Thursday, May 15, 2008

Robert Murphy On Sraffa: In Error

Some discussion with Peter Boettke has inspired me to point out some technical mistakes in Robert Murphy's on-line comments on Sraffa and reswitching.

I begin with Murphy's comments on reswitching. He looks at Samuelson's example in Samuelson's "Summing Up" article. Murphy implicitly suggests that reswitching is only possible in models in which a finite number of techniques are available:
"What Samuelson has done is simply invent a fictitious world in which there are only two ways of producing a particular good... Böhm-Bawerk felt that [his] story was accurate, because at any given time there are more technically efficient but very time-consuming processes 'on the shelf' that are unprofitable at the market rate of interest, but would become profitable at lower rates."
But reswitching is possible when a continuum of techniques lie along the so-called factor price frontier. That is, the possibility of reswitching is consistent with the existence of an uncountably infinite number of techiques. It is also consistent, of course, with the existence of only a countably infinite number and only a finite number of techniques.

Murphy also writes an equally informed comment on Sraffa's book, The Production of Commodities by Means of Commodities. I will adopt Austrian - in fact, Misian - terminology. Sraffa compares prices in Evenly Rotating Economies (EREs) in which the same commodities are produced with the same inputs. Under Sraffa's assumptions in the first part of his book, the construction of the so-called factor price frontier is perfectly valid mathematically. Murphy notes that Sraffa does not model utility-maximization and states that if utility maximization is introduced into the model, the location on the frontier becomes determined uniquely:
"Sraffa's techniques leave no room for the individual members of society to influence the methods of production that end up being used (whether or not there is a surplus), ultimately because there are no individuals in Sraffa's models... However, if we also require that the market rate of interest reflects the subjective premium placed by consumers on present versus future consumption—a feature lacking in Sraffa's aggregate models—then this will eliminate the multiplicity of equilibrium rates of interest."
But Murphy is, again, mathematically incorrect. Multiple equilibrium rates of interest can arise in an ERE model with utility maximization, including intertemporally.

One might look outside a model of an ERE. Murphy suggests he wants to consider models of an approach to an ERE:
"Sraffa's method of determining equilibrium prices in a surplus economy already assumes that the system has settled down at the optimum level of production in all possible lines."
The Arrow-Debreu model of intertemporal equilibrium, despite all its problems, is sufficient for my point here. In such a model of an economy not in an ERE, the equilibrium rate of interest at any point in time for loans of a given length is also not necessarily unique. Not only can multiple equilbrium rates of interest arise, so can a continuum of equilibrium interest rates, if the technology is modeled as discrete.

Why might Murphy be inclined to insist on mathematical error? Consider his statements:
"Sraffa derives results that depict a tradeoff between the real wage and rate of profits. In particular, Sraffa's analysis suggests that in a developed economy, the proportion of the 'surplus' that goes to the workers versus the capitalists is arbitrary, and not at all 'determined' by technological or economic facts... Although he was wrong to condemn interest as an unnecessary and exploitive institution, Sraffa was perfectly correct to criticize the conventional, mainstream justification of the capitalists' income."
But none of these claims, including about exploitation, are made in Sraffa's book.

22 comments:

YouNotSneaky! said...

Still waiting on evidence of the pervasiveness of reswitching in "actually existing economies" ...

Gabriel said...

It boggles the mind how much attention thought experiments involving exogenous shifts in interest rate can generate!

That being said, it would be fun to have a fully specified model in which the government sets the interest rate as a political outcome. (Since that's what I take to mean that particular theory of distribution.)

YNS!, while you wait, how about a new post, to help time pass faster? ;-)

Patch said...

(2006) Han, Zonghie and B. Schefold: An Empirical Investigation of Paradoxes: Reswitching and Reverse Capital Deepening in Capital Theory, Cambridge Journal of Economics 30.5, 737-765.

YouNotSneaky! said...

That's the 3.65% paper. 3.65%. Wonder how big measurement error is?

Anything else?

Robert Vienneau said...

Gabriel, Sraffa doesn't have a theory of distribution in his book. You're only describing one coherent theory. Others exist

Patch, "younot sneaky" is deliberately being rude and stupid. He's aware of the existence of such references as Albin (1975), Asheim (2008), Han and Schefold (200?), Prince and Rosser (1985), and Zambelli (2004). He basically wants to me to continue to respond to his bluster and balderdash from a comment section of another blog.

YouNotSneaky! said...

And you're being passive aggressive, dodgy, and ... confused? I've pointed out, oh, at least twice now, that the Zambelli paper is not an empirical paper at all yet you completely ignore this and keeps insisting that somehow it is. How is this possible? You are either confused as to what constitute empirical work or are just trying to pull a fast one.

You once again mention Han and Schefold, that patch already mentioned (double counting there) which finds the phenomenon in 3.65% of cases. Somehow this gets interpreted as encouraging evidence for widespread existence of reswitching. How, I have no idea.

Prince and Rosser and Albin documents that reswitching happened at one point in the mining or lumber industry. Great! This is exactly what I'm looking for. Now, is there more like this? Note that I'm not Garrison (2006) who says that NO instances of it have been documented. There you've picked too easy of a target which you keep shooting at instead of answering my question. I'm asking for evidence that these instances are widespread enough so that basing policy on their existence is a valid prescription.

Finally, the Asheim paper is the ONLY one which I had trouble accessing which statement you immiedietly generalized and claimed I was using inability to access as an excuse for my ignorance. Which was not true and it makes me wonder if "confused" is the proper way to describe your situation here.

Gabriel said...

YNS!, what sort of observations would qualify as sufficient proof to meet your challenge? (Enough to outweigh the issues of measurement error and model mis-specification and so on.)

Patch said...

Well, I don't really get it: What kind of policy based on the existence of reswitching are you speaking of? To me it seems that this whole debate is more about showing that it would be plain stupid to base policy on the kind of kindergarten economics that requires "putty" or "leets" or similar fictitious capital goods to work properly and to be able to make right policy recommendations.

YouNotSneaky! said...

Robert brought up reswitching in the context of the minimum wage. So there's the policy.

Gabriel said...

Patch, to paraphrase...

"To me it seems that this whole debate is more about showing that it would be plain stupid to base policy on the kind of kindergarten economics that requires X to work properly and to be able to make right policy recommendations"

where X could very well be "well behaved demand functions", "rational choice", "market clearing", etc. etc. etc.

What would make one assumption more attackable than another is the empirical relevance. Which explains the discussion.

Robert Vienneau said...

patch understands the conversation.

Gabriel, "well-behaved demand functions" are not an assumption. In (incorrect) marginalist theory, they are supposed to be derived on the basis of more basic assumptions. What are the special-case assumptions that you would like to introduce to rule out, say, capital-reversing? Neither empirical evidence nor better knowledge of the literature will help you with this question.

Over on Crooked Timber, younotsneaky! asked for empirical evidence of the existence of "Wicksell effects". I have a reason for generally not responding on my blog to younotsneaky's non sequiturs.

younotsneaky! says, "Robert brought up reswitching in the context of the minimum wage. So there's the policy."

No, I did not. I brought up capital-reversing.

Even if I had brought up reswitching, this would not justify the equivocating claim that I was "Basing policy on [the] existence [of reswitching] is a valid prescription." (It is equivocating because when a mathematician says "there exists", he is not making an empirical claim.)

Some might incorrectly think that a minimum wage above the (?) market-clearing wage must have a disemployment affect. That is, they would think that economic theory, at least if markets are competitive, justiifies their belief.

The theoretical possibility of capital-reversing shows that this belief is wrong.

Empirical evidence is not relevant to this point. Empiricalism could address this question: why do economists teach claims known to be logically invalid?

YouNotSneaky! said...

Annnnnndddddd...... once again Robert dodges the question.

By focusing on irrelevant details (like insisting that I should have said "positive Wicksell effects" rather than just "Wicksell effects", for example, among others).

Here, let me quote Barkley (whose paper Robert includes in the list of references) from the EH discussion list, though of course it should be well understood that Barkley in no way endorses my position on this matter, or any other position, for that matter. I just think he makes a lot of sense that's all;

"There are of course a variety of reasons that one might give for arguing that "reswitching
is irrelevant" (as Joan Robinson put it). Tony Brewer mentions one, the claim that it has
never been empirically observed. I would suggest that this is not the case, although it
is probably true that it is a relatively unusual empirical phenomenon within profit rate
ranges that are empirically relevant."

http://eh.net/pipermail/hes/2001-June/003861.html

But Robert says that empirical evidence doesn't matter here because 2+2=4. Ok. So if we rule out, on empirical basis, the possibilities of ... lemme be careful with my terminology here ... "these things" (and we all know what we are talking about here) then what is left of all this Sraffian stuff? Unless there is something else here, smugness of its proponents aside, it is nothing but a particular framework for coming up with contrived, empirically irrelevant counterexamples to some common neoclassical stories.

(btw, the 2+2=4 analogy is completely inapplicable here since all that Robert manages to establish is things that COULD happen, not that are guaranteed to happen in a way that two plus two is guaranteed to equal four. Hence, my query for empirical relevance. This is a basic distinction between the universal and the particular which I'm guessing Robert is choosing to ignore for polemic reasons. It makes for better a sounding argument but not for a better argument. Or even a good one. Why does Robert continue to claim things known to be logically invalid?)

I would also like to note that no where in this conversation, nor in any previous one that I ever had with Robert I called him names or insulted him. I disagreed. I said he was wrong. I was full of "bluster and balderdash" in the sense that I made my disagreements obvious when I though he was wrong. And when he dodged questions I said so. But if Robert's gonna call me "rude and stupid" I'd prefer he'd drop the phony courtesies and call me that in second person.

Gabriel said...

Robert,

Yes, yes, assume what you need to assume for well-behaved demand. Let's not be too pedantic!

My point of view is this... there are models in which "these things" don't happen and if those models are empirically successful, those are good models.

Also, regarding the claim of "logical invalidity"... you are free to deduce a contradiction from any of the applied models you criticize. But no one ever does.

If the use of the word "capital" bothers you, you can just read "consumption-investment good".

Robert Vienneau said...

Younotsneaky mistakenly claims: “we all know what we are talking about here”. I doubt it. In particular, if one is familiar with Ian Steedman’s work over the last decade or so, one would suspect that the Sraffian internal critique of neoclassical theory is not exhausted by reswitching and capital-reversing. Some of the numerical examples I have presented might even go towards this point, but not very far along this direction.

Younotsneaky writes: “this Sraffian stuff … is nothing but a particular framework for coming up with contrived, empirically irrelevant counterexamples to some common neoclassical stories.” This is confused for at least two reasons.

1) No evidence has been presented that “common neoclassical stories” constitute an empirically general case. Over on Crooked Timber, I included the following Graham White quote by citation at two removes:

"the absence of empirical results either way cannot be used as a defence of the orthodox position that the absence of reverse capital deepening is the ‘general case’. Orthodox analysis has no a priori basis on which to presume that what it considers to be the general case is in fact the general case. Such a defence would require a logically coherent argument as to why one should expect technologies admitting reverse capital deepening to be less likely than those that do not. No such argument has been provided by orthodox theorists."

(2) Although I might find a particular framework convenient for developing examples, the interesting characteristics of my examples are not dependent on some sort of special case or “particular framework”. For example, capital-reversing does not require a linear production framework with a discrete technology. Capital-reversing can arise in models with continuously differentiable production functions. Capital-reversing does not require only circulating capital to exist; one can use a model with fixed capital. Capital-reversing does not require that there be only one non-produced factor of production (homogenous labor); one can use models with many non-produced factors of production. Although this is disputed, capital reversing even has implications for models on non-steady state prices. (I can cite both Burmeister and Rosser here.)

Suppose one were not ignorant of mainstream responses to the Cambridge Capital Controversy. Then one would know that Bliss and Hahn, for example, claim that the “particular framework” was only a case of the more general framework of a General Equilibrium model of intertemporal equilibrium. (I, along with others, dispute this.) And they claim GE neither relies on nor provides a general defense of these “common neoclassical stories”. They don’t restrict this lack of a general defense to some sort of Sraffian “particular framework.”

Younosneakly’s balderdash continues: “Why does Robert continue to claim things known to be logically invalid?” This is based on a misrepresentation of what I say. I do not say one should raise the minimum wage because that will increase employment. I say that what you find in, say, a microeconomics textbook is supposed to be a general framework, maybe simplified for teaching purposes. And these “common neoclassical stories” are presented as logical deductions from assumptions in a model. To show that these claims are logically invalid, I do not need to show that, say, capital reversing is “guaranteed” always and everywhere to follow from these assumptions. I only need to show the existence of one counter-example consistent with the assumptions. And I need not show the empirical existence of this counter-example.

I have pointed out this already to younotsneaky over on Crooked Timber. So he is repeating errors. My query to state his special-case assumptions was directed to Gabriel. So I guess younotsneaky feels free to dodge that question.

The negation of an universal statement is not another universal statement.

n short, I’m not the one confused about the “distinction between the universal and the particular”.

Anyways, if one read that HES thread referenced by younotsneaky, one would have read Mathew Forstater. After providing a reference to an application and commenting on the peculiar sociology of the economics profession, Forstater writes: “In my graduate training I was taught that the issue of the empirical relevance of reswitching was neither relevant nor an issue. The empirical relevance of a logical inconsistency is not a scientific question.”

On that thread, Anthony Brewer responds in a way that I find confused. And tempers fly on that thread, too.

Gabriel said...

Robert,

I do not claim to be able to provide parsimonious restrictions for a baseline general equilibrium model that would rule out the phenomena you bring up. I agree that they would be useful, but that's not what I'm saying.

I'm saying there's no reversing or re-switching in Solow's growth model or in any of the hundreds of particular models used in applied work. If there was, then these problems would show up as a matter of calculus.

Sure, in a sense would you prefer a model with many goods to a model with a single consumption-investment good, but if the price for that is ambiguous signs on slopes... applied people say "pass" with good reasons.

Re: "logical invalidity", deduce the contradiction from a model in a major textbook and I'll believe you. If instead you mean that the verbal description joined with the models claims more than the models strictly imply, that's another matter, I think.

Lastly, and unrelated, you say "Capital-reversing can arise in models with continuously differentiable production functions.". Could you please provide a reference for that? It sounds interesting. Thanks!

Anonymous said...

Thank you for a thorough and detail ed response.

"the Sraffian internal critique of neoclassical theory is not exhausted by reswitching and capital-reversing. Some of the numerical examples I have presented might even go towards this point, but not very far along this direction."

Sure. But the basic point, for the purposes of this discussion, is the same - no monotonic relationship between factor intensity (and possibly employment) and factor price.

"1) No evidence has been presented that “common neoclassical stories” constitute an empirically general case."

On the contrary, labor demand curves have been estimated in numerous cases and they do seem to be downward sloping in most cases. If you think that these estimations are based on a faulty theoretical scaffold, then you can just think of it as "controlling for things which are likely to affects how much people wish to work, there is a negative relationship between wages and number of workers". Or in other words, there is plenty of evidence of diminishing returns to labor all over the place. Of course this doesn't clinch the case that reswitching (etc.) doesn't happen, or that intertemporal considerations don't play a role, even a "perverse role" occasionally, but it does make it seem like the "neoclassical story" is the usual one.
Try to explain 100,000 years of Malthusian stagnation without recourse to diminishing returns to labor.

"following Graham White quote...:

"the absence of empirical results either way cannot be used as a defence of the orthodox position that the absence of reverse capital deepening is the ‘general case’. Orthodox analysis has no a priori basis on which to presume that what it considers to be the general case is in fact the general case. Such a defence would require a logically coherent argument as to why one should expect technologies admitting reverse capital deepening to be less likely than those that do not. No such argument has been provided by orthodox theorists.""

I missed your inclusion of this quote. Presumably it was on an earlier thread. But THERE IS in fact a fairly straight forward reason for excluding certain phenomenon from consideration based on empirical evidence. Here I'll explain it with reference to reswitching. In particular to your own paper (a very useful one in fact - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=687492) on how to construct reswitching examples. Take the simplest case of one good and two techniques. Derive the wage-profit curves for both. Graph'em. Now, for reswitching to occur those guys gotta cross more than once. As in Figure 2 of your paper.

Ok. Now take a big red marker and draw a vertical line at some rate of profit, say 10%, and labeled it "maximum rate of profit empirically relevant", or "maximum rate of profit usually observed in the real world". For empirically-relevant reswitching to occur, those two curves have to intersect twice to the left of this line, rather than just anywhere. This makes it far more unlikely that this phenomenon will in fact be observed.

In this case, empirical data adds a constraint which allows us to differentiate between possible and feasible results. Note that this isn't even "direct" evidence but rather just a logical implication of the model.

Of course one would need to close the model with something which will determine wages and profit rates but as you've indicated before this isn't hard. Take the pure rate of time preference. But that's like 3%. It's going to be hard to get those to cross themselves twice that quickly.

"(2) Although I might find a particular framework convenient for developing examples, the interesting characteristics of my examples are not dependent on some sort of special case or “particular framework”."

You misunderstand what I mean by "particular framework". But ok.
BTW, if there is ONLY fixed capital, can it occur?

"Although this is disputed, capital reversing even has implications for models on non-steady state prices. (I can cite both Burmeister and Rosser here.)"

I'm not sure what you are exactly referring to here. A different way to put it may be that you can get "Sraffa-like" effects when you consider non-steady state prices.
The Price and Rosser paper is along those lines, since it doesn't compare steady states.


"Younosneakly’s balderdash continues: “Why does Robert continue to claim things known to be logically invalid?” This is based on a misrepresentation of what I say. I do not say one should raise the minimum wage because that will increase employment."

So the context of the discussion doesn't matter? And anyway, my comment on you claiming things which were logically invalid (i.e. it appeared that you were saying that just because something COULD be the case it MUST be the case) was more general.

"To show that these claims are logically invalid, I do not need to show that, say, capital reversing is “guaranteed” always and everywhere to follow from these assumptions. I only need to show the existence of one counter-example consistent with the assumptions. "

No. There is one good which can be used for investment or consumption. Some auxiliary assumptions. Everything else follows. This is the story. You want to tell a different story which has a possibility of a different ending. This is not showing that the other story is invalid. This does not constitute a counter example.

Now. You can say the first story is stupid and a bunch of hogwash because it is too simplistic or whatever. But at that point you do need to come up with a number of relevant EMPIRICAL counter examples.

"The negation of an universal statement is not another universal statement."

Exactly! And I never said that it couldn't happen. But in the absence of universal statements you have to go to the data to see which particular set of cases is more likely.

" peculiar sociology of the economics profession, "

The sociology of the economics profession is irrelevant as to whether reswitching and capital reversals actually occur in the real world. On the other hand, they're very rare appearance might have something to do with the sociology of the economics profession - the fact that it tends to ignore them.

As an aside, this talk of "sociology of the economics profession", while in some context a useful and interesting pursuit, in many other contexts basically borders on the ad-hominen. I could just as easily start talking about the "sociology of the heterodox economists" who prefer to shut themselves up in their bunkers, attack strawmen and chant their mantras, rather than develop an adequate theory of their own, support it with empirical research and also engage the rest of the profession in a meaningful dialogue rather than smug poses of the dedicated holders of the one true faith. But that'd be unfair, since it ain't exactly like that.

As a second aside, I also note that you extensively updated your original post on Empirical Evidence Exists On Sraffa Effects (http://robertvienneau.blogspot.com/2006/05/empirical-evidence-exists-on-sraffa_16.html)
Thank you. Couple comments;
First, it's striking how many of the examples come from stuff which essentially deals with environmental issues or natural resource extraction. I'm guessing (and I think Barkley says a similar thing on the Eh net) that this is because the phenomena are tied to the issue of discounting and in those two areas that plays a very big role. I would certainly be willing to consider as plausible that Sraffa effects are more frequent in natural resource extraction and in relation to environmental issues.
Second, again, I don't think all those analytical results and simulations are really about the likelihood of reswitching and capital reversals. Zambellis' isn't.
Third, it's also worth while to once again reference this book review: http://www.eaepe.org/?q=node/view/233
which offers a fairly negative assessment of the likelihood of these effects.

Finally, I still don't understand why Han and Schefold keeps getting quoted as evidence for relevance of these effects given how few cases they actually find (note the above book review quotes it as well, but in the support of an opposite conclusion)

" And tempers fly on that thread, too."

There was an unfortunate diversion from the topic apparently.

younotsneaky!
(sorry, google account problems)

Robert Vienneau said...

I'm not sure that YouNotSneaky! has a single valid point. I'll confine myself to one example.

"Third, it's also worth while to once again reference this book review which offers a fairly negative assessment of the likelihood of these effects."

Reati argues the neoclassical framework, in which firms choose among known processes with known costs, is mostly inapplicable. Instead, innovating firms lead to a new technique that is likely dominant for the whole range of feasible interest rates. That is, innovation moves the whole so-called factor price frontier outwards.

Since Reati rejects the framework, he also finds, say, reswitching unlikely. His treatment cannot knowledgably and validly be cited in support of the unlikelyhood of reswitching within the neoclassical framework.

Gabriel said...

Robert,

What does it mean for reswitching to be unlikely within a framework versus unlikely in the world?

Both YNS!'s and Reati's point is that reswitching is unlikely in the world (maybe for different theoretical reasons, but why would that be relevant to their conclusion?)

Also, although unfamiliar with any other texts by him, I understand that Reati doesn't "rejects the framework" but rather extends it with (or stresses) innovation.

For him, switches of known techniques is less likely, as a matter of empirics, than switching to new techniques.

I really thought that YNS!'s comment went to the heart of the issues, so I'm surprised to see you dismiss it entirely.

Robert Vienneau said...

Gabriel is, perhaps, misusing the word "switching".

Here's one of those other examples I mentioned that is neither an example of reswitching nor capital reversing.

Suppose firms know of a single process for producing output in each of two industries. So the the technique in use is (I0, II0). Suppose then the firms discover a new process I1 for producing output in the first industry, and that the new technique (I1, II0) is dominant over the whole range of the so-called factor price frontier for (I0, II0).

So firms adopt this new technique (I1, II0). Now suppose firms discover a new process II1 for producing output in the second industry, and, once again, the new technique (I1, II1) is dominant.

It can be the case that the technique (I0, II1), in which the first industry uses the process originally known, is even more dominant. So what one sees is firms adopting a new process in the first industry and then re-adopting the original process after a new process is adopted in the second industry.

As I understand it, I am describing the numerical example presented in:

Fujimoto, Takao (1983) "Inventions and Technical Change: A Curiosum", The Manchester School, V. 51, N. 1 (March): 16- 20

Suppose that the interest rate is given and Sraffa prices prevail (ignoring periods of transitions). Then the amount of labor employed per unit output in the first (non-vertically integrated) industry first rises and then falls as the wage rises.

So the observed data doesn't show well-behaved labor demand curves here. And, as I understand it, this is neither an example of reswitching nor even switching.

My point remains. Economists do not have a multi-good model in which common neoclassical stories are well-founded, that is, in which the conclusions logically follow from the assumptions.

And, as Gabriel and YouNotSneaky! are demonstrating, economists are socialized to be anti-intellectual. Consider their unwillingness and lack of curiousity about the details and logic of an argument. At least Gabriel says that he cannot state his special-case assumptions.

Gabriel said...

Thanks for the reference regarding what constitutes "switching".' Will look into it.

>> "My point remains. Economists do not have a multi-good model in which common neoclassical stories are well-founded, that is, in which the conclusions logically follow from the assumptions."

Of course your point stands, given that it was never challenge in this discussion. For all practical purposes, all taking part accepted the logical possibility of "Sraffa effects".

The challenge that YNS! made was for you to argue for the practical relevance of these effects, within the context of a minimum wage discussion.

My own suggestion was that the reason why the uncouth neoclassicals dare extend their policy advice to circumstances in which their reasoning doesn't follow (in the sense of logical inference) from standard assumptions is because experience shows that, to the best of out econometric dissection, factor demand really slope downwards and parables from the single good model are empirically tenable in the real world.

In other words, we'll settle for policy useful in this world, not in all (logically) possible worlds, in some of which Sraffa effects would frustrate neoclassical parables often enough, in practice.

Lastly, say what you will about me, but it's transparent, at least to me, that YNS! put serious thought into, and time reading on, the reswitching and reversing literature.

YouNotSneaky! said...

"Fujimoto, Takao (1983) "Inventions and Technical Change: A Curiosum", The Manchester School, V. 51, N. 1 (March): 16- 20"

While once again Robert resorts to discussion of issues which are irrelevant to the subject (again, no one said that "these effects" aren't theoretically possible, or even that they're NEVER empirically observable) it seems that Fujimoto has a better grasp of the situation; he does refer to his result as a "curiosum". I assume Robert realizes that a curiosum is something which is of interest precisely because it is rarely observed.

And I think Robert testifies pretty well to his own socialization here.

Gabriel said...

Don't fight! We can all be friends!

And speaking of it, I'm still waiting, maybe someone is going to throw a reference at me regarding "these effects" happening with differentiable production functions.