Wednesday, August 22, 2012

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?

6 comments:

Nick Rowe said...

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

I wasn't talking about uniqueness of equilibrium. I was talking about whether the 2-period rate of interest was necessarily the same as the 1-period rate of interest. (It isn't, of course).

2. "A question, for me, is whether this is a coherent thought experiment."

Yes it is a coherent *thought-experiment*. A farmer's demand for fertiliser may depend on many prices. We can imagine designing an experiment where the experimenter varies one price, holds the others constant, and observes how the farmer responds. The fact that an exogenous change in (say) the technology of producing fertiliser will (almost always) cause almost all equilibrium prices to change, in a way that depends on *everyone's* preferences and technology and expectations etc. doesn't mean we can't do *thought-experiments* on a single farmer.

We can talk about the effect of (say) price of milk on the quantity of milk demanded, without necessarily having to talk about everything else that affects the quantity of milk demanded, or saying why the price of milk changed.

3. "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:.."

No I don't. I'm just making sure the reader understands the difference.

4. "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."

No I don't.

5. "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."

I explicitly mention that possibility in my post:

"Suppose there are two different breeds of sheep. One produces lots of wool, and the other lots of meat. Shepherds switch from one breed to the second depending on the relative prices of meat and wool. Since you can have half the sheep being the one breed, and the other half being the second, the PPF is still (weakly) concave to the origin. It has two corners, and a straight downward-sloping bit between the two corners where both breeds are used."

6. "Nobody over there notes that fixed capital and land are special cases of joint products."

I explicitly mention "capital" (and "machines"):

"Not all capital goods are like sheep, but most are."

"But machines and houses and students and refrigerators are like my car, and so are like sheep."

OK, I did not mention "land". Good point. I missed one example I could have added to my long list.

7. "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."

Oh yes one does. Because the marginal use value of mutton may diminish at a different rate than that for wool. So you need both demand schedules (plus the supply schedule for sheep, unless it's horizontal, which it most certainly isn't in the case of sheep, because sheep need land) to solve for the 3 equilibrium prices.

Nick Rowe said...

BTW: " The quantity demanded, also known as requirements for use, if you will, enters into the story."

We are agreed that people's preferences for wool and mutton are an essential part of the story in understanding the relative prices of wool and mutton.

We are agreed that fixed capital is like sheep in that both create two (or more) joint products.

So people's preferences for present and future consumption are also an essential part of the story in understanding the relative prices of present and future consumption, aka interest rates.

Nick Rowe said...

P.S. The two posts you respond to here are really the second and third in a sequence. You might have missed the first, which is also right up your street:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/08/how-i-spent-my-gap-year.html

Robert Vienneau said...

Thanks for confirming that the post on joint production is related to the one on reswitching. I did not not notice this one.

If I ever decide to post on why I find some writing styles annoying, I will try to remember to compare Rowe to Marshall. In my self-delusion, I thinks my tastes here are at least somewhat independent of whether I agree or disagree with what I perceive the author to be saying.

Nick Rowe said...

If you find my writing style annoying, that possibly explains why you did not read my posts very carefully.

You might also be interested in this post on the loanable funds theory, since I think you have strong views on that topic.

neroden@gmail said...

Shortage of wood and high labor usage in charcoal production led to the opening of mineral coal mines to use coal for heating.

High production of coal -- leveraging the large fixed costs in the mining -- made the steam engine a viable device.
...(cut to fit 4096 char)
But at this point we find that the coal is being *refined* for better use in its ironworking, heating, and steam engine applications. The refining process generates a whole lot of waste products.

The companies then looked for ways to sell the waste products. At this point, joint production becomes *crucial*. The joint production is what drove the creation of coal-gas-operated stuff (lighting, heating and so forth). It also drove most of the chemical industry, which used coal tar early on as a primary raw material.

(Cuts to fit length -- basically, same deal with oil industry)

The *entire* structure of industry for over a hundred years was driven by path-dependent choices from two causes:
(1) replacing a component of an installed system where resources were running out -- without replacing the whole system (whale oil -> kerosene, charcoal -> coal)
(2) Finding something to do with the waste products, converting single production into joint production.

In the case of gasoline, the switchover from kerosene production with gasoline as a byproduct to gasoline production was a slow process.

It's also worth pointing out that the use of the waste products was often a case of *induced demand*.

There was *no* demand for coal gas or coal tar, or methane from oil refineries or gasoline, initially. (The internal combustion engine was not originally planned to run on gasoline, either.) Advertising and marketing *created* such a demand, because these waste products were plausible-though-imperfect substitutes for other things for which there was a demand.

I have never seen a "mathy" economic model which incorporates advertising and marketing as one of the *core* elements, and I think this is one (more) of the really big problems with microeconomics.

When the most important economic changes of the last 200 years were driven largely by phenomena which conventional micro and macro *rarely even discuss*, you have a sick academic field.