Sunday, June 07, 2009

Backstop Technologies And Natural Resources

1.0 Inroduction
Patch writes:
"I just finished reading Pasinetti's

Lectures on the Theory of Production (New York: Colombia University Press and London: The Macmillan Press Ltd., 1977.).

It is a readable introduction of production price models and it gave me an idea of what actually is the difference between prices optimizing the use of endowments and production prices. But then again I found some problems and I thought I might ask you before I send an email to Pasinetti himself.

The most important problem is, how do the production models work if you don't have an endowment? If you need commodity A to produce commodity B AND VICE VERSA, you can't start off producing at all because you don't have the necessary A to produce B and vice versa. The second problem maybe already is solved but I don't know: Can you use these models to say anything about natural resources? These resources are 'given', but you don't have to use them up in the first period so you still need an optimization I think."
Luigi Pasinetti, I think, has an ability to distill his ideas and express them remarkably clearly. His Lectures is a great textbook, and I could easily imagine Pasinetti getting a "Nobel" prize. Perhaps Sraffa's abstractions can be combined with Joan Robinson's emphasis on historical time to provide insight into actually existing capitalist economies. If so, such an advance might be based on Pasinetti's work, especially on structural economic dynamics.

I think both of Patch's questions are good questions, and I am going to decompose each into two.

2.0 Proportions and Endowments
One can think of the first as asking one of the following:
  1. What happens if the means of production are not in the proportions needed for steady growth at the start of a production period?
  2. What happens if none of some input needed for a cost-minimizing technique exists at the start of the production period?
An orthodox economist might want to analyze the first question by talking about intertemporal equilibria, the turnpike theorem, or tranverses between long period equilibria. However:
"5. Thus, if Sraffa's propositions are to be contained in an 'orthodoxy', which as [Frank] Hahn states has the endowment of factors among its data, such a datum should be present also in Production of Commodities. But how can Hahn trace it since that datum is not there?

6. Hahn attempts to do so when he introduces a simplified model of 'neoclassical theory' involving two commodities - wheat and barley - each of which is both a capital good and a consumption good. He asserts that, in order to obtain Sraffa's uniform rate of return on the two capital goods, the initial endowments of wheat and barley must bear some particular proportion to each other, because 'It cannot be part of the doctrine of Sraffa that you are uninterested in whether there is enough ... wheat and barley to meet demand" (Hahn, 1982, p. 365; emphasis added). In other words, Hahn finds it inconceivable that the simple answer to the question he raises in that passage might be:
Yes, it can, and it is, part of the doctrine of Sraffa's that distribution and normal prices do not require the initial endowments of wheat and barley for their determination.
Clearly, Hahn has begged his question here. He has assumed, and not proved, that what constitutes a characteristic feature of 'neoclassical' theory by his own definition of it - the determining role of factor endowments - is present in Sraffa's analysis. To that extent he has assumed what he intended to prove, namely that Sraffa's analysis is a 'special case' of neoclassical theory.

In fact, as he tells us in his Preface, Sraffa's standpoint is that 'of the old classical economists from Adam Smith to Ricardo', and, as we shall presently see, this standpoint does not attribute a determining role to 'the endowment of agents'. Therefore, his analysis can hardly be a 'special case' of the 'neoclassical' theory, which does admittedly rest on such a role." - P. Garegnani, "Sraffa" Classical versus Marginalist Analysis", in Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory (Edited by K. Bharadwaj and B. Schefold), Unwin Hyman (1990).

The second question is addressed by postulating the existence of a backstop technology in which, say, B can be produced without the existence of any A. I think this accords well with experience. Maybe no industry in the USA today produces without inputs of computer software and hardware, at least indirectly. Yet clearly this situation has come about without computer software and hardware being produced forever in the past.

3.0 Natural Resources
I think of natural resources as falling into two kinds:
  1. Resources, like land in classical economics, that are given in quantity, cannot be manufactured, and provide services over a production period without ever suffering any diminution.
  2. Resources, like oil, that are used up over time and cannot be replaced.
Land is usefully thought of as a case of joint production. Many economists, including Pasinetti himself, have analyzed joint production. I think of Christian Bidard, Bertram Schefold, and Heinz Kurz & Neri Salvadori. I even have an example treating land in the theory of joint production.

Although issues exist in extending Sraffa's results for single production to the theory of joint production, I think how to treat exhaustible resources in the long-period method is more problematic. As I understand it, Kurz and Salvadori have treated exhaustible resourses in what they call the guano model.


BruceMcF said...

It would seem that you brushed up against one answer to (2) as you were answering (1).

The question is whether "reproduction prices" actually means reproduction.

Clearly, consumption of a non-renewable resource in excess of the available rate of supply of a renewable backstop resource is, intrinically, not indefinitely reproducible.

This suggests that if we were to determine actual prices of reproduction, and fictitious prices of reproduction under the fiction that pretends that non-renewable resources are in fact, renewable, we would arrive at different relative prices.

Robert Vienneau said...

I'm not sure that I accept that Sraffa's approach can handle a non-renewable resource like oil. I need to read more here. I think you are suggesting an interesting criterion for policy, though.

BruceMcF said...

As far as the question of the prices of reproduction go, there are of course no prices that will reproduce crude oil, so incorporating their prices into a Sraffian system mandates a quasi-reproduction concept, and it could well be that different specifications of quasi-reproduction will give different results.

Prices at the margin of production capacity would of course be in the nature of scarcity rents in a post-classical system, and it would only be prices within the margin of production that could be described using prices of quasi-reproduction.

The prices of reproduction of the equipment to harvest renewable energy sources is, by contrast, well posed within a "Sraffian System", without requiring a quasi-reproduction concept. However, for these as well, prices at productive capacity become scarcity rents on the surplus, so the prices of reproduction are within the productive capacity.

There is a substantial policy application for this, of course, given that under marginal cost pricing, low marginal cost, high fixed cost energy resource harvesting like wind-power can shoot itself in the foot by pushing the wholesale market price of electricity below the rate that will finance the capital cost of the turbine. Feed-in tariffs can be seen as a way to ensure that equipment to harvest renewable power can cover its reproduction price.

Patch said...

Sorry for the delay but thanks for your answer, Rob.
I read a bit and found this article you might be interested in:
"A critique of post-sraffian approaches to exhaustible resources",