Tuesday, December 29, 2020

The Truncation Of The Economic Lives Of Machines

'Paradoxes' and 'Perversities'
Reswitching'One good'5
Schefold reswitching3
Schefold roundabout3
Recurrence of technique (without reswitching)Baldone9
Recurrence of truncation (without reswitching or recurrence of technique)Two sectors with fixed capital2
Non-monotonic variation of economic life of machine (without reswitching or recurrence of technique or of truncation)Baldone10
'Non-continuous' variation in economic life of machine associated with infinitesimal variation in rate of profits'One good'1, 5
Baldone7, 8, 9, 10, 11
Increased economic life of machine associated with lower capital intensity'One good'1, 3, 4
Schefold reswitching2
Two sectors with fixed capital1, 2, 3, 4
Baldone9, 10, 11
A lower rate of profits associated with a decreased economic life of a machine'One good'1, 3, 4, 5
Schefold reswitching2, 3
Two sectors with fixed capital1, 2, 3, 4
Baldone8, 9, 10, 11
Decreased roundaboutness associated with a lower rate of profitsSchefold roundabout2, 3, 4

I have been exploring simple models of fixed capital, of the production of commodities with machines that last more than one production period. And in these models, the efficiency of machines varies with age. An older machine might require greater care or produce more of a finished commodity after it has been broken in. The choice of technique becomes a question of the choice of the economic life of a machine. In the jargon, managers of firms decide on whether to truncate the use of machine and for how long.

One might think intuitively, but wrongly, that by first producing a machine and then using it in the production of a finished good that one was adopting a more capital-intensive technique than by directing producing the finished good. Likewise, one might wrongly believe that extending the economic life of a machine increases the capital-intensity of a technique. And that a lower rate of interest (or a higher wage) provides incentives to the managers of firms to adopt more capital-intensive techniques.

One can see that these beliefs are incorrect by looking at specific numerical examples. The table at the head of this post provides examples of curious phenomena seen for the fixed capital. Links are provided to specific examples. (The numbering of regions for the 'one good' example are not consistent over the years that I have been working on models of fixed capital.) I think that some of these effects have not been noted in the literature before, albeit I always suspect that Kurz and Salvadori's 1995 textbook might have a homework problem that I now understand the point of.

The truncation of machines is another aspect of the Cambridge Capital Controversy (CCC). But it was not made much of during the 1960s.

My research project of looking at parameter perturbations to identify fluke switch points and partitions of parameter spaces is hardly exhausted. Some research areas to investigate include:

  • Create and perturb examples of reswitching and capital reversing, for example, in models of fixed capital in which machines operate with constant efficiency.
  • Perturb coeficients of production and requirements for use in models with land, paying particular attention to the order of efficiency, the order of rent, extensive rent, and intensive rent.
  • Perturb coefficients of production and requirements for use in general models of joint production.
  • Revisit the above considering perturbations of relative markups among industries, instead of coefficients of production.
  • Develop computer programs to aid in these analyses.

And besides extending my results, I still need to make an effort to submit much of what I have for publication.

I have decided that applying these results in sensitivity studies of empirical results with National Income and Product Accounts (NIPAs) is probably beyond me. One might consider how perturbations and fluke switch points relate to specific types and biases of technical change. And one might state mathematical theorems and provide proofs.

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