Abstract
The paper considers the division of a production system into departments i and ii introducing a further division of department i into a homothetic and a complementary sector. It shows the existence of nontrivial upper and lower bounds for the capital stock and the wages that depend on this division contributing, among other results, to explain the quasilinearity of the wage-profit curve found in some empirical researches.
Highlights
El artículo estudia la división de un sistema de producción en los departamentos i y ii e introduce una división posterior del departamento i en un sector homotético y otro complementario
The division of a production system according to the final use given to the products of each enterprise, either as means of production or consumption goods, was originally introduced by Smith (1981: 288) and reformulated by Marx (1992: 471) who, like his predecessor, employed this division mainly to study the reproduction of the economic system
Von Neuman (1945) built a homothetic production system to study economic growth in a general equilibrium model and, from a perspective inspired in Ricardo (2004), Sraffa (1960) built another system of this type to study the relations between prices and income distribution
Summary
The first function represents the capital stock (equal to the cost of the means of production), the second one the wage and the third one the capital (equal to the amount invested), each variable being measured with the real income Using this notation we can write (2) in the following forms: a) KSr + w (1 + tr) = 1 and b) Kr + w = 1. We will assume in the four sections that t = 0 and its other possible values will be considered only in seventh section Under this assumption, the real income is equal to net product and for this reason, we will talk only about the last one in the corresponding sections
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