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We construct a perfectly competitive model of two symmetric countries producing tradable commodities and a public consumption good. Destination- or origin-based taxes are levied on the consumption of the tradable goods. In both countries, a fixed wage leads to involuntary unemployment. We derive the Nash equilibrium consumption taxes under the two taxation principles with endogenous world prices, and compare them to (i) the cooperative rates, and (ii) the rates when world prices are fixed. We demonstrate that with endogenous world prices, the induced terms-of-trade effects cancel out under the destination principle, but they prevail under the origin principle of taxation. Nash equilibrium destination-based taxes are inefficiently low when the exporting sector in each country is non-labour-intensive. The Nash equilibrium origin-based taxes can be either higher or lower than the corresponding cooperative rates.

This paper uses a panel of about 6000 French establishments to test some implications of the modern theory of dynamic monopsony or upward-sloping labour supply curves for average firm wages. Panel estimates provide strong evidence of a much larger long-run employer size–wage effect (ESWE) than found previously, while controlling for worker quality and compensating differentials with lagged wages, and for profitability (rent-sharing). Employment expansion also has a positive effect on wages, providing further evidence for upward-sloping labour supply (as distinct from the effect of shocks in a perfectly competitive labour market).

Working with the classical expressions of demand, supply and market adjustments, the French engineer Jules Dupuit developed a model of competitive market adjustments in different time dimensions that anticipated Marshall's 'period analysis' on all important points. Dupuit's attempt to handle the complexity of economic phenomenia in a scientific fashion, by utilizing the ceter-is pcar iblus method, and the integration of this method with the 'facts' of production in a 'typical' industry, generated a huge payoff for subsequent generationis of economists. The payoff was enhanced by Marshall's refinements, anid realized by Marshall's teaching, which took root in so many able students and disciples.

Popular characterizations of union preferences assume that the income of laid-off union members is exogenous. There is evidence, however, of intra-union distribution schemes such as severance payments, unemployment insurance, retraining arrangements and early retirement schemes. This paper develops a model of wage and severance pay determination by a trade union and a firm bargaining in a right-to-manage framework. The important point differentiating the model in this paper from the orthodox union model is that it is efficiency-improving in the sense that it makes full-insurance possible and marginal productivity is equal to the opportunity cost of labour. Moreover, with redundancy pay on the bargaining agenda, both the right-to-manage and the efficient bargaining union models are characterized by the same efficiency conditions. This has implications for empirical research which attempts to distinguish between these two models, since the outcome of both models is the same. Finally, the union-firm bargaining model can also be compared with the outcome of the implicit contract model with redundancy pay. There is an important difference between the two approaches, however. While the result in this paper derives from an imperfectly competitive labour market where unions and firms bargain over wages and redundancy pay, the implicit contract result derives from a perfectly competitive labour market in which competitive forces lead to an efficient outcome.

A natural club monopoly exists when economies of scale are so significant relative to population size that, in the efficient allocation, the entire population is included in a single club. Under these circumstances, an uncontested monopolist will inefficiently exclude some individuals from the club if marginal congestion costs are sufficiently high when the entire population is included. If admitting that the entire population is profit-maximizing, then the facility size chosen is also efficient. A perfectly contestable monopoly is always efficient. "External" economies of scale exist when the cost of each facility declines as more facilities are provided. This externality leads a competitive market to provide too few clubs, but a monopolist will provide an efficient allocation because it internalizes the cost externality. Copyright 1990 by The London School of Economics and Political Science.

The purpose of this paper to identify and evaluate the welfare consequences of differences in the size distribution of firms in the imperfectly competitive market equilibria of comparable industries whose firms are organized along labour-managed and entrepreneurial (profit-maximizing) lines, respectively. In zero-profit market equilibria the two forms of organization yield the same outcome. Where product differentiation or cost asymmetries allow positive equilibrium profits to be earned, however, we expect the two industry structures to differ. Firms that are profitable will produce less output in a labour-managed than in an entrepreneurial system, thereby raising prices and allowing new entry. This suggests a labour-managed industry structure that, relative to the entrepreneurial structure, involves a larger number of firms, each producing a lower level of output (Meade, 1972; Vanek, 1970). This paper examines these conjectures in the context of a specific model of monopolistic competition. The welfare performance of these equilibrium industry structures is then compared, and specific examples in which the labour-managed structure is socially preferred are given.

In a recent paper, Dasgupta and Stiglitz (1980a) have suggested that there is a paucity of microeconomic theory to explain the rate and direction of technical progress and, more particularly, the links between invention, innovation and market structure. There and elsewhere (e.g. 1980b) they have sought to remedy this situation. They have focused their attention on rivalry among firms producing a given product in the R and D activity itself, given various market preconditions, and have analysed situations where research expenditure reduces the expected unit costs or brings forward the date of invention of the given product in a regular manner. In this paper we examine another aspect of the general question. We hark back to an earlier debate (Arrow, 1962; Demsetz, 1969; Kamien and Schwartz, 1970), which looked at an inventor outside the final product industry who has sole property rights in a new process for producing the given product, which is a discrete rather than marginal improvement over the old process, and who may sell to a monopolist or a competitive industry. In our chosen framework the inventor has monopoly control through an input involved in the production process.1 The earlier debate centred around what was meant by similarity of demand conditions between industries of differing market structures. However, we feel that the most policy-relevant comparison is Arrow's original one between two industries with the same 2 demand curve. Theoretically, it is easiest to make consistent welfare comparisons when the area under the demand curve is the same in monopoly as in competition; and practically, assessments of merger proposals in the United Kingdom, for example, involve criteria such as whether a more monopolistic structure will give more or less technical innovation.3 On the other hand, we believe that the assumption of a pure (marginal and average) cost-reducing invention adopted in the original debate was rather naive. Progress often occurs through a particular input, and as relative factor prices change, fixed proportions are unlikely to obtain. The situation we have in mind is as follows. At present, production takes place using input 1 and some others. The invention is a new set of processes (an isoquant) combining a new input, 2, rather than 1, with the other inputs in variable proportions, which enables a Hicks-neutral improvement over the old production function. The question is whether the inventor, in control of the new input, will make greater profits from its use in an industry that is monopolistic or one that is perfectly competitive. For example, if monopoly provides the inventor with more profit we would expect, all other things equal, more invention in areas where user industries are monopolistic and swifter innovation of potentially widely applicable input inventions such as microprocessors into monopolistic industries.

The main purpose of this paper is to present, for a two-commodity world, a method of deriving the production possibility curve directly from the isoquant diagram. While two such derivations exist in the literature, those of Savosnick and Travis,2 their techniques are not useful for all purposes. In particular, neither allows the comparison of the shapes of the production possibility curves under alternative production conditions, such as is the case where factor intensity reversals occur. Our approach will be, first, to present a geometric method of deriving the production possibility curve from the representative isoquants of the two commodities, and then to use this derivation to illustrate how the relative shapes of the production possibility curves differ when factor intensity reversals prevail. We will then use these curves to illustrate the traditional factor-intensity-reversal results. Our analysis will also make clear the factors which determine the shape of the production possibility curve, and will indicate the importance for the Heckscher-Ohlin theorem of explicitly excluding the possibility of factor intensity reversal. Throughout our analysis we will make the usual Heckscher-Ohlin assumptions that two goods are produced in two countries using labour and capital, that the goods vary in their factor intensities and the countries vary in their factor endowments, that both countries possess the same linear homogeneous production functions for the two goods, that perfect competition prevails, and that tastes in the two countries are identical and can be represented by utility functions which are homothetic.3 In Figure 1, point E on the ray OZ represents the endowment of capital and labour for the country under consideration. X0 and Y0 are the two isoquants for commodities X and Y which pass through E. These levels of output therefore represent the maximum possible output for the two commodities. These maximum output quantities are

Dating back to the original pioneering work of Phillips [18] in 1958, the money-wage/unemployment trade-off has been subjected to extensive empirical investigation by numerous economists using data for a number of different countries.2 In general, the trade-off originally discovered by Phillips for the United Kingdom has been confirmed, although subsequent work has shown that other variables also are important in determining the percentage change in money wages. Recently, a number of authors have sought to develop a sounder theoretical basis for the observed relationship. One theory which has recently been receiving increasing attention is the so-called expectations hypothesis. This theory develops money-wage equations which depend upon future price expectations and/or money-wage expectations, as well as the unemployment rate.3 One particularly controversial aspect of this theory is the magnitude of the coefficient of the expectations variable in the relationship. In the absence of money illusion and under perfect competition, individuals should ultimately fully anticipate the inflation, implying that the coefficient should be unity. This in turn would imply the absence of a long-run money-wage/unemployment trade-off, or, equivalently, mean that the long-run Phillips curve is vertical, passing through the "natural" rate of unemployment (Fried

Utilizing a general equilibrium framework, this paper studies the economic effects of price regulation in competitive market structures. The analysis considers both the short-run and long-run implications of price regulation upon factor rewards and allocaticns and upon the production of quality. It also characterizes the adjustment path to a competitive long-run equilibrium. The positive relation between regulated price and the production of quality is described, and the identification of who gains and who loses and how resource allocations are affected is shown to depend upon factor intensity rankings.

A widely believed story in the folklore of the economics profession is that the theories of perfect competition and monopoly were well established from the time of Marshall or perhaps Pigou's Economics of Welfare, and that the role of imperfect or monopolistic competition theory was to fill in the middle ground between these extremes. It will be shown in this paper that the folklore conflicts with the historical evidence. Robinson and Chamberlin created the theory of perfect competition in the course of inventing imperfect and monopolistic competition theory. Robinson and Chamberlin, between them, were concerned with the same issues that concerned Marshall. The difference is that Robinson and Chamberlin derived their analyses from a few clear axioms, while Marshall sought to develop his analysis from a well-informed but necessarily impressionistic description of actual business behaviour and dynamic processes. Along with the introduction of indifference analysis to English-speaking economists by Hicks and Allen, Robinson and Chamberlin gave the theory of value and distribution a complete and logically consistent axiomatic basis. Because their axioms relating to business motivation and behaviour were amenable to empirical verification, the work of Robinson and Chamberlin rendered the theory of value and distribution open to a new empirical criticism. It will be argued that the widespread acceptance of Friedman's (195 3) positive methodological position was a necessary response to these empirical criticisms if the new axiomatic foundations of the theory of value and distribution were to be as secure as those previously provided by Marshall.

A basic point in the theory of labour-managed market economies is the fundamental role of free entry in order to achieve efficiency (see Dreze, 1974; Greenberg, 1979; Ichiishi, 1977; Meade, 1972, 1979; Vanek, 1970). But modelling a framework of firm selection process can be undertaken with different approaches. Dreze, Meade and Vanek, for example, consider a perfectly competitive process; Greenberg and Ichiishi build models of coalition formation in the spirit of core theory. In the present study we take the other classical way, the Cournot oligopoly theory. In order to capture the effect of increasing competition in the Cournot oligopoly, two kinds of models have long been traditionally elaborated. In the first, the effects of an exogenously increasing number of active firms facing a given demand function are examined (see Okugushi, 1976; Ruffin, 197 1; Seade, 1980). In the second, initiated by Shubik (1959), the number of active firms and the size of the market are simultaneously increased at the same rate. In this case, what is sought is to isolate some sort of pure effect of an increasing number of competitors, and not the combined result of a greater number of firms facing a constant market. But in the two kinds of approaches the number of active firms are not explained by the theory. What is missing is consideration of the role of potential competitors. Recently Novshek (1980) proposed to give the same status to potential competitors and active firms, i.e. to consider that the potential competitors have a Cournot-type behaviour. Hence the very fact that they are not active comes from optimizing behaviour, in the same way as, for active firms, a positive production level comes from maximizing behaviour. A potential competitor taking the production of the active firms as given and maximizing his objective function remains potential only because he does not find it attractive to produce. Hence we get a unified theory which explains the number of active firms. For the case of U-shaped average cost firms, Novshek (1980) has shown that, in sufficiently large markets, first, such a free-entry Cournot equilibrium exists and, second, it is approximately a perfectly competitive equilibrium state. In this paper we study the welfare properties of free entry Cournot equilibria in labour-managed economies.' We adopt Novshek's notion of free entry which is more appealing than the classical zero profit constraint.2 A recent paper by Hill and Waterson (1983) shows that, with the zero profit definition of free entry, and strong assumptions of decreasing marginal labour productivity, uniqueness and stability of equilibria, Cournot equilibria are asymptotically efficient and furthermore have the same number of active firms in both the labour-managed and entrepreneurial frameworks. Under much weaker assumptions the graphical analysis of this paper shows that asymptotic

Many economists have remarked that there is a problem concerning price adjustments in the theory of a perfectly competitive economy, for example Arrow (1959), Barro (1972) and Koopmans (1957). Consumers' maximizing behaviour determines the demand and producers' maximizing behaviour the supply, but there is no one who decides the prices. These are determined by the "market". Of their own accord they rise in the presence of excess demand and fall in the presence of excess supply. No such problem exists in the theory of an imperfectly competitive economy. In the standard theory it is the producer's maximizing behaviour that determines prices along with output. It is usual to ensure equilibrium in the economy by assuming that the producer has knowledge of the true demand curve facing him so that output is always equal to demand. Here we shall assume that in each period the producer forms expectations of the quantities he will sell at any price, as in Negishi (1960). We also assume that, in general, these will differ from the true demand.The changes in his inventories resulting from these differences will lead him to adjust his expectations in future periods. The result is a theory of price adjustment derived from producers' maximizing behaviour in a disequilibrium economy, that is an economy in which supply is not necessarily equal to demand and expectations may not be fulfilled. We find that a producer's optimum price accelerates when he expects that other prices will increase faster than his own have been increasing, when costs accelerate and when demand is found to be in excess of that expected. More surprisingly, we find that the optimum rate of inflation of his price when his productivity is increasing is in general larger than that given by the usual macroeconomic reasoning, based on the assumption of perfect competition, that price inflation can be less than wage inflation by the percentage increase in productivity. This price-setting hypothesis predicts a correlation between changes in the optimum rate of increase of a producer's price and changes in his optimum output, which will be stable or will shift according to the behaviour of his costs, his productivity, the rate of inflation he expects for other prices etc. If we assume that this is a representative firm and argue that the aggregate variables will be related in the same way as those of this one firm, then this provides a hypothesis that could explain the empirically observed trade-off between price inflation and unemployment and the shifts in this trade-off. A well-known hypothesis designed to explain this trade-off and its shifts is the "natural rate of unemployment" hypothesis-the assumption that there is a negative short-run trade-off and a vertical long-run trade-off between wage inflation and unemployment as a consequence of wage-bargaining behaviour (Phelps, 1967; Friedman, 1968). This hypothesis predicts that at low levels of unemployment the wage inflation-unemployment trade-off would shift outwards while at high levels of unemployment it would shift inwards. This is

THE editor of ECONOMICA was so kind as to let me see the above note, and I should like to take this opportunity to add a few remarks to Mr. Bain's comments. Mr. Bain is, of course, perfectly right in pointing out that different measures of monopoly power may all be appropriate and have to be judged by the problems which we want to determine. This was indeed one of the main points of my article. I also agree with Mr. Bain that his measure of the rate of profit is highly significant with regard to the functional distribution of income, the level of employment, etc. His measure is essentially one of supernormal profits. As Mr. Bain says, it lumps together the effects of monopoly, monopsony, limit to entry, and, I suppose, also to some extent the effects of frictional forces in a competitive system, like ignorance and special degrees of uncertainty.I To lump all these factors together is perfectly appropriate for a great number of economic problems. But why call it a measure of monopoly power ? It is a terminological issue. But a clear and unequivocal terminology may help to avoid unnecessary confusion. In connection with Mr. Bain's second comment (with the main point of which I agree) a minor misunderstanding must be corrected. In my index of monopoly power it is not the subjective (ex ante) seller's demand curve that matters, but the objective (ex post) curve. If a seller in a perfectly competitive market thinks that he has a certain hold over the market, his degree of monopoly will still be zero, as he would soon find out if he acted on his erroneous belief. But while we thus get rid of the ambiguities of a subjective approach, the difficulties of quantitative measurement remain. For we shall be able to get some idea of the shape of the objective seller's demand curve only if the firm in question has experimented in its price policy under circumstances which are roughly comparable. And this is a rare event in these days of price rigidities and price leadership. Thus the objection that no quantitative value can be given to that index will be true for the great majority of cases. But will

The theory of derived input demand has been examined intensively for the situation in which there is only one variable input. Only special cases, however, of the theory of jointly-derived input demand functions have been investigated. In 1938 both Mosak and Allen analysed related factor demands under the assumption of perfect competition in the commodity and factor markets.2 Somewhat later Samuelson studied the same problem without the assumption of perfect competition in the product market.3 However, he imposed a different restrictive condition, namely that the firm under consideration be confined to movements along a given production isoquant in response to changes in relative factor prices. The purpose of this article is to generalize the theory of jointlyderived input demands by removing some of the restrictive assumptions contained in earlier studies. In particular, the following assumptions are made: (a) product demand is a function of and varies inversely with product' price, the prices of related commodities remaining unchanged throughout ;4 (b) the firm in question is a perfect competitor in the factor market; and (c) there is a given production function whose first partial derivatives are positive and monotonically decreasing over the relevant range of input quantities. In the case of two variable inputs the results are quite clear and readily explicable in terms of well-known economic magnitudes. Section II is devoted to an exhaustive analysis of this special case. The general case is presented in Section III. The results, in some instances, are not as precise as in the two-factor model. Nonetheless, the general properties of jointly-derived input demand functions may be stated straightforwardly.

Paul Samuelson [5] [6] and Peter Diamond [2] have developed growth models in which the attempt by each economic unit to maximize its utility does not lead to a social optimum. It would be possible for all generations to consume more per capita, if economic growth were directed by an omniscient social planner. Their models are free from the usual sources of inefficiency encountered in price theory. They explicitly assume perfect competition, perfect foresight and no external economies or diseconomies. The purpose of this paper is to introduce government institutions which may have little foresight, which will not engage in central planning or use direct controls but whose existence will guarantee that the equilibrium solution will be optimal. I am interested in determining the minimal amount of government which is sufficient to produce long-run optimality. Our concern is with the Samuelson-Diamond model whose basic features may be briefly outlined. Two generations are alive at any time: a younger generation which works, and a retired generation. Population born at time t is (1 + n)t; and the participation rate is 100 per cent. of the younger generation. There are (1+ n)tl1 retired people who were born during the preceding period. The periods are of equal, but arbitrary, length. Savings of a worker are designed to maximize his lifetime utility; and his decision involves the substitution between future and present consumption, subject to a constraint. Let c1(t) be consumption of a worker during his youth and c2(t +1) his consumption during retirement one period later. Utility depends upon [c1(t), c2(t + 1)], the pattern of lifetime consumption. As an example, Diamond selected a utility function for the individual

IN the course of his very interesting article on " Rationalisation and the Theory of Excess Capacity" (ECONOMICA, February, 1936), Mr. C. L. Paine has occasion to criticise a doctrine of my own. In dealing with the "ideal " output and constitution of an industry subject to purely "irrational " imperfection of competition, I have stated that " the reproduction of the conditions of the average degree of competition [wllich prevails in industry in general] is what is required."' Mr. Paine finds this doctrine a difficult one to swallow, and prefers to " fall back on the common-sense view that if competition would not be imperfect but for the imperfection of knowledge, then the reproduction of the conditions of perfect competition ought to be the objective of any scheme of intervention."2 The argument which Mr. Paine criticises is, as he himself points out,3 best illustrated by imagining a completely symmetrical world in which an equal degree of irrational imperfection of competition prevails in the production of every cominodity. Then, by symmetry, the value of the marginal product of each factor of production would be the same in every use, and any diversion of resources would result in a net loss to society. Mr. Paine rejects the argument by an appeal to common sense. But what common sense tells us is that if all commodities were produced under conditions of perfect competition the ideal arrangement of resources would be established. Now the very same distribution of resources is established in a world in which an equal degree of imperfection of competition prevails everywhere. It follows that in such a world inLerference has no part to play. The reproduction in all industries of the conditions of perfect competition would leave the situation just as it was before, so far as concerns the arrangement of resources and the national dividend. On the other hand, the reproduction in some industries and ntot in others of the conditions of perfect competition would result in a mal-diversion of resources, and the national dividend would suffer. The trouble with Mr. Paine's argument is that, associating imperfection of competition with ignorance, he is eager to quell it wherever it may appear. He fails to realise that unless he succeeds in disposing of it on every front, he may cause a serious distortion to the horizontal structure of production.

One of the proposed conditions for equilibrium in a non-zero-stum, many-person game is that the outcomes lie in "the core". The concept of the core seems to have numerous applicationis to economics, but up to the present almost its sole application has been the demonstration that competitive market equilibrium is in the core.2 This article will attempt to apply the same concept to the theory of clubs-voluntary organizations for mutual benefit-of which a special case is the provision of public goods. The results inidicate further possibilities for development of this concept in political economy. This should not suggest, however, that the core concept is a silmiple one and its application without difficulty. At best the notion is complex and at times the analysis is difficult to manipulate.3 In the most general terms, a position in the core is supposed to represent a stable allocation or outcome of a game, one from which there is no tendency to movement caused by coalition formationi and dissolution. In specific terms, the core is the set of undominated imputations; an allocation in the core is one for which there exists no blocking coalition. A mathematical definition of the core, due to Luce and Raiffa, may be given: If the set of payments to the n players in a game is denoted as x=(x1, x2, ..., x.), then an imnputation belongs to the core if it satisfies this requiremenit

The purpose of this note is to extend the reasoning on international trade and factor prices, developed by Professors Ohlin' and Samuelson,2 by considering the effects of changes in factor prices on the prices of non-traded goods. The model used is that of Professor Samuelson, with two modifications. We assume two countries which, following Samuelson, we call " Europe " and " America ", and two factors of production, which we call " labour " and " land". The two countries are endowed with the two factors in different proportions, "Europe" having relatively much labour and little land, " America ", relatively much land and little labour. Each country has the same production function, relating inputs of the two factors and outputs of the products, and this function shows constant returns to scale. The industries of each country are assumed to work under conditions of perfect competition, and factors of production are mobile as between different uses in their home country, but cannot move across national frontiers. The " law " of diminishing marginal productivity is assumed to operate everywhere. The modifications of the Samuelson model are those which are necessary in order that there may be both traded and non-traded goods. Instead of two goods only, we assume that there are four, which we call A, B, C and D. The four goods are assumed to use the factors of production in different proportions. The actual proportions used would depend, of course, on the factor price ratio, but we suppose that, at any given wage-rent ratio, A would use a higher proportion of labour to land than B. We therefore describe A as " labour intensive ", and we assume that our four goods, in order of their labour intensity, rank A, B, C and D. Finally, in order that we may have both traded and non-traded goods, we must assume some obstacle to international exchange, and we suppose that this takes the form of transport costs. First, consider the two price systems as they would be if each found its own equilibrium without any international trade. Prices will depend, of course, on demand for the products as well as on the supply of the factors of production. Except in the unlikely event of demand conditions being so dissimilar as to offset the difference in factor endowment

This paper briefly analyses the equilibrium factor price and output implications of replacing the common assumption of identical production functions in the free-trading countries by the assumption of differences in neutral technical advance. The results which follow have already been independently established, though by a method that requires the reader to work through a good deal of algebra.' The demonstration offered here, on the other hand, has the pedagogical advantage of requiring no more than simple box-diagram geometry. A neutral technical advance in the production of a certain good occurs when the outputs associated with successive iso-product curves of a homogeneous and linear production function are all proportionally increased without any change occurring in the shape of these curves. And the exercise that follows-one in comparative statics-contrasts, first, the inter-country differences in factor prices, and secondly, the inter-country output ratios, which occur when there exists a differential technical advance in the production of one or both goods in one of the free trading countries, with the factor-price-equality result reached when the production functions of the free-trading countries are identical. The conditions sufficient to establish the factor-price-equality result are assumed here to exist when we replace the identicalproduction-functions postulate by that of differences in neutral technical progress between the trading countries. Thus, we assume that in each country perfect competition prevails in all sectors (ensuring therefore that all goods are priced at their unit costs); that relative factor intensities for each good remain unchanged for all factor endowments; that the number of factors does not exceed the number of products-indeed, the box diagram confines us to the two-good two-factor case, although the algebraic treatment has not gone beyond this case either. Finally, in order to avoid some obvious elaboration, we deal only with the "normal" case in which the country producing more of a good, say M, also exports M. 2 We are enabled thereby to talk unambiguously of that country's "specialising in M.

The main part of this paper will be devoted to a reformulation of the theory of monopolistic competition. It might be regarded as an indication of how I should develop and present the theory if I were doing it all over again todayin I95I. The underlying principles remain the same; but the order of development in building up the structure is different, and there are a number of shifts in emphasis designed to avoid the many errors in interpretation which have grown up and which have become current in the literature. A second brief part will be devoted to a statement of the difference between the theories of monopolistic and imperfect competition. The theory which I propose does not deal with a particular market form, as has been supposed. Its subject matter is very broad. In includes all monopolies and monopoly elements in the economic system. It likewise includes all competition, if those rare cases of pure competition in the market structure may be regarded as special cases where the monopoly elements are zero. It is a blending of two theories, each of which has been developed in economic analysis under certain perfected conditions. It is thus not a theory of " imperfections " in any sense, but a general theory, designed to replace that of generalised pure competition (of Marshall or of Walras, for instance) as a point of departure and as a basis for the analysis of the entire economy. It has no particular relation to microas compared to macro-economics, since it deals with the entire economic system in which both of these types of theory have their being. Let us begin our analysis of the structure of the economy by looking briefly at the essential unit of which the structure is composed, namely the firm. It has received a great deal of attention in recent years-Professor Hicks has commented ad nauseam-but I think a great deal of attention was needed in order to restore the balance as against an earlier long

ONE of the most important consequences of the raising and spending of taxes is the resulting change in relative factorprices. Yet writers have paid surprisingly little attention to this. When considering the effects of a tax upon the production or sale of a particular commodity, they have considered mainly the effect upon the price of that commodity. If the amount of any factor employed in producing a particular commodity is small relatively to the total supply of that factor, the effect of such a tax on relative factor-prices may be negligible; but when this is not so, or when a number of commodities are subjected to such a tax, it may be of great importance. Similarly, discussions of the effects of an incometax have centred around such questions as whether income-tax enters into commodity prices, whether it discriminates against saving, and whether it stimulates or checks the supply of work and saving. Little attention has been given to its effect upon relative factor-prices. In order to consider briefly how the raising and spending of taxes affect the relative prices of factors of production, I shall make a number of simplifying assumptions. I shall assume that only two commodities are or can be produced-say wheat and steel. I shall assume that there are only two factors-say land and labour-and that any unit of land is a perfect substitute for any other unit of land in the production of either commodity, and similarly that any unit of labour is a perfect substitute for any other unit of labour in the production of either commodity. I shall further assume that tastes and knowledge and supplies of factors remain constant during the period under discussion, that there is perfect competition, and that the economy is in equilibrium before the tax is imposed and reaches a new equilibrium after the tax has been imposed. The problem concerns the relative prices of land and labour in

This is an article about rules, devised and advocated by certain economists, for the control of business and other undertakings: rules, such as the one which says that marginal cost ought to be equal to price, which prescribe what are claimed to be correct relationships between an undertaking's cost and revenue. I have attacked the rules before, in a paper' which has received some notice.2 The following observations, on four crucial and interconnected issues, succeed a re-scrutiny of some of the fundamental theoretical literature3 which must have guided me in the preparation of that article and one which immediately preceded it.4 While I am still following the same line of attack, seeking to expose the non-objectivity and non-implementability of the rules, I am this time offering a little more than a hint that the rules ought to fall away with the ground on which they were built, that is to say, with the notion of perfect competition or competitive equilibrium. This notion requires, I believe, to be replaced by a different notion of equilibrium which was, I feel, implicitly recognised in the earlier of my two articles to which I have just referred.

An input-output transaction matrix may be conceived in terms of an equilibrium position of two sets of interacting forces. The broadest way in which we can define them is 'to denote one set of forces as technical factors expressed through production functions and the other set as market factors expressed through allocation functions. Though technical factors influence production, it is widely recognised that there are various alternative technical combinations in any economy and under different market situations different combinations are actually taken up. An input-output matrix then represents an equilibrium solution for two sets of equations somewhat analogous to demand and supply functions. Under a competitive market and non-scarce resources allocation functions will play a minor role in the set up, and special conditions may be formulated under which production coefficients will determine the equilibrium. But under a monopolistic market with scarce resources allocation functions will determine which among a large group of alternative processes and combinations will be taken up by any particular sector. That is, production functions are forced to play a minor role. We can in this sense associate with an input-output matrix two sets of coefficients. One of these sets has been familiarised by Leontief as production coefficients, or, technical coefficients. They express the relationship xjj =ccjX5 where x, is the output of the ith sector sold to the jth sector and Xi is the output of the jth sector. We can similarly also assume the' existence under different circumstances of the relation xi, =A jXi where xi, is as before the output of the ith industry going to the jth sector and Xi is the output of the ith sector. According as supply or demand conditions predominate either of the relations may approximate reality or neither of these simplified situations may actually approximate reality at all. Leontief has formulated an idealised situation where the set oc, is assumed fixed and the set Ail is allowed to change freely with any change in the final demand. Such conditions may be assumed to hold approximately so long as there is no scarce factor and so long as suppliers are able to offer more of any commodity at the existing price. Leontief's formulation thus takes up for consideration a situation where there is even in the short period a large unused capacity in most sectors such that any change in the final demands do not set

THE ultimate " causes of price "-to use a Classical term-lie deeply embedded in the psychology and techniques of mankind and his environment, and are as manifold as the sands of the sea. All economic analysis is an attempt to classify these manifold causes, to sort them out into categories of discourse that our limited minds can handle, and so to perceive the unity of structural relationship which both unites and separates the manifoldness. Our concepts of " demand" and " supply" are such broad categories. In whatever sense they are used, they are not ultimate determinants of anything, but they are convenient channels through which we can classify and describe the effects of the multitude of determinants of the system of economic magnitudes. These ultimate determinants are, on the one hand, the patterns of choice between alternatives of all individuals, and on the other, the pattern of technical limitation of resources such as labour time and raw materials and the transformation functions of these resources into commodities and services. It is possible to show, algebraically, how these billions of determinants operate to create and to change the structure of economic quantities (prices, volumes, etc.). Such algebraic demonstration, after the manner of the Lausanne school, though logically necessary, is not practically valuable in the solution of particular problems.' For this task we need to be able to divide the multitude of causes into a few broad workable categories, of which the Marshallian demand and supply analysis is an admirable example. It is not the purpose of this paper to overthrow the Marshallian methods, or to question their limited validity. Rather is it to suggest a new dichotomy of forces in the special case of market price in a competitive market, not into " demand " and " supply ", but into " price determining factors" and " quantity determining factors ". For many purposes it wduld seem that this new dichotomy is much more useful than the old, and leads to results which could not have been attained with the demand and supply apparatus. It should be noted carefully that the situation discussed in this paper is that of the determination of market price in a perfectly competitive market on a single " day ", the " day ", of course, being as short as we wish to make it and being defined by the condition that the market is cleared and that all transactions which can be accomplished under existing conditions have been accomplished. This itself, of course, is a fiction, though a useful and necessary one: our mind finds it difficult to grasp the slippery and continuous processes of the actual world without first " fixing " each position in our mind before proceeding to the next. The simplest approach to dynamic economics is through a succession of static pictures, just as the representation of movement on the screen is obtained through a rapid succession of stationary projections. In the "' market day " therefore we make the following assumptions: (i) the quantity of exchangeables (goods and money) possessed by all the people in the market does not change during the course of the " day ". All that happens is exchange, in the simplest and most literal sense of the world-i.e., a rearrangement of ownership of the goods and money in the market. At the end of the day some people have more money, some less; some have more commodity, some less, but the increases must be exactly balanced by the declines as the total quantities possessed by all marketers have not changed. (ii) We will assume that the price that clears the market, is discovered immediately and prevails all through the " day ", and that all transactions made during the " day" are made at that price. This assumption does not quite correspond -to reality: nevertheless if the " day " is sufficiently short no serious errors are likely to be introduced by it, and it enables us to sidestep anumber of highly

Resale price maintenance (r.p.m.), the marketing practice by which the producer or brander of products requires subsequent resellers to offer them at minimum or stipulated prices, has been a subject of discussion and analysis for over a quarter century. There does not, however, seem to exist in the literature any formal analysis of the optimal choice of price and margin by a manufacturer (brander) practising r.p.m. The purpose of this article is to investigate some aspects of this problem in the context of a simple model. Our analysis leaves out of account the two most frequently advanced explanations of r.p.m., each of which involves an assumption of a cartel or of cartel-like behaviour at either the manufacturing or the retailing level.' We investigate here the possibility that r.p.m. might be introduced on the initiative of a single manufacturer dealing with a large group of competitive retailers. Any discussion of price policy must assume some degree of monopoly power on the part of the policymaking firm. We consider here a model in which a single-product monopolist manufacturer sells directly to a large number of competitive single-product retailers, each operating under identical conditions of demand and cost. Throughout, the discussion is in terms of static, long-run equilibrium analysis. Under the conventional assumptions about the determinants of market demand and production costs, the monopolist manufacturer has no incentive to practise r.p.m. Given the market demand schedule, the manufacturer's average revenue schedule is determined by deducting the retail margin directly from the demand price.2 Since the highest average revenue curve will be that associated with the smallest retail margin, the manufacturer has no incentive to increase the margin through r.p.m. Perfect competition and free entry among the retailers will ensure that the retail margin per unit is just equal to the minimum average retail operating cost per unit, the competitive long-run equilibrium solution. No smaller margin can be offered without forcing the retailers into bankruptcy; any larger margin simply reduces the profits of the manufacturer.

If we introduce a measurement of the degree of monopoly it is already clear that we use the word "monopoly" in the modern (Chamberlinor Robinson-) sense, viz. meaning the absence of pure competition. Only if monopoly is taken in this wider sense is there any meaning in the term "degree of monopoly". Now, to have a measurement of that degree of monopoly might have different advantages in analytical and practical problems. There are different ways in which the degree of monopoly might be measured, but before going into a discussion of their relative merits I want to introduce an " index of monopoly power" which is based on one of the diagrammatic devices used by Chamberlin in his Theory of Monopolistic Competition. The diagram I am going to use is introduced by Professor Chamberlin as an alternative demonstration of the equilibrium of the firm under conditions of product differentiation.' Here I reproduce only that part of the diagram which is relevant for my argument. In Fig. i, CC' is the familiar cost curve of a single firm. We assume now that the product2 of this firm is in some way differentiated from the products of other firms producing the same commodity. We then can draw two different demand curves for the firm's product, dd' and DD', each based on different assumptions. Assuming that at present the firm charges the price OP and sells the amount OM, dd' shows the various prices which could be obtained for different outputs, provided the competing firms do not change their price. DD' on the other hand shows which prices would be combined with various levels of output, if the other firms change their price (or output) in the same or some other predetermined way as the firm in question. Chamberlin makes the simplifying assumption that all firms charge the same price, OP, and that DD' represents the price-output relation

Professor Jerome L. Stein puts forward two hypotheses in his recent review article.1 He argues, firstly, that Angus Maddison and A. Lamfalussy reached misleading conclusions in their analyses of Western economic growth. The use by these authors of a simple Harrod-Domar model, it is suggested, provided a shaky and insufficient framework. Stein's second hypothesis is that modern economic growth theory can provide much more insight into the growth process, in particular because it allows exploration of the rate of growth of productivity. The modern economic growth theory Stein makes use of is that of the neo-classical approach which, as is well known, owes much to the work of (amongst others) Solow, Swan and Meade, who attempted to break away from the rigidity implicit in the Harrod-Domar model. The neo-classical model builds on strong assumptions, the most important being those of perfect competition and full employment. If factor substitution is possible, if the factors are paid the value of their marginal products and if investment of an amount equal to fullemployment savings is undertaken, then it can be shown that the steady state equilibrium rate of growth is the natural rate. Thus, the model stresses considerations on the supply rather than on the demand side and, consequently, it is not surprising that Stein finds it difficult to give much weight to the issue of aggregate demand which Maddison in particular found to be extremely significant. Stein does effectively use the neo-classical growth analysis to demolish Lamfalussy's surprising conclusions that the efficiency of British net investment in increasing manufacturing output per head was at least as high as that of German investment, and that in order to raise the growth rate the United Kingdom needed to increase the investmentoutput ratio. Lamfalussy did qualify his conclusion. He wrote, "on the assumption that there have been no diverging structural changes within manufacturing, progress must have been slower in Germany than in Britain". Structural changes were not defined but it was possible to reflect that the author was at least aware that a complex of factors affected productivity. It was possible for the reader to assume that some of these must have been inadequately reflected in the available statistics. It is well known that Britain in the post-war period has encountered numerous problems in adjusting the pattern of production and in overcoming psychological resistances to change. The statistical residual