The aim of the present paper is to provide a logical reconstruction of the Marxian Theory of Value. This reconstruction is based upon the concept of abstract as opposed to that of homogeneous labor. Abstract labour is a social relation that holds in a market economy, (at least) whenever the profit rate is uniform; it consists in a comparison of the different labors through the exchange relationship. The author proved in a different place (see García de la Sienra, 1987) that (...) there exists a mathematical representation of abstract labor which is unique up to similarity transformations. The existence of this function — which is none other than the value function — is the basis of the present axiomatization, which includes detailed reconstructions of two of the most important models of the theory. (shrink)

The aim of the present paper is to attack some of the conceptual problems that arise when the framework of mathematical learning theory is applied to the description of the behavior of the firm, in setting prices and production quotas, in a competitive market. The goal is to depict the process by which the firm fixes prices and production quotas as a stochastic learning process. A solution to such problems is proposed which is based on statistical-decision concepts. The conceptualization of (...) the behavior of the firm by means of concepts pertaining to mathematical learning theory gives rise to certain mathematical problems, which are formulated here in rather precise terms. (shrink)