The classical notion of competition revisited

We compare and analyse two different conceptions of market competition: the walrasian notion of perfect competition and the Classical notion of free competition: while the former may be described as an equilibrium state in which atomistic agents treat prices parametrically, the latter is a situation in which agents, endowed by market power, fix prices strategically. We show that price undercutting or outbidding are the typical phenomena that, for the Classical authors, may be observed in a market characterized by free competition. We investigate some problematic aspects of the neoclassical notion of perfect competition and we reconstruct the Classical theory of free competition, as developed, in particular, by Adam Smith and Karl Marx, in the light of the modern notion of mixed strategies equilibria.Classical Economics, Competition, Adam Smith, Karl Marx, mixed strategies

In Favor of Rigor and Relevance. A Reply to Mark Blaug

The paper discusses Mark Blaug’s recent criticisms of “Sraffian economics”. It is shown that none of the criticisms stand up to close examination. Blaug commits a number of elementary blunders and mistakes the mathematical form of an argument for its content. He variously contradicts himself and puts forward bold contentions that cannot be sustained. The paper concludes with an obvious plea for rigor and relevance.Piero Sraffa;Mark Blaug; General Equilibrium

Bertrand-Edgeworth competition in an almost symmetric oligopoly

We analyze a Bertrand-Edgeworth game in homogeneous product industry, under effcient rationing, constant marginal cost until full capacity utilization, and identical technology across firms. We solve for the equilibrium and establish its uniqueness for capacity configurations in the mixed strategy region of the capacity space such that the capacities of the largest and smallest firm are sufficiently close.Bertrand-Edgeworth competition; mixed strategy equilibrium; almost symmetric oligopoly; Mixed strategy equilibrium

Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly

The paper extends the analysis of price competition among capacity-constrained sellers beyond the cases of duopoly and symmetric oligopoly. We first provide some general results for the oligopoly and then focus on the triopoly, providing a complete characterization of the mixed strategy equilibrium of the price game. The region of the capacity space where the equilibrium is mixed is partitioned according to the features of the mixed strategy equilibrium arising in each subregion. Then computing the mixed strategy equilibrium becomes a quite simple task. The analysis reveals features of the mixed strategy equilibrium which do not arise in the duopoly (some of them have also been discovered by Hirata (2008)).Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium

White Elephants and Other Non-basic Commodities: Piero Sraffa and Krishna Bharadwaj on the Role and Significance of the Distinction between Basics and Non-basics:

After the publication of Production of Commodities by Means of Commodities ( Sraffa, 1960 ), a lot of attention was devoted to 'reswitching', that is to the fact that a technique is cost-minimising at two disconnected ranges of the rate of profits and not so in between these ranges. We owe Krishna Bharadwaj (1970, Schweizerische Zeitschrift für Volkswirtschaft und Statistik, 106, 409–429) an important contribution to the debate by stating and proving a general result concerning the maximum number of switches between two techniques that have at least one switch point on the wage-frontier. She proved that the maximum number of switches coincides with the number of distinct commodities, without double counting, that enter directly or indirectly into at least one of the alternative methods of production. This means that if the alternative methods produce a commodity that is basic in both techniques, then non-basics in both techniques play no role in this, whereas if the alternative methods produce a non-basic commodity in at least one technique, then a role is played also by those non-basics that enter directly or indirectly into the production of at least one of the alternative methods of production. JEL Code: B12, B21, B31, B51, D24, D5

Besicovitch, Sraffa, and the existence of the Standard commodity

The proof of the existence of the Standard commodity contained in Sraffa's book (section 37) has been debated recently. Lippi (2008) has argued that the algorithm in section 37 of Sraffa’s book is not precisely stated and does not need to converge to the desired eigenvalue and eigenvector. In this paper I will show that also the proof provided by Besicovitch to Sraffa on 21 September 1944 is incomplete, but it can easily be completed

Besicovitch, Sraffa, and the existence of the Standard commodity

The relationship between the proof of the existence of the Standard commodity contained in section 37 of Sraffa’s (1960) book and the proof supplied to Sraffa by Besicovitch on 21 September 1944 is explored. Some reasons which led Sraffa to omit this proof in his book in favor of an incomplete argument is postulated