Abstract
While the routine use of Leontief’s closed model is limited to the case in which the whole income of an economy goes to wages, this paper shows that the model also permits the representation of production programs corresponding to every level of income distribution between wages and profits. In addition, for each of these programs, the model allows calculating the price system and the profit rate when this rate is the same in all industries. Thus, the results obtained in Sraffa’s surplus economy are established following an alternative way, this makes it possible to build a particular standard system for each level of income distribution between wages and profits. Besides, the fact that the model includes the set of households as a particular industrial branch permits to build a balanced-growth path of the economy in which the quantities of work used in each industry as well as the goods consumed by the workers are studied explicitly, unlike what happens in von Neumann’s model. The paper also shows that, under a weak assumption, the balanced-growth rate is independent of the worker’s choice.
Highlights
In the specialized literature, Leontief’s closed model is an instrument of analysis applied mainly to calculate certain relations between inputs and outputs in an industrial system and to calculate prices in the particular case when all the income goes to wages (e.g., Berman & Plemmons [1], pp. 258-265; Dorfman, et al [2], pp. 245-264; Leontief [3], pp. 33-65; ten Raa [4], pp. 11-12)
I show that it is possible to use it to calculate the price system and the profit rate corresponding to every level of income distribution between wages and profits when the rate of profit is the same in all industries
Since the replacement does not alter prices or the profit rate, it follows from Equation (26) that the value of λÆ has not changed, and according to Equation (33), the growth rate is still equal to g1, the vector q normally would have changed, as can be inferred from system (34)
Summary
Leontief’s closed model is an instrument of analysis applied mainly to calculate certain relations between inputs and outputs in an industrial system and to calculate prices in the particular case when all the income goes to wages (e.g., Berman & Plemmons [1], pp. 258-265; Dorfman, et al [2], pp. 245-264; Leontief [3], pp. 33-65; ten Raa [4], pp. 11-12). I show that it is possible to use it to calculate the price system and the profit rate corresponding to every level of income distribution between wages and profits when the rate of profit is the same in all industries. A distinctive feature of Leontief’s closed model is that the set of households are included as a particular branch of industry whose inputs are the goods consumed by workers and whose output is work. This procedure is an accounting devise facilitating the analysis whereas, in the balanced-growth path, the profit rate measures the growth of the quantity of labor provided by the set of households Including this introduction, the paper is divided in 9 sections and an Appendix.
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