Nick Rowe On Reswitching And On Joint Production

1.0 Introduction

Nick Rowe has recently posted about two of my themes, reswitching and about joint production. He goes through some of the baseless defensiveness of economists who do not know their ideas on price theory were shown decades ago to be mistaken.

2.0 Multiple Rates Of Return?

Rowe points out the importance of worrying about uniqueness in certain contexts:

"How does the rate of interest affect his decision? (But watch out for that "the", because it hides a massive implicit assumption.)"

As I understand it, reswitching is compatible with a unique price solution to the problem of the choice of technique, properly formulated. I demonstrate that with this example, in which I give an algorithm for finding steady-state prices, given the real wage.

That algorithm does raise questions for the mathematician. Under what conditions will the equation for Net Present Value yield a unique, economically relevant rate of interest? And will the algorithm converge to a cost-minimizing technique? Perhaps the cost-minimizing technique will cycle through α, δ, γ, and back to α. These questions are particularly salient in the case of joint production. I have addressed these questions for one such example.

Let me turn to another remark from Rowe:

"Suppose the price of fertiliser goes down, holding the prices of all the different types of food constant. Will the farmer use more fertiliser?"

A question, for me, is whether this is a coherent thought experiment. The analysis of prices of production shows that it is not. If firms adopt cost-minimizing techniques, one price cannot be varied independently of all others. Otherwise, firms will refuse to produce some of the inputs needed for the next production period. Plans will be mutually incompatible. As Ian Steedman has shown, the answer to Rowe's question is indeterminate in an open model of firm equilibrium in which account is taken of which prices can be exogenous and which must be endogenous.

3.0 Analysis Of Fixed Points As A Start On Dynamic Analysis

Rowe writes as if it is a point in favor of neoclassical theory that a comparison of steady states differs from an analysis of a traverse path:

"But first notice something important. When I said 'as the rate of interest starts out high and slowly falls' I am not talking about a process that is happening over time. I am not saying 'suppose r is 100% in the first year, 99% in the second year, 98% in the third year...'. I can't be saying that, because In doing the NPV calculation I have assumed that r stays exactly the same in all years. I have assumed a perfectly flat term structure of interest rates. It's that assumption which lets us talk about 'the' rate of interest. Rather, I am imagining different possible worlds, and asking what happens as we slowly traverse from the first possible world, where r is and always will be 100%, to a second possible world where r is and always will be 99%, etc. And I am looking at what technique a farmer would choose in each of those many possible worlds."

Cambridge economists, such as Geoff Harcourt or Ian Steedman, were always clear that the analysis of the choice of techniques was about a logical point, not a process in historical time. Joan Robinson, of course, would not accepts Rowe's fudge about "slowly" traversing. This is the mistake she accused Samuelson of, although he denied that he ever meant his words to be taken in that way.

In response to capital-theoretic difficulties, neoclassical economics increasingly turned to analysis of temporary and intertemporal equilibrium. Two kinds of dynamics arise in such models:

• The dynamics of equilibrium paths.
• Instantaneous out-of-equilbrium processes that might approach such paths, for example, a tatonnement process.

Mathematicians begin the analysis of dynamics with an examination of bifurcations and the stability of limit points. Steady states, as examined in the analysis of the choice of technique, are limit points for temporary and intertemporal equilibrium paths.

I think it an open question whether capital-reversing and other Sraffa effects can be used to reveal the instability of either dynamics. Both defenders and Cambridge-Italian critics of mainstream economics have asserted that capital-reversing examples are not necessary to expose such instability. Basically, neither J. R. Hicks' model of temporary equilibria nor the Arrow-Debreu model of intertemporal equilibria are descriptive of actually-existing capitalist economies.

4.0 Reswitching With Continuous Substitution

In discussing joint production, Rowe suggests the usual confused claim that the issue is between substitutability and fixed-coefficients of production, as in Leontief production functions. He does not say that continuous substitution rules out reswitching. But, given the context, it would not be surprising if some of his readers took away that muddled view.

Of course, reswitching examples have been available for a long time in which the cost-minimizing technique varies continuously along the so-called factor-price frontier. In these examples, each capital good can be used and produced only with fixed coefficients. A continuum of capital goods exist however.

Furthermore, a continuously differentiable production function can be approximated as close as you like by a linear combination of fixed coefficient processes. So I do not know why some economists cannot let go of this canard.

5.0 Land And Fixed Capital As Examples Of Joint Production

Rowe does not seem to know about some standard analyses of joint production. The wool-mutton cases provides room for firms to simultaneously adopt two processes for producing both, but in different proportions. The quantity demanded, also known as requirements for use, if you will, enters into the story. But one still does not need to talk about schedules for supply and demand.

Some of Rowe's commentators bring up netput vectors. Nobody over there notes that fixed capital and land are special cases of joint products. I find joint production useful for analyzing depreciation and for analyzing rent. These special cases show why one cannot ignore joint production; it is ubiquitous in actual economies, even apart from oil refineries and other industrial processes that might be of interest to some chemical engineers. One might also turn to American institutionists for an analysis of overhead costs. Issues of joint production and the resulting accounting conventions have something to do with why industrial firms often adopt administrative pricing.

An analysis of joint production also presents an opportunity to construct more examples of Sraffa effects, which, of course, encompass more than reswitching. I do happen to have handy an example with fixed capital. This case illustrates that, given technology, a lower interest rate will not necessarily induce firms to operate machinery for a longer number of production periods. Sometimes the cost-minimizing technique at the lower interest rate mandates that the firm junk old machinery sooner.

6.0 Conclusion

I do not see why mainstream economists cannot learn price theory. Will what is entailed by intertemporal equilibria or how to analyze depreciation in the Von Neumann model always be a mystery?