1 – Introduction
1The Italian economist Enrico Barone (1859-1924) is well known for elaborating the theory of marginal productivity and for his seminal contributions to the socialist calculation debate. Schumpeter [(1954) 1976: 994] mentions him several times, and there are studies on different aspects of his economic thought.  In this paper we follow the development of Barone’s ideas on the concept of perfect competition throughout his career as an economist.
2The literature on the history of the concept of competition reveals many different approaches. One of these obviously concerns perfect competition; it is usually said to start with Cournot, passing via Knight to end up with Joan Robinson and Chamberlin.  Nevertheless, although Knight would appear to owe his “rigorous notion of equilibrium” to Pareto and Barone [Marchionatti, 2003: 66],  the secondary literature on perfect competition does not mention Barone, probably because none of his writings is devoted exclusively to the subject of competition. Another important reason is that most of Barone’s works have not been translated into English.  In this paper we shall be making extensive use of quotations drawn from the original Italian edition of Barone’s works, with the aim of demonstrating that the Italian economist deserves a place in the history of the notion of perfect competition.
3The paper is organized as follows. Section 2 analyzes various definitions of competition given by the Italian economist, while section 3 deals with the conditions he thought needed to be realized for perfectly competitive equilibrium. Then section 4 considers the outcomes Barone believed perfect competition could achieve, and section 5 deals with the institutional context, namely Barone’s demonstration that theoretically the outcomes of perfect competition could also be achieved in a planned economy. In section 6 Barone’s methodology is illustrated, while section 7 examines his description of the adjustment process required to reach equilibrium. Section 8 shows some graphs that Barone draws to illustrate the working of perfect competition, and section 9 considers other meanings of the term competition for Barone. Finally, section 10 gives an overall evaluation of his contribution to the issue against the background of the secondary literature on the history of the concept of perfect competition.
2 – Definitions
4Barone was already speaking of competition with the adjective “perfect” in 1896, when dealing with the equality between marginal productivity and the price of each input: in particular, he writes, this equality is realized only “in a perfect competition régime” [(1896) 1936: 200]. For Barone, the “régime” of perfect competition suggests a system of market governance  and not the behaviour of the actors in competitive markets — in short, it is a market structure. He defines the other market structures he examined in the same way — i.e., the “régime of monopoly,” the “individualist régime,” and the “collectivist regime.”  In the same essay of 1896 Barone uses “indefinite” with competition as well as “perfect,” indicating with this term the opposite situation to monopoly; he writes that this expression comes from Walras,  and in the Principi he uses it again: “Indefinite free competition” [(1908a) 1936: 45, his italics].  It is worth noting that the term competition appears very early on in the Principi, on the third page, with a different meaning: with a less than completely price elastic demand, as we would say today, a reduction of supply “will establish among consumers … a competition which will considerably raise the price” [(1908a) 1936: 7]. In this case, Barone, like Smith, has the term preceded with the indefinite article.  Rather than a “régime” of governing institutions, competition in this example implies competitive behavior from buyers to raise the price of the good. We address this question later in the article.
5In his early writings the simple expression “free competition”  can also often be found, a commonly used term in that era meaning “free entry.”  However, from a passage in Barone it would seem that for him “free competition” is not just a synonym of “free entry”, but it is a realistic approximation of the limit concept of perfect competition. He states that the characteristics of free competition are “realized all the better the more it is perfect”  [(1908b) 1936: 294], which means that the real “free competition” tends to the ideal “perfect competition”. With the passing of time the adjective “perfect” becomes the one Barone uses the most in his writings: in 1921, in the introductory chapter of a treatise of his on Transportation Economics, he speaks of “perfect free competition” [(1921) 1936: 391], of “perfect competition régime” [p. 405, 437] and also simply of “perfect competition” [p. 392].
3 – Conditions
6In this section we set out the characteristics necessary for perfect competition to be achieved, as they appear in Barone’s economic writings.
- Product homogeneity is mentioned by Barone only once, in the Principi, when he states that to determine economic equilibrium the entrepreneurs must produce “the same product” [(1908a) 1936: 8]. The impression one gets from reading his works is that Barone considers this an implicit condition for perfect competition, because in the chapter about monopoly [(1908a) 1936: 297–9] there is a section dealing with “multiple prices” where he presents price discrimination applied through an artificial product differentiation.
- The question of the number of firms deserves special exploration. Sometimes Barone explicitly states that a multiplicity of economic agents is necessary for competition. For example in 1895, referring to the input market, he identifies the competitive régime among capitalists with the situation in which: “All the capital is not concentrated in the hands of one capitalist alone, but is divided up among several of them” [Barone, (1895a) 1936: 122]. The idea that competition requires a large number of agents is also confirmed elsewhere. For example, he often states that, because firms are price takers, we need to follow Walras’ hypothesis that they are numerous [Barone (1896) 1936: 195].  In the “Ministry”, too, Barone considers price taking behaviour as the result of the presence of “several competitive enterprises” [(1908b) 1935: 251].
7He also expresses the conviction that when the firms are few, they continue to compete, to the point that he wishes for the good of society they would call something of a truce.  Barone also considers the idea that competition may lead to a natural monopoly with only one single firm surviving, but he believes that even in this case exposure to competition would not necessarily disappear, since in his opinion potential competition was always just around the corner.  In fact, even in the case of natural monopoly, which he defines perfectly  and that he several times recalls, the firms “left on their own, arising from competition, will always have to fear potential competition … from other similar firms that could spring up” [(1908a ed. 1909) 1936: 289 his italics].  In these cases obviously he is not dealing with perfect but with imperfect competition, or oligopoly,  or even natural monopoly.
8Barone derives price taking behaviour from the assumption that there are many firms in the market, but on some occasions he suggests that this outcome doesn’t depend on the number of firms.  This variety of opinions on the relation between number of firms and the competitive price finds confirmation in his very own words: “Between the greater or lesser multiplicity of firms … and the greater or lesser effectiveness of competition, there is not always … a necessary relation.” [(1908a ed. 1909) 1936: 287]
- As for free entry and exit, it is clear from an examination of Barone’s writings that for him competition consists above all in the “substitution of entrepreneurs with lower cost for those that produce with higher cost” [(1908a ed. 1909) 1936: 287]. He complains that sometimes competition is “lazy,” or “not very lively,” specifically referring to the process of entry and exit [(1908a ed. 1909) 1936: 287–9; (1911-12) 1937:  316–7]. Sometimes he states that it is the firms with lower cost that crush those with higher cost; for example in the construction of the supply curve Barone put firms in increasing order of cost and shows that if a new firm enters the market producing at the same cost as the first one, the last one sustaining the highest cost of production is forced to exit the market [(1908a) 1936: 8–9]. We shall be coming back to this process in section 8 on the graphical representations of competition.
- We haven’t found in Barone’s writings any mention of the role of perfect information as a requisite of competition, with the exception of the admirable metaphor of the Ministry of Production, the only one subject to be “omniscient”. In section 7 we shall trace the reasons for this choice of Barone’s.
4 – Outcomes
9In this section we deal with Barone’s model of perfect competition, with the economic characteristics of its equilibrium, and with its efficiency properties.
4.1 – Equilibrium 
10Barone [(1908a) 1936: 37–40] describes his model of free competition as follows:
- tastes, technology and the initial endowments of factor services are given
- prices are cried at random for m goods and n services
- each individual then determines how much of each service to supply and how much of each good to demand.
- n equations that express what he calls the physical necessities of production: the quantity of each service supplied must suffice to produce the required quantities of goods;
- m equations that are specific to each economic regime; for free competition the price of each good must be equal to their cost of production.
4.2 – Characteristics
11We shall pause here over the outcomes Barone believed perfect competition could achieve, examining them one at a time.
- We have already met many cases where he describes the agents as price takers in perfectly competitive markets: here every capitalist “taken in isolation, makes his calculations as if the wage remains what it is, as if he had no means to modify it” [(1895a) 1936: 123]. For Barone a characteristic of this type of market structure is in fact that “each entrepreneur … will consider as constants (because he is unable to change them himself) the prices of the product and of the services” [(1908b) 1935: 252]. 
- Barone speaks of the unique price that is determined under perfect competition; for example, analysing again the market of inputs, he states: “it is only by virtue of the competition that the capitalists carry out between themselves, that a unique wage ends up by being established, and a unique interest rate” [(1895a) 1936: 123].
- Zero profits are considered by Barone to be a perfectly correct outcome, given the hypotheses, of Walras’ system of equations. We would point out that it was precisely thanks to Barone’s theory of marginal productivity [Barone, 1895b] that Walras, starting from the third edition of the Elements [Walras, (1874) ed. 1896], considered the zero profit in perfect competition no longer a hypothesis but a result [Jaffé, 1964]. We recall that in this article Barone states that it is only under free competition that “all the output in numéraire will be distributed among factors of production. It is not possible to conceive of free competition without that result” [(1895b) 1983: 185, his italics]. And that “Walras’ ideal entrepreneur who makes neither profit nor loss after having paid for all the services that he hires … corresponds precisely to [these] concepts” [(1895b) 1983: 186]. In the same article he demonstrates that the equality between the price of inputs and the value of their marginal product is “[a]nother important effect of free competition” [(1895b) 1983: 185]. The outcome of zero profits is reiterated many times in his writings, both citing Walras’ idea “of an entrepreneur who – in the conditions postulated of competition between entrepreneurs – makes neither gain nor loss” [Barone, (1896) 1936: 194–5; see also Barone, (1911-12) 1937: 279], and also – as has been seen – illustrating “the tendency of free competition to reduce the price to the cost of production” [Barone (1908a) 1936: 9]. It is also expressed by Barone with reference to the market of capital: “In a régime of free competition… the net rate [is] everywhere equal to the interest on saving. This is none other than another way of saying the equality of price to the cost of production.” [Barone (1908a) 1936: 30] If the profit in the real world exists, for Barone, as we shall see, this is because of the slowness of the adjustment process toward perfect competition equilibrium; therefore in principle it is a temporary phenomenon [(1908a) 1936: 9, 35; (1911-12) 1937: 312].
- Among the most original of Barone’s outcomes is certainly the one on the minimum efficient scale and on the optimal number of firms. Already in the Principi he is stating that “competition also tends to define the size of firms” [(1908a) 1936: 24], and “forces each firm to stay within the limits of decreasing costs” [(1908a) 1936: 25]. And again: “The quantity produced overall, when competition is fully operative, tends to be divided up among firms producing at the minimum cost, so that each of them produces a certain quantity, corresponding to the limit of decreasing costs.” [(1908a ed. 1909) 1936: 288] As we have already mentioned, his demonstration that technology may determine the presence of a limited number of firms in the market (or even just one) also derives from these reflections on the minimum efficient scale [(1908a ed. 1909) 1936: 287–9]. Thus, as we have said, for Barone it is competition that determines the optimal number of firms.
- But the outcomes that Barone repeatedly and insistently spells out as typical of perfect competition are the following: “The cost of production equals the prices and the costs of production are at a minimum.”  [(1908b) 1935: 254] Barone first expressed this important result of competition in 1895: “Given the prices of the factors of production and the quantity produced, the average cost of production must be a minimum, the value to which the price of output is made equal by the effect of free competition.” [(1895b) 1983: 186] In section 8 we will see further developments of this result.
4.3 – Efficiency
12We now come to the outcomes of free competition in terms of efficiency. Barone shows that the perfectly competitive equilibrium is characterized by optimality. We have already spoken of the fact that for him competition makes the least efficient firms exit the market, allowing those remaining to exploit the scale economies to the full. This process for Barone leads the price to be equal to the minimum cost of production, and he states that this is advantageous for the “social organism, for which consumers’ rent increases continuously” [(1908a) 1936: 35]. He gives a demonstration of this statement showing in a diagram that when the price decreases, profits tend to zero, while the consumers’ rent increases: on the whole he shows that there is a welfare improvement, as the consumers’ gain is larger than the firms’ loss [Barone (1908a) 1936: 15].
13Nevertheless, he recognizes that as well as this advantage, competition in the meaning of exit also involves a social cost, which is the “destruction of the fixed capital of the firms it devours” [(1908a ed. 1909) 1936: 327], so competition creates victims, too. It is true that for Barone the bankruptcy of the firms producing with higher costs is only a healthy “elimination of the organisms less able to manage” [(1908a ed. 1909) 1936: 619], yet he does not think that for this reason society as a whole should passively suffer the damage: in fact for Barone those that lose their jobs “are the inevitable victims of competition, of crises, and it is useful if society, which benefits overall every time there is economic progress, does not abandon them” [(1911-12) 1936: 95].
14For Barone, even if “perfect competition” is a limit state, the “free competition” that is realized in the real world is the only market structure that allows us to obtain the most efficient outcome; in his words: “To change this equilibrium artificially, to place obstacles or binding limitations before the automatic functioning of the forces that competition unleashes or liberates, is to lose sight of that equilibrium that gives the maximum of utility, and destroy wealth in the sense we frequently use: i.e. of utility it would have been possible to make, and that is not made.” [(1908a) 1936: 255] 
5 – The institutional context
15As we have already mentioned, the outcomes of perfect competition for Barone can be obtained in a planned economy, as well as in a private market economy.  In his “Ministry of Production” article [Barone, 1908b], he applied the Walrasian general equilibrium approach to a “collectivist régime”, in which non-labor resources are collectively owned and price and allocation decisions are made by a centralized Ministry of Production.
16Nearly half of Barone’s “Ministry” article deals with the “individualist régime,” essentially a private-property market economy where individuals own all productive resources, have property rights in their goods and resources, and are free to allocate their resources and expenditures as they see fit. Unlike the neoclassical model of perfect competition, his individualist model is not, however, a single market structure, but “one in which free competition, monopolies and cartels are all present” [Barone, (1908b) 1935: 247]. Since our paper is focused on Barone’s analysis of perfect competition, we will limit our inquiry to the place of perfect competition in the context of Barone’s “Ministry” paper.
17The problem facing Barone’s Ministry of Production is essentially the problem facing the individualist regime, i.e.: “to solve the problem of combining … individual and collective services in order to procure the maximum welfare of its people” [Barone (1908b) 1935: 265, his italics]. By excluding “metaphysical” utility from his analysis, Barone is able aggregate welfare without aggregation of individual ordinal utilities, although the exclusion of utility maximization leaves a considerable hole in the concept of economic welfare.
18In Barone’s “Ministry” model national income is a measure of welfare, and changes in national income measure changes in welfare. The Ministry establishes a set of shadow prices of goods and resources, (?i) which the individuals take as constant, like the price takers in the perfectly competitive economy. Individuals then allocate their time and resources and choose the combinations of goods (ri) and saving (e) to maximize their individual welfare (?), where
20Since ? is a cardinal magnitude in Barone’s model, the task of the Ministry is to determine the shadow prices and outputs (Ri) that maximize society’s economic welfare (?), which is simply the sum of the individuals’ welfare — i.e., to maximize
22The Ministry determines outputs (Ri) and shadow prices (?i) equal to the average cost of production and the average costs of production are at a minimum [(1908b) 1935: 254]. These two results – to which, as we have seen, he several times returns – Barone also calls the “two fundamental laws” of perfect competition.
23Barone writes that it is evident:
That the Ministry of Production in this perfecting of its first approximate and indeterminate solution (the sole criterion of perfection being the maximum collective welfare) comes to the conclusion that production should be so organized that (with the systems of technical coefficients, of the ?i’s and R’s) the cost of production may be minimized and that the equivalents for the products and for the additions of capital may be such as will correspond to their respective costs of production.
That the system of equations of the collectivist equilibrium is none other than that of the free competition.
25This suggests a role of the Ministry of Production in the collectivist régime similar to the auctioneer in the Walrasian general equilibrium model, but Don Lavoie points out that, although Barone could have substituted the Ministry for the Walrasian auctioneer as the mechanism to adjust prices and outputs to equilibrium, he didn’t do this [Lavoie, 1985].
26However, in his “Ministry” article, Barone takes a somewhat more practical approach to the problem of welfare maximization. He argues that the Ministry of Production cannot solve equations necessary to maximize welfare a priori, but must reach the maximum social welfare by ex post trial and error or by large-scale “experiments” [(1908b) 1935: 286–9]. As we have noted earlier, Barone paid more attention to exit than entry in the long run. In the “Ministry” article, there is no discussion of how the Ministry of Production would reproduce the effects of entry. Barone only argues that if the Ministry were capable of introducing more efficient technologies, the “firms with higher cost, succeeding the least” [Barone (1908a ed. 1909) 1936: 645] should exit the market, generating the same outcome as freedom of exit in individualist market economies.
27At the same time he claims that in practice this wouldn’t happen in the collectivist régime, because the Ministry would be under political pressure to let “firms survive that it would be in the interests of society if they disappeared” [(1908a ed. 1909) 1936: 340], which would negate the gains in efficiency and welfare from the innovations.  He writes that some collectivist writers lamented the destruction of firms (those with higher cost) in competitive markets [(1908a ed. 1909) 1936: 645]. If the Ministry of Production in a collectivist state could not remove firms with higher cost from the market, there would be weak (if any) incentive for entrepreneurship and innovation. The role of entrepreneurship and incentives to innovate are among the most difficult issues for the collectivist economy.  If the Ministry is hesitant to eliminate higher-cost firms from markets, there could also be a serious moral hazard problem that would contribute to inefficiency. This moves Barone out of the Walrasian abstract general equilibrium analysis into real-world issues of political economy.
28However, in Barone’s analysis of the collectivist régime, the Ministry apparently has made all of the trial-and-error adjustments and/or conducted the experiments to reach the optimal solution. He simply shows the conditions that must be satisfied for this result and at least the theoretical possibility that the Ministry could attain these conditions in a collectivist economy.
6 – Methodology
29After having examined the outcomes of competition once equilibrium is reached, we raise the issue of the analysis – which Barone calls “dynamic” – of the path towards equilibrium.  Barone uses the word “dynamics” to indicate in general the study of the interval needed for equilibrium to be re-established after a change in the data. 
30During his career Barone always said he was a great admirer and disciple of Walras, and we know that in his famous “Ministry of Production” article he applied the Walrasian general equilibrium approach. However, in his opinion, the Walrasian method is of no use for studying the adjustment mechanism, since it offers us the new equilibrium “without having to work out the intricate series of intermediary steps that the individual takes during the period that extends from one equilibrium to another” [(1894b) 1992: 25].
31During this transitory period, for instance, when a change in a price has no effect on other prices but only on demand, Barone finds the Marshallian analysis more appropriate.  He writes: “Marshall’s method … provides us with a first approximation of dynamic phenomena, which is not only theoretically correct but also extremely useful in practice” [Barone (1894b) 1992: 17]. The fact that Barone turns to Marshall’s partial analysis is due precisely to the presence of frictions that make a shock spread more slowly. The Marshallian analysis interpreted in this way seems therefore to logically presuppose the presence of dynamic phenomena in Barone’s sense.
32This raises the issue of the compatibility of Walrasian general equilibrium and Marshallian partial equilibrium analysis, or the possibility of a unified theory of markets that includes partial and general equilibrium components [Donzelli, 2008]. As we shall see in the next section, when he is dealing with competition, he often abandons the general equilibrium approach and uses Marshall’s partial equilibrium analysis.
7 – Adjustment
33The study of the transitional period is essential for Barone because it is only this that confers descriptive realism on the economic theory; in his own words: “The analysis of equilibrium – which is indispensable … – if it is not then integrated with the analysis of all these dynamic phenomena, of all these phenomena of adaptation, would give rise to very different conclusions from the phenomenon in the real world,” and he adds significantly “In this lies the aspect missing in many economic theories” [(1908a) 1936: XVII, his italics]. 
34Barone describes both the forces which in practice drive the economy in the direction of equilibrium, and those that slow down its attainment.  Among the former we find the auction mechanism: “There is – he writes – no other more efficient means than to put up for auction, so to speak, the quantity of saving available, and to assign its use to the people who can pay the higher interest thanks to the greater productivity of their firms. And this is what free competition does.” [(1908a) 1936: 62] According to Barone, the same result is obtained with speculation: “Speculation in general … carries out an important economic function. Speculation in commodities competes, indeed, to solve the problem of the adaptation of supplies to demands, helping the avoidance of sudden jumps in prices.” [(1919-20) 1936: 398] And again: “The speculators in stocks are intermediaries between saving and capitalization, just as the speculators in goods are intermediaries between production and consumption. Speculation in bonds serves as a compass for the practical solution to this problem: to divide up or share out the new saving in such a way that – as far as possible – it produces the same net rate of return everywhere, a condition we know to be essential for the achievement of the maximum of utility in capitalization.” [(1919-20) 1936: 438–9] As we have seen, to skip the path up to equilibrium Barone develops the theoretical figure of the Ministry: “Speculation solves … a problem before which a hypothetical omniscient economist, ministry of production in a collectivist State, would not know how to proceed differently from it.” [(1919-20) 1936: 408, see also 412–3]
35We come now to Barone’s description of the movements that take place when the path towards equilibrium is slowed down by the presence of “frictions” [(1908a) 1936: XVII], in his opinion easily the most frequent case. We find an example of this in his analysis of the markets of input in which Barone comments on the following figure.
36“In the real world – he writes – on the subject of the factors of production, there are almost always two phases …: supposing that the demand passes from AB to A’B’, the new equilibrium point M’ is not reached immediately; in the first phase equilibrium is established in m with the new demand and the existing quantity OM: it is only afterwards that, because of the reaction of the new price mP on the quantity supplied …, this extends (or diminishes) tending to the new equilibrium M.’” [(1908a) 1936: 48] With regard to the speed of convergence towards a new equilibrium he specifies that “for the saving, the phase of passing from m to M’ proceeds with a certain speed; for property capital there is greater or lesser speed; for the land, on the other hand … there is no passing from m to M’, because lands cannot be reproduced; for labour the passing from m to M’ is slow.” [(1908a) 1936: 49] And again: “The difficulty over the adaptation of production to consumption is already very serious for direct goods; it becomes increasingly serious, to the extent we are dealing with instrumental goods of an increasingly higher order.” [(1908a ed. 1909) 1936: 606] This concept is generalized in the 1932 edition of his Principi [(1908a, ed. 1923) 1936: 11]:
The so-called law of supply and demand would like to give summary form to dynamic facts. To express it more exactly, we distinguish: a) provisional equilibrium, in which the price is determined by the demand and by the amount available; b) the distant equilibrium … as far as the quantity produced is great or contracted, so as to equal the price at the production cost of the marginal firm. (The real world generally consists of provisional equilibria.)
38It would seem that Barone’s provisional equilibrium corresponds to that of Marshall’s very short, or “market,” period, in which supply is fixed (perfectly inelastic). This is the case in Marshall’s “temporary equilibria of demand and supply, in which ‘supply’ means in effect merely the stock available at the time for sale in the market; so that it cannot be directly influenced by the cost of production” [Marshall, (1920) 1961: 330].
39In the analysis of competition too Barone employs dynamics, meaning the study of the adjustment toward equilibrium and of the impediments that are opposed to them. In his manual on Transportation Economics he deals precisely with the issue of perfect competition: “In the real world – he writes – we are dealing with provisional equilibria, not with definitive equilibria – we would say dynamic, not static, – competition is never perfect.” [(1921) 1936: 437–8, his italics] The link between competition and dynamics in Barone is therefore clear: dynamics studies the adjustment, which is slow because competition is never perfect.
40He attributes the slowness of the adjustment to the fact that, after an exogenous shock, “[e]ven if an individual is gifted with an excellent hedonistic sensitivity, the task of adjustment must proceed through trial and error” [(1894b) 1992: 25].  It is precisely the presence of these attempts, and their being essential to Barone’s system, that in our opinion justifies his decision already mentioned to omit the hypothesis of perfect information. We recall that only the “omniscient” Minister of Production knows all the parameters, solves the system of equations and finds the solutions: no adjustment process should be needed for him.
41Again, like Walras, Barone explains the general equilibrium outcome generated by the Ministry without much (if any) explanation of the nature of the “experiments” or adjustments. This suggests a single general equilibrium model showing the collectivist outcome, but there is little practical applicability to actual problems of adjustment. If the Ministry makes adjustments to move from disequilibrium in the short run, it is moving from the Walrasian approach to the Marshallian market model.
42As we have seen earlier, Barone repeats that free competition tends “to reduce the price to the cost of production” [(1908a) 1936: 9 and 35], but we shall see in section 9.1 that if “competition is not sufficiently active” [(1911-12) 1937: 316] this tendency does not necessarily culminate in the achievement of the final perfectly competitive equilibrium.
8 – Graphical representations
43To show the originality of the contribution to the subject of competition provided by Barone through his graphs, we start with the construction of the supply curve, where he represents the movement of entry and exit of firms.
44Barone writes: “The quantities OA, AB, BC are those produced by entrepreneurs 3, 2, 1 with costs of production, per unit of product, represented by the height of the rectangles. … If in the market another entrepreneur 4 intervenes, who produces at the same cost as entrepreneur 3, this intervention will be able to squeeze entrepreneur 1 out of the market. … Continuing, one tends towards equilibrium N: the quantity produced and consumed OD, to the price ND corresponds the lowest cost of production.” [(1908a) 1936: 8–9] Notice that in this diagram the entrant has the same average cost as the third firm, therefore in this case Barone is considering simple entry, not innovation. As technology is given, it is the entry of new firms with the same average cost which makes the supply function horizontal in the long run.
45If the following graph of Barone is not “by steps,” but represents continuous functions, this is thanks to the idea that it is dealing with “a large market and several competitive entrepreneurs” [(1908a) 1936: 9, our italics].
46In this graph Barone illustrates the effect of competition in the following terms: “The competition of the entrepreneurs tends to push point M toward point N, to straighten CD on CN and to reduce the area MHC to zero.” [(1908a) 1936: 9–10] In other words, the short run market supply curve, which is a continuous and increasing function, in the long run became horizontal to the level of the minimum average cost, thanks to competition (i.e. entry of efficient firms, and exit of those with the highest costs). This same graph is taken up again in a very simplified version in the Principi di economia finanziaria concerning the shifting of consumption tax.
47Barone writes: “We will adopt increasing cost curves; and, when necessary, we will also take into account the continuous dynamism of the market … so that the ab tends to lean towards the am.” [(1911-12) 1937: 312]
48It is worth noting the characteristics of Barone’s competitive supply curves.  First, they are apparently long-run supply curves, because they are generated by the entry and exit of firms, which is impossible in the short run. Furthermore, the long-run supply curve is the locus of prices and outputs at which the industry is in long-run equilibrium.
49Are his supply prices average or marginal costs? As for his increasing cost curves and unlike the graphs “by steps,” they are undoubtedly marginal costs. This was explicitly stated by Barone himself in various works when commenting on his graphs,  and also in a letter to Pantaleoni in 1897: “The ordinate of my curve shows that the selling price is equal to the cost of the last unit in equilibrium. NB: it is this curve that when intersecting the demand curve gives the equilibrium price: and no others.” [in Magnani and Bellanca, 1991: 76]
50The marginal costs, of course, are also average costs if the firms are operating at the minimum point on their average cost curves where marginal cost equals minimum average cost. In the Principi [(1908a) 1936: 21] there is a graph, impressive for its originality, which actually suggests that his supply curves could be referred to firms operating at their minimum average cost:
51This is the representation of a function of total cost through which he explains that: “The competition between entrepreneurs, decreasing the price OC, annuls profit and tends to push point Q toward point P, which means that it tends to force entrepreneurs to stay within the limits of decreasing costs, which they have surpassed to obtain maximum profits; … competition will also define the capacity of the firm; this means that the [total] quantity produced will tend to distribute itself among the firms that produce at minimum cost such that each one of them produces OH, which corresponds to the limit of decreasing costs.” [(1908a) 1936: 24, his italics]  He thus shows that on the curve of total cost the price tends to shift towards the minimum long run average cost, and also shows the corresponding equilibrium size of the firm.
9 – Other meanings of competition
52In the history of the idea of competition, the literature distinguishes between Competition as an End-State and Competition as a Process, to cite the title of a well-known essay by Blaug , and says that the former prevailed from the 1930s, and led people to forget the process view of competition. Even though this paper is focused only on Barone’s end-state conception of competition (and on the adjustment toward the end state), it is perfectly possible to examine his thinking by concentrating on competition in the other sense. Indeed, as will have been noticed, many of Barone’s ideas which we’ve met with already evoke other approaches. We are very keen to complete this paper with a section on the other ideas of competition in Barone, because we don’t want to create misunderstandings over the complexity of his thinking on this issue, and we don’t want this side of his contribution to be forgotten.
9.1 – Equilibrium is never reached
53We wish to introduce the argument by speaking first of all of the limits he saw in the idea of perfect competition: we have already pointed out that Barone said without hesitation that “competition is never perfect” [(1921) 1936: 438, author’s italics]. This is the reason why, as we noted in section 2, he prefers to speak of “free” competition: perfect competition for him is only the hypothesis of a limit state necessary for the study of equilibrium.  This doesn’t mean, as we have seen, that he thinks of the latter as anything other than a very powerful concept, the indispensable “fabric” on which “embroidery” can be carried out,  and “embroidery” for him is the study of dynamic phenomena, necessary to the uncovering of correct explanations of facts in the real world. If Barone thinks competition is never perfect, it is because he believes that in the real world final equilibrium is never attained. Going back to figure 1, Barone argues that during adjustment demand continues to vary “so that the real world gives us a picture, not so much of definitive equilibrium, – to which it continuously tends without ever reaching it – but of a series of successive provisional equilibria between a demand that changed and a pre-existing quantity, which then expands or contracts through the reaction of prices on it” [(1908a) 1936: 48]. He goes more deeply into these dynamics illustrating with graphs a cobweb oscillation around equilibrium without ever culminating in it: in one of his figures which we don’t show here it can be seen, after an increase in demand, production increases slowly, then overtakes consumption, then falls behind, etc. [(1908a, ed. 1909) 1936: 603–4]; for Barone this was a basic general conviction, in fact he says that “the point of equilibrium in dynamic changes is always gone beyond” [p. 635]. In any case the reason why for Barone the final equilibrium is never reached is that during this oscillation new shocks make their appearance; in his words: “Before an equilibrium is reached, other causes intervene to change the data … and to determine a new one.” [(1908a) 1936: 45, his italics; see also XVII.]
9.2 – Imperfect competition
54We will briefly recall here the other meanings he gave to the term competition, such as: price undercutting, war, selection, game, and so on. It is important to point out that in Barone’s Principi there is a chapter entitled Monopoli e Sindacati [Monopolies and Syndicates] devoted to the situation where just a few big firms remain on the market, which come to agreements and that organise themselves into trusts. We may say that Barone in actual fact is here dealing with oligopoly,  and in this chapter he even goes so far as to outline games.  This is why he sometimes calls competition “a selection” [(1908a ed. 1909) 1936: 303], “a war” [p. 327] that “is declared” between individuals and between nations [(1911-12) 1937: 378], that “liberates” forces [(1908a) 1936: 255]. Firms he considers here are not price takers, but on the contrary they do have some degree of monopoly power. He also speaks explicitly of firms which compete in prices and that modify the quality of the product: “Competition often takes place between private producers not in the sense of lowering the price maintaining the good quality of the goods, but in the sense of lowering the price but making the quality deteriorate and falsifying it” [(1911-12) 1937: 118].
55We would like to stress that in Barone, as in other marginalists of that generation who made contributions to the subject of competition (such as Clark, Hadley, Wicksell, Moore, and H.C. Adams), overlapping notions of competition are present: as we have seen, Barone interrelates the idea of perfect competition, which for him is only entirely theoretical, with that of dynamic competition inherited from the classical thinkers, and with another idea that was to be developed later in modern Industrial Organization. Also in Barone’s case, therefore, Blaug’s comment  that Cournot’s “end-state conception of the properties of market-clearing equilibria … did not succeed in wiping the slate entirely clean of an interest in competitive processes” [p. 66] is verified. Barone in fact, while he takes important steps forward in developing the conception of perfect competition as a market structure, never abandons the idea of competition as an active behaviour, as it happened in the same period for American economists [Morgan, 1993].
10 – Conclusion
56In this section we give an overall evaluation of Barone’s contribution to the notion of perfect competition, seeking to define the place that in our opinion he should occupy in the history of this concept. In the historical literature on perfect competition Walras appears regularly, Pareto occasionally,  while Barone is never mentioned,  as we pointed out in the introduction. In this paper we have seen that Barone provided many contributions to the notion of perfect competition.
57His definitions were perhaps not new, since Moore in 1906 allows us to glimpse an already consolidated use of the expression “a régime of perfect competition” [Moore, 1906: 212].  But as we have seen Barone distinguishes a real (free) competition from an ideal (perfect) one.
58A very original aspect is the distinction we find in Barone about the implications of the number of firms, according to whether it is regarded as a condition for perfect competition or as its result. In the first case the number of firms must be high for each firm to be price taker;  in the second this number is endogenously determined. This last important contribution of Barone’s is still totally unacknowledged. As we have seen, it is linked to his treatment of entry and above all of exit, which allows the firms in an industry to achieve their minimum efficient scale.
59We know that Barone owes part of his international fame to his theory of marginal productivity and to his product exhaustion theorem. And yet in the secondary literature these are not indicated as perfect competition outcomes which were found by Barone as early as 1895.
60The same year he also gave another important contribution, stating that it is competition which, in the long run, drives down prices to the level of minimum average cost. On the equality of price with minimum average cost he later provided [1908a] a rigorous demonstration, also through graphs, showing that it is entry and exit that generate the horizontal average cost function. Another original and important element in the history of perfect competition is his demonstration that the long run equilibrium price is also equal to marginal cost, a statement that he illustrates through his very innovative graph with the movements along the total cost curve (Fig. 5). 
61Barone’s contribution to the definition of the concept of Pareto-optimum and to what would later be called the first theorem of welfare economics is well known; Petretto  shows that he also had a pivotal role in the development of the theory of the efficient allocation of resources.
62A difficult part of Barone’s contribution examined in this paper concerns the adjustment mechanism toward perfectly competitive equilibrium. As we have seen Barone deals with this phenomenon by using a method, inspired by Marshall, which he calls dynamics. On the complex question of economic dynamics Barone is recognised as a pioneer [Tusset, 2009: 271–2], but in our paper this method is considered only as far as he applies it to competition, in particular in describing the provisional equilibria due to the fact that “competition is never perfect”.
63At this point what remains is to identify Barone’s role in the history of the theory of perfect competition. To do so we need to reconstruct his network of relations and influences with the other economists of the time who contributed to this field. Barone used very few quotations,  but in his works from the 1890s all the major economists in the literature on this issue are mentioned: Auspitz, J.B. Clark, Cournot, Dupuit, Gossen, Edgeworth, Fisher, Jevons, Launhardt, Lieben, Marshall, Pantaleoni, Pareto, Von Thünen, Walras, Wicksell, and Wicksteed. We must therefore suppose that he knew them and followed their work. Barone’s contributions to the question of perfect competition, though not specifically devoted to this issue, were certainly part of the lively debate taking place in those years, revolving around the developments and criticisms of Walras’s theory of general economic equilibrium. It is well known that Walras did not provide a strict definition of perfect competition [Stigler, 1957; Dennis, 1977]; moreover his tâtonnement hypothesis was even considered “heroic” [Schumpeter, 1954; Dennis, 1977]. Blaug [1997: 77] states that he essentially left “a geographical map of the towns in a country without a map of the roads between towns”. This unsatisfactory situation prompted a series of articles, especially from Edgeworth [1881, 1889] who tried on the one hand to give a more sound definition of competition [Stigler, 1957] and on the other to formulate a different process of adjustment, i.e. re-contracting” [Dennis, 1977]. The contribution of Auspitz and Lieben  should also be seen in the context of the discussion of the dynamic problems generated by Walras’s tâtonnement [Dennis, 1977].
64This was the setting of Barone’s articles of the 1890s. In his essay on dynamics (1894b) he explicitly states, as we have seen, that he considers the Walrasian theory unsuitable for studying the path towards equilibrium, and is therefore seeking in Marshall an alternative to tâtonnement. In 1895, on the other hand, the need for Barone to specify the conditions of perfect competition arose directly from his intention to provide a more convincing version of the contribution made by Wicksteed .
65His next works [1908a; 1908b] came after the publication of the books by Pareto [1896-97;1906], J.B. Clark  and Wicksell . All these economists have a recognised place in the history of the theory of perfect competition: Pareto for the properties of equilibrium [Dennis, 1977],  Clark for defining the conditions necessary for perfect competition [McNulty, 1968; Morgan, 1993], and lastly Wicksell for indicating results similar to those presented by Barone in Principi, such as the definition of minimum efficient scale, and the role of entry in driving profit to zero [Backhouse, 1990]. What was Barone’s role in this second round of the debate? There is no need to dwell further on the originality of his Ministry article, even limiting ourselves to the theory of perfect competition. As for Principi, it is certainly a mixture of original contributions by Barone and of re-workings of other authors’ recent theories. In our opinion it deserves a place in this history, not only for his originality, but also because his exposition is deeper, clearer, more exhaustive, more analytic, and accompanied by graphs that for their time were truly remarkable.
66Before concluding, we once again wish to point out that perfect competition is not all there is to Barone’s thinking on this subject: we don’t want it to be forgotten either that he attributes a purely instrumental character to this concept, or his constant effort to remain anchored in the real world through the employment of other concepts of competition. This gives his analysis a bit of a split personality—Walrasian general equilibrium outcomes in the long run, and Marshallian dynamic adjustments of individual markets in the short run. We conclude by pointing out that the question of the relationship between the Marshallian and Walrasian models of competition remains unsettled, as evidenced by a substantial scholarly literature on the subject. 
This paper was presented at the conference The Foundations, Definitions and Usages of Perfect Competition, January 13th-14th, 2011, University of Paris Ouest Nanterre la Défense, Paris. This explains why it is mainly focused on the issue of perfect competition. It was also presented at the XII AISPE Conference, Florence, February 21st - 23rd, 2013. We thank all the participants, in particular Carlos Andrés Álvarez Gallo, Marco Dardi and Joseph Ostroy. We also thank an anonymous referee for very useful suggestions. The usual caveat applies.
University of Salento (Lecce, Italy). E-mail: firstname.lastname@example.org
University of Maryland, Baltimore Co. (USA). E-mail: email@example.com
Barone’s fundamental contribution to the development of U-shaped average cost curve is highlighted by Keppler and Lallement [2006: 748-750], and that to the concept of natural monopoly by Mosca . The legacy of Barone in Public Finance is analyzed by Fausto in several articles [2003; 2006; 2008] while his originality in the foundation of the new welfare economics is stated (in Italian) by Petretto . For a detailed and contextualized analysis of Barone’s thought (in Italian) see Michelini [2001; 2005; 2007]. On Barone see also Bousquet , Jaffé , Kuenne , Caffè , Maneschi and Thweatt , and Dooley . Bradley and Mosca  have examined the content and the context of Barone’s “Ministry” [1908b]. On Barone’s other non-economic work (military, political, and historical), see (in Italian) Gentilucci .
We will come back to this literature in the conclusion in section 10.
The role of Barone alongside with Pareto is often recognized by the literature on the equilibrium theory in historical perspective. Among others see Phillips and Stevenson [1974: 326]: “In the latter part of the nineteenth century, equilibrium theory was being developed from the works of major economists such as Menger in Austria, Jevons, Edgeworth, and Marshall in Great Britain, Pareto and Barone in Italy, Walras in France, and Wicksell in Sweden.”
Barone’s Principi [1908a] were translated into German in 1927 and into Spanish in 1942. His “Ministry” [1908b] was translated into English in 1935. In English are also available Barone [1894a; 1894b]. In this paper the translations are ours, where they are not already available.
In the Principi a similar expression can be found: “a free competition régime” [(1908a) 1936: 26].
Barone speaks of these other régimes in [(1908a) 1936: 39] and [(1908b) 1935: 246].
In Barone’s words: “From Walras, and also here, we deal with the case of an indefinite competition among entrepreneurs” [(1896) 1936: 195]. But before Walras, the expression obviously comes from Cournot.
The Principi di Economia Politica was published for the first time in 1908, and then in many other editions up until the end of the 1920s. The edition of 1936 contains the original version plus all the various additions and changes; moreover, it includes university lecture notes and articles that Barone wrote over the years. Through the dates of the bibliographical references we shall be giving an account of these later layers so as not to lose sight of the evolution of Barone’s thought over the years. On the various editions of Barone’s Principi di Economia Politica see Michelini .
This indication on competition in Smith can be found in Backhouse [1990: 59]. It should be recalled that this kind of competition between buyers (or between sellers) within an industry is called by Cairnes “commercial”, whereas that among entrepreneurs to enter a market is called “industrial” [Cairnes, (1874) 1888: 303 fn].
For example in Barone [(1896) 1936: 155, 190, 207; (1908a) 1936: 34, 36].
Think of the meaning Jevons gives to “free competition” amongst the conditions defining his “perfect market”. On this see also Dennis [1977: 190].
The translation of this sentence in the English edition is not faithful to the original Italian: “The maximum is more nearly attained the more perfectly they [the characteristics] are realized” [(1908b) 1935: 289].
See also his famous review of Wicksteed: “If the product is not monopolized, that is to say if the entire demand in the market is satisfied not by one but by several producers, an increase in production by one of them will not appreciably change the price.” [Barone, (1895b) 1983: 184]
Barone writes: “When competition (i.e. the régime of struggle) has only left in the landscape of production just a few big firms, the continuation of the war is enormously costly for the firms that won through.” [(1908a ed. 1909) 1936: 326–7] We shall be coming back to this in § 9.
We therefore deduce that Barone believed that there were potential competitors also in the case of scale economies and sunk costs, so that his theory cannot be thought of as analogous to that of contestable markets.
In Barone’s own words: “In some cases it is … the question of the most economic size of the firm which leads, through competition, to one single firm.” [(1908a) 1936: 25] This subject is dealt with in Mosca .
Mises [(1949) 1996: 276] used railroads as an example of an apparently natural monopoly with very large sunk costs that faces competition from another industry (automobiles and airplanes): “The bigness and economic ‘power’ of the railroad companies did not impede the emergence of the motor car and the airplane.” See Bradley [2010: 254–7].
We will deal with these cases briefly in section 9.
Already in 1908 Barone speaks of the “limiting case to which free competition tends, in which there are one or more competing entrepreneurs who make no profit and who produce at the same cost” [(1908b) 1935: 252, our italics].
Like the Principi di economia politica, also the Principi di economia finanziaria published in 1937 consist of a mixture of articles and lecture notes, most of which were written in the years 1911-12. Unlike the former, however, we shall not distinguish between the various editions, because in this paper we don’t deal with subjects of Public Finance; the citations and quotations from the Principi di economia finanziaria here mainly play the role of confirming and strengthening statements Barone made elsewhere.
Barone for example writes concerning a reduction of the alcohol tax: “The subsidy was intended to be a way of getting out of the wine producing crisis: an absurd idea, because to resolve the crisis the only way was to reduce production, in other words make the producers with higher cost bankrupt” [(1911-12) 1936: 242]. The case of the sugar industry is similar [(1911-12) 1936: 243-51].
There is a similar set of conditions in Barone’s “Ministry”, see Bradley and Mosca [2010: 15].
He often comes back to this subject: in the “full régime of free competition, each individual in the market … acts … subject to the market prices of products and services” [Barone, (1908b) 1936: 259–60, his italics].
As we shall see the same definition frequently recurs in the Principi [Barone, 1908a] as well as in other works.
Barone explains that even in a “stationary society” a certain amount of saving is needed for the replacement of worn out capital [(1908a) 1936: 29].
There are innovative contributions on efficiency also in Barone [1908b]; see Bradley and Mosca .
On the connection of the concept of perfect competition with the socialist calculation debate of the 1930s see Machovec [1995, ch. 3] and Blaug [1997: 77–9].
Barone writes that by remaining bound to the previous technology the Ministry procures “a destruction of wealth in another sense – in the sense that the greater wealth which could have been realized will not be realized” [Barone, (1908b) 1935: 288].
Michelini  has gone very thoroughly into this subject.
On the dynamics of Barone’s thought, see Tusset [2009: 270–1], and (in Italian) Michelini [1993: 17], Bellanca and Giocoli [1998: 203].
One of Barone’s examples is the introduction of a tax [(1894b) 1992: 24], which is taken up again later in his textbook on financial economics [(1911-12) 1937: 271]. But elsewhere Barone also considers changes in tastes, in the amount of available capital, in population, technology and duties.
So much so that Pareto wrote to Pantaleoni in 1908: “I don’t know whether [Barone] wants to take into account the interdependence of the phenomena.” [De Rosa, 1960: 85] In Schumpeter’s words Barone “was the man who … formulated the limits of the validity of Marshall’s partial analysis” [(1954) 1976: 858]. Actually he wrote to Wicksell that he did his best to reconcile Walras and Marshall [Jaffé (1964) 1983: 189].
Concerning this point, Blaug argues that Walras “simply gave up the effort to provide a convincing account of how real-world competitive markets achieve simultaneous multi-market equilibrium” [1997: 72].
As we shall be seeing in section 9, for Barone there are also forces which totally impede the achievement of the new equilibrium.
Barone writes: “In the new market equilibrium which arises as a result of the action of [a] disturbance (and no others) … there is an implicit assumption that the individual has already made adjustments to his production and consumption (supply of services, demand for goods) in accordance with the new prices.” [(1894b) 1992: 24]
Barone’s industry supply curve is also analyzed in Opocher and Steedman [2008: 253–6], who are focused on its interrelations with other markets’ prices and quantities.
In his (translated) words: “Every ordinate [of the cost curve] represents the marginal cost” [(1894a) 1959: 437]; and again: “Let a marginal cost BM … correspond to the quantity OM produced [by] the entrepreneur.” [(1896) 1936: 191]
This passage is also quoted in Keppler and Lallement [2006: 749–50], from which we have taken this translation. We would like to point out here that Barone also describes in detail to draw a diagram with the U-shaped average cost curve, without drawing it.
We recall that for Barone that of perfect competition is not the only régime allowing us to calculate the equilibrium price and quantity: “Let us state the conditions of equilibrium, dealing first with free competition, afterwards introducing monopolies and cartels.” [(1908b) 1935: 247]
Having set out the kernel of his economic theory, Barone adds: “Out other studies will not, on the whole, be other than embroidery on this general fabric.” [(1908a) 1936: 45] The same term recurs later: “It may be useful to set out a first rough synthesis of the phenomenon [of competition] to then carry out some embroidery.” [(1911-12) 1937: 275]
The situation where “the number of entrepreneurs is very limited – writes Barone – represents something intermediate between monopoly and indefinite competition” [(1896) 1936: 195]. On the history of the term “oligopoly” see Chamberlin .
Barone writes that in the case of duopoly “there are only two ways: either war or coalition. War may exclude one of the two from the market; but its costs are enormous not only to the defeated one, but also to the winner” [(1908a ed. 1909) 1936: 313]. In the same chapter he also deals with the problem of the behaviour of a cartel towards a new firm: “If, instead of aggregating new firms, the syndicate decides to declare war on them to get rid of them, having recourse to the means of a momentary and abrupt lowering of prices to destroy them, and it succeeds, the expenditure of the struggle … ends up … by adding to the cost of production, thinning out the profits.” [(1908a ed. 1909) 1936: 325–6]
Schumpeter , Stigler , Dennis , Backhouse  and Machovec  deal briefly with some of Pareto’s ideas on competition.
There are only two exceptions. The first is in Dennis  who writes that “no theorists in the 19th century made any serious attempt to build upon Walras’s tâtonnement procedure to construct a dynamic proof of market equilibrating tendencies. However, the literature is immense, and the Italians in particular (eg. Barone, of whom I have read nothing, unfortunately) began to show much interest in Walras’s work by the 1890s” [p. 232, fn.3]. The second is in Machovec  who, radically critical towards the perfectly competitive model, assigns to Barone the role of having “encouraged the appealing ahistorical notion, directly rooted in Walras, that the basis of ownership was irrelevant to the achievement of static efficiency” [p. 75].
Moore [1906: 211] asked the following question: “In what respect is the idea of competition changed when the modifiers ‘perfect’, ‘unlimited’, ‘indefinite’, ‘free’, ‘pure’, are added?” It does seem to us, however, that in his article Moore doesn’t give an answer to his own question.
Although, as we have seen, for Barone there can sometimes be price-taking behaviour with very few firms or even with only one.
In a different perspective, i.e. referring to the elaboration of the U-shaped cost curve, also Keppler and Lallement  write that Barone “provides a clear statement of profit maximization: price equals marginal cost” [p. 748].
Pareto, in a letter to Pantaleoni in 1906 says of Schumpeter: “He writes … without quoting … getting away with it by claiming that whoever knows the subject will be able to distinguish his work from that of others: a bit like Barone.” [De Rosa, 1960: 360]
Machovec  even maintains that Pareto [1896-7] places importance only on the functions describing behavior, just as Barone [(1894b) 1992: 25] writes about Walras: “The … method based on Walrasian formulae … rather than resolve the problem, formalises it in an equational form.” In actual fact, in Pareto there is a detailed examination of the dynamic phenomena [Donzelli, 1991; Tusset, 2009].
There is a large literature on the relationship between Walrasian general equilibrium and Marshallian partial equilibrium. For example, see Donzelli , DeVroey [1999; 2009] and Colander .