Cambridge Capital Controversy Applied At The Level Of The Firm

For a number of decades, Arrigo Opocher and Ian Steedman have been developing arguments that apply the CCC to industries and even individual firms. They also draw on mainstream literature in microeconomics, from the 1960s and 1970s. Their 2015 book is a major statement of their position. Since their book's publication, they have continued research in this vein.

The CCC applies whenever you see a production function with capital measured in numeraire-units. This can be an aggregate production function for the economy as a whole, at the level of an individual industry, or even for an individual firm. Arguably, any model with such a component is incoherent. Opocher and Steedman, in their book, however emphasize a representation of technology in terms of cost functions. They consider cases with a rate of profits of zero and issues that arise even with disaggregated capital inputs or, even, no capital inputs.

I recently skimmed Steedman (2018). This looks at the incoherence of representing technology with capital-labor isoquants. Since constant returns to scale are assumed, the distinction between analysis at the firm and industry level is not definite. Many of Steedman's papers, with and without Opocher, present exercises for the reader. But I reacted to the following as if he was trolling me:

As was noted above for the general case, each k_j and each l_j is a known function of r; in the specific case of our example, (4), (5) and (7) permit the explicit calculation of k₁(r) and l₁(r). Since l₁(r) is always increasing, (d²k₁/dl₁²) has the same sign as [(dl₁/dr)(d²k₁/dr²) - (dk₁/dr)(d²l₁/dr²)] [Notation changed] ..., and some calculation leads to the conclusion stated in the text; unfortunately, the equations involved are rather long and tedious, so they are left for the amusement of the interested reader. In our example, it is possible to find k₁(l₁) explicitly but, again, the equation is not a pleasant one.

I suppose I may someday take up this challenge.

References

• Arrigo Opocher and Ian Steedman (2015). Full industry equilibrium: A theory of the industrial long run. Cambridge University Press
• Arrigo Opocher and Ian Steedman (2016). Recurrence: A neglected aspect of the Sraffian critique of marginalism. Metroeconomica 67(3): pp. 1-6.
• Ian Steedman (2018). Industry-level capital-labour isoquants. Metroeconomica: pp. 1-6.