Infeasibility Of All Machines Truncated

Figure 1: Factor Wage Curves For Feasible Techniques

There are 12 coefficients that can be varied in my minimum multisector model in which production in all sectors can require both fixed and circulating capital. I do not think I am being very orderly in exploring this twelve-dimensional space.

This is a fluke case in which the maximum rate of profits is zero for both the Alpha and the Beta techniques. If only new machines are used as means of production in producing new machines and in producing corn, no surplus product is available to pay out as wages and profits. Likewise, if a machine is run for its full physical lifetime of two years in the machine sector, but truncated in the corn sector, no surplus product is, once again, available. But this is a feasible technology in that a surplus product is available when machines are operated for a full two years in the corn sector. (If a_{1, 1} and a_{1, 2} are slightly increased, the maximum rate of profits is negative for both the Alpha and Gamma techniques. Then this would be a non-fluke case.)

Managers of firms choose among feasible techniques by deciding whether or not to operate machines for two years, or to truncate their use, in the machine sector. As shown by the wage frontier above, their decision varies with the distribution of income. Baldone (1980) notes the possibility that for a viable technology with fixed capital, the truncation of the economic life of a machine may result in a non-viable technology. In an already long paper, he does not have a numerical example, however. By the way, Baldone has an appendix with a numerical example of the recurrence of truncation.

For completeness, Table 1 specifies the coefficients of production. I also define the techniques, which are unchanged from previous posts exploring this model. I would be impressed if somewhere in this twelve-dimensional space, almost all phenomena noted in the literature for models of fixed capital and new cases could be found. I have yet to locate cases of reswitching in this model. By definition, I will not be able to find a 'one-good' model with reswitching in this model (albeit what happens if the coefficients of production are the same in the two sectors, perhaps extended to have the machine last three years?).

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)	(IV)
Labor	1/10	8	43/40	1
Corn	0.875	2.1875	0.125	0.282386
New Machines	1	0	1	0
Old Machines A	0	1	0	0
Old Machines B	0	0	0	1
Outputs
Corn	0	0	1	0.56
New Machines	2	5/2	0	0
Old Machines A	1	0	0	0
Old Machines B	0	0	1	0

Table 2: Techniques

Technique	Processes
Alpha	I, III
Beta	I, II, III
Gamma	I, III, IV
Delta	I, II, III, IV

References

• Salvatore Baldone (1980) Fixed capital in Sraffa's theoretical scheme. Trans. in Pasinetti (1980).
• Christian Bidard (2020) The wage-minimisation property. Working paper 2020-17.
• Luigi L. Pasinetti, ed. (1980) Essays on the Theory of Joint Production. New York: Columbia University Press.
• Bertram Schefold (1980) Fixed capital as a joint proudct and the analysis of accumulation with different forms of technical progress. Trans. in Pasinetti (1980).
• Paolo Varri (1980) Prices, rate of profit and life of machines in Sraffa's fixed capital model. Trans. in Pasinetti (1980).