The first interpretation, the “mathematical solution,” views the market socialists as assuming away the problem of rivalry and proposing a nonrivalrous static price system in the hopes of simulating a competitive equilibrium. The second interpretation, views the market socialists as introducing genuinely rivalrous competition into their models without, however, being aware of the serious implications of this, particularly with respect to the question of what “common ownership of the means of production” means if rivalrous competition is permitted. Each of these alternative interpretations fails, in its own way, to appreciate the rivalrous basis of the market process.
Thus the Marxists condemned rivalry, the Austrians asserted its necessity, and the neoclassical market socialists either assumed it away or failed to recognize the consequences of its introduction into their models. The reinterpretation of the calculation debate that is offered in this study will attempt to locate the fundamental difference among these paradigms n their disparate views of rivalry and try in that way to explain what the controversy was essentially about.
—Don Lavoie, introduction to Rivalry and Central Planning: The Socialist Calculation Debate Reconsidered (Cambridge: Cambridge University Press, 1985), 25.
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