10 Neoclassical Economics from Triumph to Crisis 10.1. The Neo-Walrasian Approach to General Economic Equilibrium 10.1.1. The conquest of the existence theorem The rise of Nazism led to a diaspora of intellectuals. All the fervour of study and debate which had enlivened Berlin and Vienna in the 1920s ended in the following decade; and the move to the West began for the most important Mittel-European economists, apart from those like Sch lesinger, who com- mitted suicide, or Remak, who died in a concentration camp. Some settled in London, but most went to the USA. At the end of the 1930s, von Neumann, Morgenstern, Wald, Leontief , Tintner, Marschak, Frisch, and many others were working in America. The presence of these economists in the American intellectual circles of the 1940s and 1950s had many effects on the evolution of general-equilibrium theory. Even if the resumption of the American studies on this theory was stimulated, indirectly, more by Hicks’s Value and Capital than by the con- tributions of the members of the Viennese Kolloquium, it is still true that the work of Wald, von Neumann, and Morgenstern gave a sharp impulse to that resumption. With the fixed-point theorem, Wald and von Neumann had indicated the road to be taken to solve the existence problem. Moreover, von Neumann and Morgenstern’s 1944 book, the Theory of Games and Economic Behaviour, led (among other things) to the abandonment of tradi tional techniques of differential calculus and to a reorientation of mathematical economics towards the use of the techniques of convex analysis. An important contribution of that book was also the proof of the existence of solutions for a two-person zero-sum game—a demonstration later general- ized to an n-person game by John Nash in ‘Equilibrium Points in N-Person Games’ (1950). A decisive stimulus to the resumption of the American studies on general equilibrium was given by two works by Samuelson, one of 1941, ‘The Stability of Equilibrium: Comparative Statics and Dynamics’ and one of 1947, Foundations of Economic Analysis. These works, by taking up Hicks’s 1939 lesson, placed all the main problems of the general-equilibrium model on the age nda. Even though they did not solve any of the really important problems, neither that of existence nor that of uniqueness and even less that of stability, none the less these works indicated the road to be followed. Samuelson’s argument, that all the problems faced by economics (in the neo- classical approach) can be reduced to prob lems of constrained maximization, was very important. Still more important was the priority he gave to the problem of dynamic stability. And perhaps only today are economists beginning to realize the importance of some of Samuelson’s insights in regard to dynamics. However, two results in particular were obtained at that time: first of all, the rigorous reformulation of Walrasian taˆtonnement in the form of a diff erential equation; and then the formulation of the fundamental ‘correspondence principle’, according to which each comparative statics exercise around an equilibrium point presupposes the dynamic stability of the equilibrium. In 1951s two articles were published which demonstrated the optimality properties of a competitive equilibrium: one by K. J. Arrow, ‘An Extension of the Basic Theorems of Classical Welfare Economics’ and one by Ge´rard Debreu, ‘The Coefficient of Resource Utilization’. In that period the two economists had begun to work together on the problem of the existence of solutions, and in 1952, at a meeting of the Econometric Society, they sub- mitted a key paper in which the longed-for peak was finally and compre- hensively conquered. The decisive instrument used in the conquest was Kakutani’s fixed-point theorem. The article was then published in 1954 with the title ‘Existence of an Equilibrium for a Competitive Economy’. We should also mention that, during that meeting of the Econometric Society, L. McKenzie presented a model of competitive equilibrium of international trade in which, under less general hypotheses, he solved the existence problem by means of mathematical techniques similar to those used by Arrow and Debreu. McKenzie’s paper, ‘On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems’, was also published in Econometrica in 1954. It is so similar to the work of Arrow and Debreu that some economists, perhaps rightly so, refer to the demonstration of the existence as the ‘Arrow–Debreu–Mckenzie model’. The Walrasian ‘new testament’ was written in 1959. The author was Debreu, the title, simple and lapidary, Theory of Value. It is useful to present a brief summary of it here, if for no other reason than to show the beau ty and the simplicity of the Walrasian dream come true. The model assumes that the following data are known: (1) the number of co mmodities, l; (2) the number of producers, n; (3) the number of co nsumers, m; (4) the technology available to each producer; (5) the physical constraints and psychological characteristics of each consumer, including tastes; 381 neoclassical economics (6) the initial endowment of resources of each consumer; (7) the share of the profits of each producer which belongs to each consumer. The commodities are a set of goods and services specified in terms of their physical characteristics and place and time location. Thus, a good which is available today at two different locations is considered as two different commodities. The same is true for a good which is available on two different dates. Each commodity is given a price. The price vector is p ¼ðp 1 , , p l Þ: The price is paid at the moment a deal is struck. All deals are struck at one place and at one time, even those on commodities to be delivered in the future. The prices of the latter are therefore ‘futures’ prices. This fact makes Debreu’s model one of inter-temporal equilibrium. It is worth pointing out here that various attempts at formalizing a general inter-temporal equilibrium model had already been made by several eco- nomists, including Frisch and Tintner. One of particular interest was made in 1943 by Debreu’s teacher, Maurice Allais, of whom we must mention at least two important books: A ` la recherche d’une discipline e´conomique: Premie`re partie: L’E ´ conomie pure (1943) and E ´ conomie et inte´reˆt (1947). Allais, by assuming that each economic agent is endowed with preferences over both present and future consumption, also studied the optimality properties of the general inter-temporal equilibrium. In particular, in his 1943 book, Allais proved, before Arrow and Debreu, both the first and second fundamental theorems of welfare economics; while in E ´ conomie et inte´reˆt he introduced, eleven years before Samuelson, the famous overlapping-generations model in the study of dynamic economic processes. Further developments in the inter-temporal equilibrium model are to be found in ‘Capital Accumulation and Efficient Allocation of Resources’ (Econometrica, 1953), an article by another famous student of Allais, Edmond Malinvaud. Let us now return to Debreu’s model. The technological constraints of producer j are represented by a pro duction set, Y j , which contains all the technical combinations between inputs and outputs accessible to that pro- ducer. A ‘production plan’ is one of these combinations, and is expressed by the vector y j ¼ ( y j1 , , y jl ), in which inputs are represented by negative elements and outputs by positive ones. The producer will choose a produc- tion plan so as to maximize profit p j ¼ py j . For each consumer, for example i, a consumption set, X i , is defined, which contains all the combinations of commodities which the consumer can buy and sell. For some goods there are physical constraints. For example, it is impossible to sell more than a certain number of working hours per day. Furthermore, a preference ordering which expresses his tastes is defined for each consumer. Finally, given the resource endowment of consumer i, s i ¼ (s i1 , , s il ) and his profit shares, y i ¼ (y i1 , , y in ), his wealth is defined, which is w i ¼ ps i þ y i p, where p ¼ (p i , p n ). A ‘consumption plan’ for 382 neoclassical economics consumer i is a vector x i ¼ (x 1 , x l ) whose negative elements are the goods sold and whose positive elements are the goods bought. The consumer will choose x i within X i with the objective of maximizing his own satisfaction under the budget constraint px i < w i . A state of the economy is an (m þ n)Àple,(x, y) ¼ (x 1 , x m , y 1 , y n ) which includes all the plans of action of all the consumers and producers. Each element of the (m þ n)Àple is a vector of l elements. In such a state of the eco nomy, the net total demand is z ¼ x À y À s. An equilibrium is an (m þ n þ 1 )Àple,(x*, y*, p*) ¼ (x 1 *, x m *, y 1 *, y n *, p*) such that: x* maximizes the satisfaction of all the consumers; y* maximizes the profits of all the producers; all and only the available resources are used, i.e. x* À y* ¼ s. The vector of equilibrium prices is p*. Debreu proved that this vector exists under a series of hypotheses which are no less implausible than all those adopted before him and certainly more general. Here are some of the most important. Each consumption set must be convex, so that, if two consumption plans are in one set, this will also include all their linear and convex combinations. The consumers must be insatiable, in the sense that, for every chosen consumption plan, there will always be another which is preferred. An important assumption on the production side is that the total production set, Y ¼ S j Y j , is convex. This, together with the ‘inactivity hypothesis’ (i.e. 0 [ Y ), excludes the possibility of increasing returns of scale: if two production plans are in the same pro- duction set, so are all their linear combinations. Moreover, the most recent research has allowed a little weakening of this hypothesis by admitting the possibility that single producers are able to benefit from ‘moderately’ increasing returns to scale. Arrow and Hahn’s work in General Com petitive Analysis (1971) has been important in this respect. There are other particularly irksome hypotheses concerning the existence of the markets and the forecasting ability of the economic agents. As con- tracts are stipulated in the present, for all commodities produced and delivered not only in the present but also in the future, futures markets must exist for the commodities available in all future periods—a hypothesis of which it is not even worth raising problems of realism. In fact, Debreu did not do so. Besides this, it is necessary to assume that economic agents are endowed with perfect foresight, as they know with precision, as consumers, the future evolution of their own preferences and, as producers, the future evolution of technology. Debreu tried to avoid this peculiarity by introducing the notion of uncertainty, but he did so in a way which was no less odd, i.e. by attributing a further specification to goods, one relating to the ‘state of the world’. Thus, for example, a sack of corn available here and now would be a different commodity, not only from that available in another city now, or from that available there tomorrow, but also from that available here tomorrow in the case that there is an earthquake or any other act of God tonight. It is assumed 383 neoclassical economics that individuals are able to formulate plans of action with regard to all the commodities available anywhere, in all future periods, and in all possible states of the world. Besides this, it is obviously necessary to assume that there are ‘contingent’ markets for each possible state of the world, as all indi- viduals must be able to make deals in them. Many believe that this is a more reasonable way to account for behaviour with regard to future even ts—more reasonable than perfect foresight, for example. Finally, we mention another set of unlikely hypotheses concerning, for example, the non-existence of externalities both in production (external economies or diseconomies of scale) and in consumpt ion (any phenomenon of interdependence among consumers’ tastes and between production and consumption, fashions, hidden persuader s, etc.). 10.1.2. Defeat on the grounds of uniqueness and stability Even though the goal of existence had been reached, the difficulties for neoclassical economists were not over. In fact, they were only just beginning, because it was also necessary to demonstrate that the equilibrium is in some way unique and stable. There are two reasons why uniqueness and stability are indispensable. One is, let us say, of a philosophical nature and is fundamental. We shall discuss it in the next section. The other, of a methodo- logical nature, will be dealt with straightaway. The problem originates from the fact that a great deal of the reasoning with which the neoclassical economist explains the social meani ng of the economic variables, prices, wages, etc., are the result of some comparative statics exerci se. For example, in order to say that the relationship between the prices of two goods expresses their relative scarcity with respect to con- sumers’ tastes, one simply says that it is equal to their (marginal) rates of transformation and substitution. These marginal rates are defined in terms of ratios between ‘variations’ of the two goods. In reality these ‘variations’ are defined as the differences between the values that the variables assume in two different equilibrium states, even if they are interpreted as changes around a third intermediate equilibrium. If these exercises are to be correct, as had already been pointed out by Samuelson with the correspondence principle as early as the 1940s, the equilibrium around which they are undertaken must be stable and unique. If it were not so, even a very small change around the equilibrium would lead the economy far away from it, and the various rates of substitution, transformation, and the like would become meaningless. All the most important neoclassical arguments about the economic role of scarcity, the sovereignty of the consumer, the allocative efficiency of markets, etc., could no longer be sustained, for the simple reason that the concepts and the reasoning of comparative statics would no longer have any economic meaning. 384 neoclassical economics Now, it is possible to obtain the desired results of stability and uniqueness, but the price in terms of the restrictiveness of the hypotheses is far too high. As early as 1936 Wald obtained results of uniqueness and stability by using some special hypotheses such as ‘diagonal dominance’ or ‘gross sub- stitutability’. Then in 1943 the global stability of the taˆtonnement process under hypotheses equivalent to those of gross substitutability was proved by Allais through applying Lyapunov’s second method. The gross sub- stitutability hypothesis implies that the aggregate excess demand of a com- modity decreases when its price increases, or the price of any other commodity decreases. Diagonal dominance implies that the aggregate excess demand of a commodity is more sensitive to a change in its price than to a change in the prices of all other commodities. The results of the most recent research on this argument are not very different from those obtained by Wald and Allais. In particular, it seems that the gross substitutability hypothesis is crucial to obtain stability. In fact, it was one of the hypotheses adopted by K. J. Arrow and L. Hurwicz in their article ‘On the Stability of Competitive Equilibrium I’ (1958). In this article cases were shown of economies characterized by a stable equilibrium under various special hypotheses—but this type of reasoning was not very elegant or general. The following year, however, a general theorem of global stability was obtained which still today remai ns a milestone in the evolution of stability theory. It is to be found in the article ‘On the Stability of Competitive Equilibrium II’ by K. J. Arrow, H. D. Block, and L. Hurwicz. The most important of the hypotheses on which the theorem depends concerns the continuity of the excess demand functions, and, alas, gross substitutability. The result was received most enthusiastically and raised confidence in the possibility of generalizing it by removing some of the most restrictive hypotheses on which it depend ed—so much so that in the following year another four or five significant articles on this subject were published. But among these there was one by Herbert Scarf which served immediately to dishearten the optimists. It was entitled ‘Some Examples of Global Instability of the Competitive Equilibrium’ (1960), and showed cases of rather simple economies in which equilibrium existed but was unstable. One important result obtained by Scarf was the demonstration that it is possible to obtain instability simply by introducing a complementarity hypothesis, and this was considered as a confirmation of the key role of the hypothesis of gross substitutability in obtaini ng stability. By 1964, when M. Morishima’s Equilibrium, Stability and Growth was published, the centrality of gross substitutability had become a more or less accepted fact. Subsequently, there have been no great steps forward in this field of research. However, it is worth mentioning some small advances made by Arrow and Hahn in 1971 and by S. Smale in 1976. The trick consisted of the modification of Samuelson’s traditional taˆtonnement equation so as to obtain global stability without having to make very restrictive hypotheses about the 385 neoclassical economics excess demand functions. Unfortunately, however, it was necessary to introduce a few substitute hypotheses which were devoid of economic meaning. In 1992 Saari provided a generalization of the instability result: a general equilibrium can be unstable even if its parts, i.e. the sub-se ts of the economy, were stable. In other words, the stability properties of ‘small’ equilibrium systems do not carry over into bigger systems. The moral of the tale is now part of the official doctrine, and is that stability is not an intrinsic property of the general-equilibrium model. Things are not very different in regard to the problem of uniqueness. Besides, the problems of stability and uniqueness are closely linked, in that, to the degree that it is possible that there are many equilibria, it is also possible that some of them are unstable. In fact, it had been clear right from the early 1950s, when Arrow and Debreu began working on the existence problem, that the general conditions used to demonstrate the existence of equilibrium were not sufficient also to guarantee uniqueness. And Debreu, more than anyone else, must have been aware of the analytical reasons for, and the theoretical implications of, this difficulty. This may explain both the rigorously axiomatic character he imposed on his research work (with the consequent refusal to listen to any criticism of irrelevance) and the almost snobbish absence from the Theory of Value of the usual neoclassical com- parative statics exercises. The explanation why not much faith could be placed in the possibility of solving the problem of uniqueness was provided by H. F. Sonnenschein in ‘Market Excess Demand Functions’ (1972). This paper was followed by others by Sonnenschein, Debreu, Mantel, Kirman and Koch which con- firmed and consolidated the results. In his 1972 article Sonnenschein finally demonstrated something that many people had suspected for some time: that the usual general hypotheses used to explain consumer behaviour, and from which the individual demand functions are derived, are not sufficient to place any significant restriction on the form of the aggregate demand functions. This showed that any hope of identifying general hypotheses on individual behaviour capable of generating aggregate excess-demand functions compatible with the uniqueness and stability of the equilibrium had to be given up. To look at the problem from another angle: it is known that the results of uniqueness and stability can be obtained with some restrictive hypotheses about aggrega te excess-demand functions; the problem is to know whether there is some set of particular assumptions about the behaviour of individuals which would justify such hypotheses. The answer is no. However restrictive the assumptions on individuals may be, the aggregate functions can assume practically any form. At most, it is possible to compel them to assume the properties of continuity and zero homogeneity and to obey Walras’s Law. These conditions are not sufficient to ensure the stability and the uniqueness 386 neoclassical economics of equilibrium. In the next section we will discuss the ‘philosophical’ consequences of this result. There only remains to add something about an attempt made at that time to find, if not an escape route, at least a way to mitigate the seriousness of the problem. This attempt originated from a double hope: to be able to isolate the problem of stability from that of uniqueness, and then to be able to tame at least the latter. Such hopes were raised by the observation that, while with stability it was desirable to have global results, in the case of uniqueness a few local results might be sufficient. This was the road taken by Debreu with an article of 1970 and one of 1976, in which he introduced the notion of ‘regular economy’. This is one with a discrete set of equilibria, so that each equilib- rium has a neighbourhood in which it is unique. Regular economies exclude the most dangerous situation: that in which, near one equilibrium, there can be an infinite number of other equilibria—a situation which would make the state of equilibrium indeterminate. Moreover, the set of irregular economies that could possibly exist must be negligible. Finally, regular economies must be structurally stable, so that a small change in the parameters cannot gen- erate a catastrophic change in the equilibria. By making use of Sard’s powerful theorem and by adopting two parti- cularly unlikely hypotheses, Debreu succeeded in demonstrating that regular economies have a set of equilibria which are not only discrete but also finite ; that irregular economies make up a negligible set; and, finally, that the set of equilibria depends on their parameters, not only in a con- tinuous but also in a differentiable way. The two unlikely hypotheses on which these results depend are as follows: first, the individual demand functions must be differentiable; second, all the goo ds must be ‘desirable’, i.e. when their price approaches zero, the average excess demand for them tends to infinity. Now the hypothesis of differentiability seems rather brave. Economists are used to treating it as if it were normal, but this does not mean it is sensible; it only means that the economist’s education is generally successful in developing special gifts in the suspension of his critical fac- ulties. First, the differentiability hypothesis presupposes that individuals are able to formulate a precise demand, for example with regard to the vari- ation in the price of cars, not only for any number of cars but for any fraction of them; then, even worse, it implies that it is possible to determine the rate of variation of the demand for cars corresponding to every infin- itesimal variation in price. And even more ridiculous, if possible, is the hypothesis of desirability; which implies that, for example, when the price of water approaches zero, individuals will tend voluntarily to drown themselves or to try to hoard the seas. But the real problem of the theory of regula r economies is not so much in the unrealistic hypotheses as in the fact that it does not help to solve the problem. In fact, once it has been proved that equilibria are not infinite, one still has to prove that they are dynamically stable. What can we do with the equilibria, even if they 387 neoclassical economics are ‘few’ in number, if they persist in moving the economy away from themselves? 10.1.3. The end of a world? The general-equilibrium model has been under critical fire ever since it appeared on the scene; critics have never shown any signs of tiredness, and have been just as determined as supporters have been in ignoring the criti- cisms. The mass of critical literature has become so great that it is impossible to deal with it in one section of a book such as this. Here we shall restrict ourselves to presenting a schematic summary of the criticisms, and of responses to them, without drawing up a list of specific contributions or of specific authors. The most widespread criticism is obviously that which calls for the need for realism, or for explanatory or forecasting power . This has also, perhaps, been the most heeded; but it has never proved decisive. Now, the fact that the general-equilibrium model is based on extreme hypotheses cannot be disputed—with its atomistic competition, the absence of externalities, the insatiability, the desirability, the differentiabil ity, the futures and contingen t markets for all the goods, and so on and so forth. What is its explanatory and forecasting power? What does it describe? What use is it? Why is it necessary to study it? The first group of answers to these questions came from Anglo-American economists such as Arrow, Hahn, Townsend, and Roy Weintraub, to mention only those who have made the most recent contributions. Given their positivist backgrounds, these economists have been especially sensitive to this type of criticism. The counter-arguments they advanced can be basically reduced to four types. First, even though it is true that the general- equilibrium model in itself has no explanatory power, for the time being, there is no reason to despair; research moves forward, loosening and generalizing hypotheses, and this process can lead to an increase in the degree of realism, so that the ‘research programme’, of which that theory is the ‘hard core’, may turn out to be progressive in the end. Second, the general-equilibrium model already fulfils a fundamental heuristic function, as it is able to inspire a great deal of research and applied work in specific fields of economic theory in which it is possible to reach, and, in fact, have been reached, notable results in the field of forecasting. Third, the general-equilibrium model represents, vis-a`-vis a great deal of research and many applications in specific fields, a general framework of theoretical reference, and acts as a deep structure capable of holding together theoretical pieces which are heterogeneous and independent of each other. Finally, the theory of general equilibrium can be used as a taxonomic instrument to classify different types of real economies by applying appropriate restrictions to them, such as the number and type of markets which are assumed to be open, the degree of competition, and the 388 neoclassical economics length of the time horizon within which it is assumed that decisions are taken. Now all these arguments are rather weak, and for the same basic reason: that they are referring to something different from the model they wish to justify, rather than to the properties of the model itself. The first argument is only an appeal to the hope that the theory could, in future, become some- thing which it is not today. The second would be valid only if it could be demonstrated that those research projects and specific applications inspired by the general-equilibrium model have actually been helped by it and have not reached sound results, by chance, despite the model. The third should demonstrate that many of the results obtained in the field of specific applications could not be accommodated within a different general theor- etical system. Finally, the weakness of the fourth lies in the fact that the special worlds that can be obtained by rejecting some hypotheses of the general-equilibrium model—for example, the hypothesis of flexible prices so as to obtain non-Walrasian equilibria, or that of exchanges in equilibrium to obtain non-taˆtonnement processes—are, in fact, the result of a negation of that model, and it is hard to see how this can be considered as one of its virtues. But there is another way of answering the question ‘What does the general-equilibrium model describe?’—one that resorts to a drastic answer: ‘Why should it describe anything?’ It is no accident that this is the path chosen, above all, by economists educated along the lines of the rationalist and conventionalist heritage of the homeland of Descartes and Poincare´; we can cite the names of Debreu and Malinvaud, but not that of Allais, their master, who has always been more sensitive to the requirements of empirical research and practical applications. Debreu, more rigorously than the others, and by following an approach inspired by the epistemological stance of the ‘Bourbaki’ group, has set out the general-equilibrium model in terms of a strictly axiomatic theory. A ‘pure’ econ omic theory such as the Walrasian one, is an abstraction. As such, it has no need to justify its own hypotheses by induction, nor to test them by empirical research; and it is necessarily ‘irrealistic’. This is just as true for general-equilibrium theory as for any other. Is the post-Keynesi an steady-state growth model more realistic? Or Sraffa’s standard commodity? Or Marx’s reproduction schemes, or Quesnay’s tableau e´conomique? A pure theory is not an imitation, reflection, or description of reality, but a metaphor, or, in Samuelson’s well-chosen term, a parable. It is this attitude that has justified the neoclassical and all the other theoretical economists in continuing to work on theory by ignoring the problems of the realism of hypotheses. From here, however, the debate moves onto new ground: that of relevance. Any theory, however pure, is never neutral in the types of problem it helps the economist to focus on or in the way in which it helps him to solve them. The general-equilibrium model has often been criticized as completely 389 neoclassical economics [...]... neoclassical theory, they all aimed at giving theoretical depth to the empirical results of the Oxford Group The most important results of the ‘marginalist controversy’ are two groups of theories: the post-Keynesian theories and the managerial-behavioural theories Then, from the late 1960s, the economic theory of the firm discovered problems which modified its content Two main lines of research have emerged The. .. both the way in which human development indicators are constructed and the choice of intervention strategies in the fight against poverty 10. 3 The Controversy on Marginalism in the Theory of the Firm and Markets 10. 3.1 Critiques of the neoclassical theory of the firm The position reached by traditional neoclassical theory in regard to the nature and objectives of the capitalist firm posed several theoretical... actually exist, the rules of the game favour the most disadvantaged groups in the assignment of resources This is the meaning of the social-choice criterion called ‘maximin’: it consists of maximizing the welfare of the subjects at the lower echelons of the social scale To accept this criterion of choice, the subjects must distance themselves—according to Rawls—from the knowledge of their own personal... 10. 2.5 Economic theories of justice One of the most interesting spin-offs from research on social-choice theory has been the deep change in the way of conceiving the link between efficiency problems and distributive justice Smith, in the Theory of Moral Sentiments, had maintained that justice is the main pillar of the social building Men are led by an invisible hand to make nearly the same distribution of. .. Considering the practical importance of issues such as inflation and unemployment, it is not surprising that the present state of the general-equilibrium model with money still gives rise to serious doubts and fiery debates 10. 2 Developments in the New Welfare Economics and the Economic Theories of Justice 10. 2.1 The two fundamental theorems of welfare economics Let us now turn to the normative component of the. .. Contemporary economic theories of justice pursue the project to define an analytical framework capable of dealing at the same time with questions of neoclassical economics 411 efficiency and of justice, thus overcoming the traditional separation of the fields of research The various lines of attack so far put forward are mainly variants, more or less radical, of the two principal traditions of thought in the field... thought in the field of political philosophy, the contractarian and the utilitarian The first, which can be traced back to the work of Hobbes, Locke, and Rousseau, conceives the State as the result of a bargaining process among self-interested agents, just as happens in a business contract between economic agents From an utilitarian perspective, on the other hand, the State is an organization that maximizes... services; the workers and the savers sell them After this, production starts The resources, the goods, and the services bought by the entrepreneur enter into the activity of the firm, but not the individuals who have sold them to the firm The decision-making subject of the firm remains an individual On the market, goods are exchanged at values that are not neoclassical economics 391 influenced by any single... comes from the work of K Arrow and F Hahn, General Competitive Analysis (1971) and J.-M Grandmont, ‘Temporary General Equilibrium’ (1977) The starting-point of the theory of temporary equilibrium has been the abandonment of the assumption that there is a complete system of markets, an assumption which is unattractive at both the empirical and the conceptual level Already Roy Radner, in a work of 1968,... Equality and Efficiency: The Big Trade-Off (1975), has elegantly summed up the liberalist viewpoint: ‘any insistence on carving the pie into equal slices would shrink the size of the pie That fact poses the trade-off between economic equality and economic efficiency’ (p 48) The inefficacy of public interventions in the field of distribution is depicted by Okun with Pareto’s fable of the bucket with a hole: ‘the . by means of lump-sum transfers. This implies admitting the existence of a dichotomy between the moment of the production of wealth and the moment of its distribution. The intervention of the public. doubts and fiery debates. 10. 2. Developments in the New Welfare Economics and the Economic Theories of Justice 10. 2.1. The two fundamental theorems of welfare economics Let us now turn to the normative. (among other things) to the abandonment of tradi tional techniques of differential calculus and to a reorientation of mathematical economics towards the use of the techniques of convex analysis. An important