Abstract
Heterogeneous capital has already come up for a wide discussion in economic literature, but various types of heterogeneous labour having unequal wage rates have been rarely discussed, although they are also observable in an economy. The reason for this seems to be, at the outset, that one of the aims of economic analysis is to make clear the distributional relations between capital and labour. As for capital goods, there is no distributional difficulty, even if they are heterogeneous, because an equal rate of profit is applied to them.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
Note that when “skilled labour j” is mentioned, j ≠ 1. Also remark that education and training necessary for skilled labour are regarded as being the same.
In Okishio(3), the counterpart of (2) is written as γ = wE + γT + σ, (in the present notation). That is, the value of capital goods in the education sectors enters into the value-creating force of skilled labour. This, however, is incorrect as pointed out here.
As shown here, if the exclusive training period is considered, self-efforts become greater than unity. This is because selfefforts exerted in the education period are accumulated in worker j and reveal themselves when worker j starts working.
The following figure illustrates the accumulation of self-efforts to skilled labour.
It should be taken note of that, as mentioned before, γ plays the role of a peculiar operator. Write, for instance x̃ − Ax̃ = ỹ and premultiply (w,v,Y), and γyIII = o, because no value is produced in the third sphere.
(L,T) in A does not give the labour matrix of the hyper-closed system, because T here is not related to the production of value.
Let m = n = s =1, and all the variables and coefficients of (LP.I) and (LP.II) are scalars. Put B = 1, and one has Λo = L/ (I-A)Na and γo = 1/Na.
In a closed Leontief economy, one has a stronger result as max μ. >; o.
It will be convenient to make a note on the difference between the assumptions: Lxa ≥ 0s in §2 and Na> 0s in §3. Since productive labour alone is conducive to the production of value, a strict inequality with respect to actual employment seems to create no problem. A similar distinction between productive and nonproductive labour, as made in the prpof of Proposition 10 can be applied to that of Proposition 17, if B, A, L and F are specified as in this subsection.
Krause’s original theorem is proved for “r ≧ o”. This proposition is a simplified version. For details, see Krause (1).
Hollander’s original theorem is the conclusion (ii) here.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fujimori, Y. (1982). Reduction of Heterogeneous Labour. In: Modern Analysis of Value Theory. Lecture Notes in Economics and Mathematical Systems, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45543-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-45543-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11949-4
Online ISBN: 978-3-642-45543-8
eBook Packages: Springer Book Archive