis on subjectivism, not confined to preference but extended to expectations, time as the dimension of changes, fragmented information, and the process of learning. In the Preface to the first edition of Grundsatze , Menger states his method, which he called atomistic and which, according to Hayek, later came to be known as methodological individualism. As summarized by Hayek, Menger's main achievement in the first edition is the “extension, of the derivation of the value of a good from its utility, from the case of given quantities of consumers' goods to the general case of all goods, including the factors of production.” In the second edition, however, Menger's view of the economy is wider than that of scarcity, maximization, and market, which he called the economizing direction of the economy. The other direction is called technical and is derived from the requirements of production, irrespective of insufficiency.

This chapter focuses on J. S. Mill and the close of classical economics. It discusses equilibrium of demand and supply. John Stuart Mill published Essays on some Unsettled Questions of Political Economy in 1844. In the same year, On the Measurement of the Utility of Public Works by Jules Dupuit appeared. Dupuit was an important pioneer of the marginal revolution. Similarly, 1848 was the year of Mill's Principles of Political Economy and that of The Communist Manifesto of Marx and Engels. New paradigms began to be developed to replace that of classical economics. Mill played the role of rear guard in the retreat of classical economics. As the history of armies shows, to bring up the rear is the most difficult task. Whether Mill played the role successfully or not depends on how the essence of classical economics is interpreted. Currently there are two different interpretations, both emphasizing the significance of classical economics to contemporary economics, that is, those of the neo-Ricardians and the new classical economics. Neo-Ricardians and post-Keynesians insist on linking Keynesian economics with classical economics rather than synthesizing it with neo-classical economics.

THE THEORY of the general competitive equilibrium, as developed by Leon Walras [64], has recently been reformulated in terms of fairly advanced mathematical methods. The first problem studied extensively was concerned with the conditions under which a competitive equilibrium exists for a model of general equilibrium. Among contributions to the existence problem, Wald [63], Arrow and Debreu [5], McKenzie [35], Nikaido [48], Gale [18], and Negishi [44] may be cited. The optimality problem of a competitive equilibrium was also investigated by, e.g., Arrow [2], Debreu [15, 16], and, in