"The Microeconomic Foundations of Aggregate Production Functions"

Figure 1: A Production Network

I here comment on Baqaee and Farhi (2018). I am still trying to absorb it. I suppose that it is nice that an economist at Harvard is revisiting the Cambridge Capital Controversy (CCC). (Where is Michael Mandler these days?)

My major criticism is they do not do what their title claims. That is, their supposed microeconomic foundations are still up in the air.

In many CCC examples, technology is specified in terms of fixed-coefficient production processes. Sometimes, more than one process is available for producing a specified commodity. This structure gives rise to a choice of technique. If one wanted, one could formulate a programming problem, in each sector, whose solution is a production function for that sector. This production function would not be differentiable everywhere.

Baqaee and Farhi, on the other hand, assume the existence of continuously-differentiable microeconomic production functions in each sector. In this paper, these production functions are specifically Constant Elasticity of Scale (CES) production functions. (As should be the case, their inputs and outputs are specified in physical units, not in price terms.)

I am willing to be convinced that this difference in starting points is a technical matter. Or that Baqaee and Farhi are making some progress towards a more complete framework that will include models of the production of commodities by means of commodities. I have some challenges, however.

There is a theorem whose status I am not sure of. It states that, given a continuously differentiable production function for a commodity that is basic, in the sense of Sraffa, for all techniques, reswitching is not possible. (Stephen Marglin was not the first to offer a proof of this theorem.) Thus, Baqaee and Farhi rule out, by assumption, many (most?) of the reswitching examples and much of the structure in the literature on the CCC. As they note, their assumptions do include an example from Paul Samuelson, in his 1966 "Summing Up" article. That example, had a flow-input, point-output structure, with no commodity basic in any technique.

Second, I gather Baqaee and Farhi think of themselves as starting with microeconomic data that is in principle empirically observable. These would be elasticities of substitution at points on factor demand curves that are chosen at an instance of time. Part of the point of the CCC is to question the existence of factor demand curves, including for intermediate inputs. In a comparison of long period positions, it is an incoherent thought experiment to vary one price at a time. On the other hand, as Han and Schefold have shown, empirical work can be based on given fixed coefficients processes. I think if Baqaee and Farhi were to take this point, they would have to rewrite a lot of their paper, including sections talking about the bias of technical change and macroeconomic elasticities of substitution between factors.

Baqaee and Farhi do have an interesting suggestion for visualizing a production network in logical time. (I've previously presented a less detailed approach from Bidard.) My diagram above is an attempt to expand on Baqaee and Farhi's approach. For each time period, four processes (a, b, c, and d) exist for producing one of two commodities from inputs of labor and those two commodities. The first two processes have the first good as output, and the second two processes produce the second good. The second commodity can be used for consumption, as well as a capital good in the production of either good. This is basically the technology for the examples in Vienneau (2005). The diagram could be simplified by not explicitly showing the demultiplexers and the summations.

References

• David Rezza Baqaee and Emmanuel Farhi (2018). The Microeconomic Foundations of Aggregate Production Functions. 26 November.
• Robert L. Vienneau (2005). On Labour Demand and Equilibria of the Firm. Manchester School 73(5): 612-619.

Some Contradictions Of Capitalism

I tend to be doubtful, albeit sometimes amused, by comments drawing on Hegel. But I thought I would adopt some of that sort of language for a post.

Capitalism constantly revolutionizes production, leading to a fantastic increase in productivity. An ever more diverse set of commodities is produced, including for consumption. Machines for making, controlling, and communicating with other machines, are constantly being introduced, reducing the labor time needed to produce any commodity.

For the diversity in commodities to be sold, workers, who constitute the most part of consumers, must develop their abilities to appreciate as much as possible. Likewise, they must developers their capabilities to be able to change the industry in which they work:

But if, on the one hand, variation of work at present imposes itself after the manner of an overpowering natural law, ... modern industry, on the other hand, through its catastrophes imposes the necessity of recognising ... variation of work, consequently fitness of the labourer for varied work, consequently the greatest possible development of his varied aptitudes... Modern Industry, indeed, compels society ... to replace the detail-worker of to-day, grappled by life-long repetition of one and the same trivial operation, ... by the fully developed individual, fit for a variety of labours, ready to face any change of production, and to whom the different social functions he performs, are but so many modes of giving free scope to his own natural and acquired powers. -- Karl Marx, Capital, Chapter 15, Section 9.

In this chapter, Marx also quotes from the Communist Manifesto, "All that is solid melts into air..."

But, yet, the time in which the worker is enjoying himself is time that he is not generating surplus value for the capitalist. And it is an accidental distinction that some goods can be marketed and some cannot. Furthermore, higher wages is a threat to maintaining the rate of profits. So the evolution of capitalism puts some constraints on what and how the workers can develop their selves. Furthermore, the development of flexibility in production capabilities is accompanied with anxiety at being made redundant in one's job, of recurrent unemployment, and the continual recreation of the army of the unemployed.

(Fans of Pierre-Joseph Proudhon might be interested that, around where the above passage appears, Marx talks about the "good side" and the "bad side" of these contradictions in the development of capitalism, in quite a different tone than in The Poverty of Philosophy.)

Catalog Of Neoclassical Responses To The Cambridge Capital Controversy

This is merely a list and, as usual, off the top of my head.

• Paul A. Samuelson (1966). A summing up. Quarterly Journal of Economics 80: 568-583.
• Mark Blaug (1975). The Cambridge revolution: Success of failure? A critical analysis of Cambridge theories of value and distribution. Institute of Economic Affairs.
• Joseph E. Stiglitz (1974). The Cambridge-Cambridge controversy on the theory of capital: A view from New Haven.
• Christopher J. Bliss (1975). Capital Theory and the Distribution of Income. Elsevier North-Holland.
• Avinash Dixit (1977). The accumulation of capital theory. Oxford Economic Papers 29: 1-29.
• Edwin Burmeister (1980). Capital Theory and Dynamics, Cambridge University Press.
• Frank Hahn (1982). The neo-Ricardians. Cambridge Journal of Economics 6: 353-374.
• Andreu Mas Colell (1989). Capital theory paradoxes: Anything goes. In Joan Robinson and Modern Economic Theory (ed. by G. R. Feiwel), Macmillan.
• Mario Ferretti (2004). The neo-Ricardian critique: An anniversary assessment.
• Gaetano Bloise and Pietro Reichlin (2005). An obtrusive remark on capital and comparative statics.
• Michael Mandler (). Sraffian economics (new developments). In New Palgrave, 2nd edition.

I could have cited many more references from Burmeister, Mandler, or Samuelson. I do not know if the last two were published as anything more than working papers. As far as I am concerned, most mainstream economists also ignore the neoclassical side of the CCC.

Women In Economics

Here is a list of female economists I have learned from or would like to know more about:

• Jane Marcet
• Harriet Martineau
• Charlotte Perkins Gilman
• Rosa Luxemburg
• Edith Penrose
• Joan Robinson
• Krishna Bharadwaj
• Anne Mayhew
• Phyliss Deane
• Victoria Chick
• Ingrid Rima
• Nancy Folbre

Obviously, this list reflects my interests and biases. This list is off the top of my head.