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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.

No one can deny the important contributions made by Johann Heinrich von Thunen (1783-1850), a pioneer of the marginal revolution in economics, as an independent discoverer of the marginal productivity theory and as the father of the economics of space. Commemorating the two hundredth anniversary of his birth, Samuelson (1983) analyzed these contributions beautifully and skillfully. Von Thunen is, however, also known by the formula of natural wage inscribed on his grave stone. Classical economists before the marginal revolution explained the wage as the subsistence wage, while modern economists after the revolution emphasized the importance of the labor productivity in their theory of wage. In between, Thunen demonstrated the natural wage as the geometric mean of the subsistence wage and the average product of a laborer. Samuelson, who evaluated Thunen's positivistic economics (the marginal productivity theory and the economics of space) very high, interpreted the natural wage of Thunen as the socially optimal wage from the point of view of the welfare economics, and criticized that it is a major felony and a crime against normative economics.In Negishi (1990), we defended Thunen against Samuelson. Following an interpretation suggested by Yamada (1934), a pioneering study of Thunen in Japan, the natural wage is derived as an equilibrium wage in a competitive stationary economy, which Thunen himself studied in his famous Der isolierte Staat. In other words, we defended the theory of natural wage as a positive theory against Samuelson's criticism which regarded it as a normative theory. To be more decisive, however, as a rejoinder to Samuelson's critical comment that Thunen maximized a strange, irrational social welfare function, we have to argue further that the so-called Thunen's social welfare function itself is a rational, reasonable function, given his own model of a competitive stationary economy. In other words, what Thunen did can be interpreted as an early, pioneering attempt to use the so-called Negishi method, Negishi approach, or Negishi theorem, which is now intensively used for the proof of the existence of a general equilibrium and the numerical calculation of a general equilibrium. See Negishi (1960), Kehoe (1991), Mas-Colell and Zame (1991) and Ginsburgh and Keyzer (1997).

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.

This paper considers two different cases of division of labor: (i) the subdivision of different operations in order to produce a particular product in a given firm or plant; (ii) the specialization of firms in the same industry. Division of labor of the former type is limited by demand for output of a particular firm or plant, while division of labor of the latter type is limited by demand for the industry as a whole. It is argued that, in the case of an industry producing a homogenous product, an increase in the scale of production of any particular firm is likely to be associated with changes in the internal division of labor. In the case of inter-firm division of labor, decreasing unit costs may result from lateral disintegration. Finally, in the case of an industry producing a composite commodity (that is, a commodity composed of many different sub-commodities), firms’, disequilibrium behavior may lead to concentration of each firm to fewer sub-commodities, in the anticipation of the entry of new firms, or as a result of it. © 2000 Elsevier Science B.V. All rights reserved.

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.

After a brief survey of the Japanese literature on Sraffa, the author explains how his own theory of the microfoundations of Keynesian macro-economics was influenced by Sraff's view of competitive markets. This view can be interpreted that firms perceive kinked demand curves. It is emphasized that Azariadis's theory of implicit contracts can explain unemployment only if we take Sraffa's not Walras's, view of competitive market.

The Shibata–Okishio theorem, which denied Marx's law of falling rate of profit, was demonstrated by the use of the Lausanne School model based on the assumptions of constant returns to scale and perfect competition, which Marx did not assume. The competition among capitalists which Marx described is a world of economies of scale and imperfect competition. The model to be used should, therefore, be either Cournot's model of oligopoly or Chamberlin's model of monopolistic competition, both of which, unlike the Lausanne model, can deal with economies of scale.

The nature and significance of input–output analysis or interindustry analysis, which was initiated by W. Leontief, can be interpreted in many different ways. It can be seen as the generalization of Keynesian multiplier theory, or as the modern version of Quesnay’s Tableau economique or Marx’s reproduction scheme, or as a degenerated linear programming model. From our point of view, however, it can be considered as an empirically oriented simplified version of the general equilibrium theory. While the importance of the analysis of interindustry input–output relations is duly emphasized, consumer demands are assumed to be given by outside information. The optimization and substitutability in production are assumed away by the use of the no-joint-output constant-coefficient production functions which are, however, numerically estimated by the data available from input–output tables. The input–output analysis can, therefore, provide numerical answers for a number of interesting problems of the general equilibrium of an economy.

Up to now we have been concerned with the description and the analysis of how a market economy, composed of consumers and firms, actually behaves to allocate resources to produce products and to distribute incomes to be spent on them. Our study aims, of course, to consider basic principles of an abstract economy under ideal conditions rather than to describe the details of actual economies. However abstract it is, nevertheless, what we have studied is to be called the positive economics, since it is ultimately to be judged by facts. Ideal or perfect conditions are assumed merely from the point of view of the simplification of the consideration, and not meant to be desirable from some ethical point of view. Theory of perfect competition is, therefore, similar to the law of motion in vacuum.

Consumption of goods in households is the main purpose and the final result of a large part of economic activity. To demand for the consumables, however, households have to supply the service of factors of production to earn their incomes in the modern market economy. The role of the theory of the household is, therefore, to explain not only its demand for goods (the consumables) but also its supply of goods (the service of factors of production). But, fortunately, the households’ supply of the factors of production can be easily explained by an extension of the theory of their demand for goods. This is the reason why we can start with the theory of the behavior of a consumer who spends the given income to demand for the consumers’ goods. While the theory of the firm is developed as the theory of the constrained maximization, i.e., the maximization of profit subject to the production function, the theory of the consumers’ behavior also considers the constrained maximization, i.e., the maximization of utility subject to the budget constraint.

Economic theory can be divided into microeconomics and macroeconomics. The neoclassical theory of microeconomics has been much influenced by the theory of classical mechanics in physics. In the latter theory, a system which consists of a number of particles can be fully described by specifying mass, position, and velocity of each single particle. Similarly, microeconomic theory tries, as we saw in preceding chapters, to describe the behavior of an economy by specifying the behavior of each single consumer and the input–output activity of each single firm. There is, however, an alternative approach in physics. Consider the behavior of the gas contained in a balloon. The gas consists of different molecules and the behavior of these molecules like the collisions among them obeys the laws of classical mechanics. If we know the position, velocity and mass of each of these molecules, therefore, we can describe, at least in principle, the behavior of the gas. From the more practical point of view, however, it is much more important to measure the balloon’s volume, its pressure, its temperature, etc., to describe the behavior of the gas. For example, it can be described by the universal gas equation, pV = NRT, where p denotes pressure, V volume, N the number of mols, R the universal gas constant, and T the absolute temperature.

In the previous chapter, it was shown that there are many cases in which competitive markets fail to allocate resources optimally. Even if we disregard the existence of such difficulties, however, what competitive markets can do is only to achieve a Pareto optimal allocation, which may not be the optimal organization of an economy, since Pareto optimality is, though necessary, by no means sufficient for it. To choose the optimal organization of the economy from many Pareto optimal allocations is the problem of the optimal distribution of incomes, in view of the second half of the fundamental theorem of welfare economics, which insists that any Pareto optimal allocation can be achieved through perfect competition if incomes are properly distributed among consumers (Sect. 7.8). Since different individuals have different opinions on how should incomes be distributed, and the market mechanism cannot be relied on to solve it, the problem of optimal income distribution is a social choice which has to be made politically through voting in a democratic society.

In Chap. 2, we considered how firms supply the consumables and intermediate goods and demand factors of production and intermediate goods, when prices in the market are given. Chapter 3 was devoted to show how consumers demand the consumables and supply factors of production, taking market prices as given. Aggregate demand for each good and aggregate supply of each good are, therefore, functions of market prices which are taken by competitive firms and consumers as given and unchanged. Thesemarket prices are, then, to be determined so as to equate the aggregate demand and aggregate supply of all goods. The general equilibrium of a competitive economy is defined as a set of prices which clears all the markets.

So far we have been assuming that markets are perfectly competitive and consumers and firms are taking market prices as given. The assumption is justified by the supposition that there are very large number of consumers and firms so that market prices are not much affected by the actions of any single consumer or firm. As a result of perfect competition, equilibrium prices are equalized to marginal costs. Perfect competition is, however, an exceptional polar case, which should be regarded as an idealistic or limiting situation, since many firms are not taking prices as given and prices are, in general, different from marginal costs in the real world. While perfectly competitive markets are homogeneous and resemble one another as happy families, imperfectly competitive markets are heterogeneous and imperfect, like unhappy families, in many different ways.

Starting with Adam Smith’s criticism against mercantilism, economists of the classical school generally advocated the free trade and were critical to the protection of domestic industries. J. S. Mill admitted, however, the protection of the so-called infant industry, though he imposes a condition which an industry must satisfy to be protected. Then, it was Bastable who followed Mill to add another necessary condition for protection. This Mill–Bastable infant industry dogma was discussed critically by some modern economists from the point of view of the dynamic theory of the gains from trade.

Adam Smith, who criticized mercantilists fot their wrong concept of the wealth of nations, considered that the real wealth is the annual produce of the land and labour of the society (Smith [1976], p. 12). According to Smith, furthermore, the high productivity of labour in civilized and thriving nations seems to have been the effects of the division of labour. International trade certainly pre-supposes the division of labour among different countries. As for the nature and causes of international trade, therefore, we can expect to learn very much from Smith’s theory of the divisions of labour. For this purpose, let us have a glance of the content of his Wealth of Nations (1776), which consists of five Books, i.e., Book 1: Of the Causes of Improvement in the productive Powers of Labour, and of the Order according to which its Produce is naturally distributed among the different Ranks of the People. Book 2: Of the Nature, Accumulation, and Employment of Stock. Book 3: Of the different Progress of Opulence in different Nations. Book 4: Of Systems of political Oeconomy. Book 5: Of the Revenue of the Sovereign or Commonwealth. An outline of each Book now follows.

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.

The basic economic model of the so-called Heckscher–Ohlin Theory is the two- country two-commodity two-factor model where production functions are linear-homogeneous and the endowment of two factors of production is exogenously given for each country. Besides the factor price equalization theorem and Heckscher–Ohlin theorem discussed in Chap. 10, we can have also two additional well-known theorems derived from this Heckscher–Ohlin model. The first one is the so-called Stolper–Samuelson Theorem (Stolper and Samuelson (1941)) which considers the effects of an import tariff on the factor prices. In other words, it concerns with the changes in factor prices caused by a change in the relative price of two commodities. The second one is called Rybczynski Theorem (Rybczynski 1955) which deals with the changes in the scale of production of two industries caused by a change in the factor endowment in the case of a small country. This is the problem of the effects of the economic growth on the relative scale of the two domestic industries, when the relative price of two commodities is assumed to be constant.

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).

In view of the acknowledged success of the post-war Japan, where export promotion policies have played an important role, the role of subsidies in export industries should be studied from the point of view of the welfare of a country in an international economy. Except for the case of domestic distortions (see Problem 3, in Chapter 13), however, it is difficult to justify export subsidy by the use of the standard two country two commodity model of the international trade theory. In fact, it seems to be a well-established fact the export subsidies always reduce a country’s economic welfare in a competitive economy with full price flexibility.

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.

The so-called modern interpretation of Ricardian theory of comparative advantage results in the drastic conclusion that each country (England or Portugal) specializes entirely in the production of a single commodity (cloth or wine). But Ricardo himself was merely concerned with marginal adjustments of production to the given terms of trade in his famous theory of gains from foreign trade. Ricardo has nothing to do with the complete specialization. It was J. S. Mill, however, who used the assumption of the complete specialization skillfully to determine the terms of trade uniquely in his theory of the reciprocal demand. Classical economists, including Bastable and W. T. Thornton, critically discussed many important aspects of Mill’s theory, but they did not seem to raise the objection to Mill’s assumption of entire specialization. It was Pareto, a neoclassical economist, who presented a numerical example for which the assumption is inappropriate.

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 classical economists, who followed Adam Smith, did not doubt that the arguments of their predecessors, the mercantilists, in favour of a chronic export surplus were based on an intellectual confusion. The classical refutation of the mercantilist principle is derived from the so-called Cantillon-Hume price-specie-flow mechamism. By this mechanism an inflow of bullion raises domestic prices, and selling dear and buying cheap tends to turn the balance of trade against the country. Purely automatic forces tend, therefore, to establish a natural distribution of specie between the trading countries of the world and there is a level of domestic prices such that each country’s value of exports equals that of imports.

To study the modern theory of the international trade, it is necessary to be familiar with the elementary theory of production. The basic model of an economy to be considered is a two-commodity two-factor one of a country. There are two industries, each of which produces a single different commodity from the input of two factors of production, say, labor and capital. The technology of an industry is given as an aggregate production function which relates the inputs of two factors of production to the output of a commodity.

In the current theory of general economic equilibrium, recontracting and tâtonnement (a French word meaning ‘groping’) are used interchangeably to denote a simplifying assumption that no actual transactions, and therefore no production and consumption activities, take place at disequilibria when prices are changed according to the law of supply and demand (Kaldor, 1934; Arrow and Hahn, 1971, pp. 264, 282). Historically speaking, however, this usage is somewhat confusing, since recontracting is originally due to Edgeworth who developed it in a direction different from that in which Walras developed his tâtonnement (Walker, 1973).

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.

Studies of von Thunen in Japan have a long history and suggest an interpretation of von Thunen's theory, which is different from those of recent studies of von Thunen in the English speaking world. A simple model of a stationary economy is constructed on the basis of such an interpretation, in which workers are assumed to be free to save in their life-cycles though the level of consumption of working families is kept at the subsistence level. Von Thunen's famous formula of the natural wage is derived from the model, which is free from the criticisms given to von Thunen's original model.

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.

The so-called Shibata-Okishio theorem (Shibata, 1934, 1939, Okishio, 1961) which denied Marx’s law of falling rate of profit, was skillfully demonstrated by the use of Lausanne School model based on assumptions of constant returns to scale and perfect competition, which, however, Marx did not assume (Negishi, 1989, 224-229).1 The process of competition among capitalists which Marx described vividly is a world of economies of scale and imperfect competition. The model to be used should, therefore, be either Cournot’s model of oligopoly or Chamberlin’s model of monopolistic competition, both of which, unlike Lausanne model, can deal with economies of scale. In Negishi (1998) it is demonstrated by the use of such models that the rate of profit falls, unless the new technology is so efficient that the reduction of the unit variable cost is very large compared with the increase in the overhead cost.

IJohnson and Pauly (1969) correctly pointed out that the condition for the optimal supply of public goods derived by Samuelson (1954) is based on the assumption that public goods are financed by efficient lump-sum taxes. They derived an optimal (i.e. second-best) condition for the supply of public goods in the presence of distortions due to nonlump-sum taxes, such as an excise tax. Like Samuelson they confined their analysis to public goods which are final products and therefore considered the voluntary theory of public finance which assumes that the basic decision-making unit is the individual consumer-votertaxpayer. Assuming that consumers take into consideration not only the monetary cost of the supply of public goods but also the welfare costs due to inefficient taxes, they showed that a smaller quantity of public goods is supplied under an inefficient tax than the optimal quantity supplied under an efficient tax, the marginal utility of money being assumed constant. The aim of this note is to extend their argument to the case of public goods which are intermediate goods, and to show that there are cases where pressures from industry on government cause an under-supply of public goods even when the financing is done by an earmarked lumpsum tax on the industry. In spite of Galbraith (1958) an under-supply of public goods has been thought to be the least likely result for intermediate public goods, since industries have more influence on governments than do consumers (see for example Downs, 1957, pp. 255-259).