How I spent my gap year

Some economists think the 1871 revolution was a big mistake, and led economics down the wrong path. They take their inspiration from pre-1871 economics, especially Ricardo and Marx, and proceed from there. Many of them are very smart and knowledgeable people. They think that most academic economists ignore them and know little or nothing about their work. I think they are right about that. And I think that many of them get frustrated because they think they've got something important to say and the people who most need to hear it don't listen or don't even know they exist and so continue down their wrong path in blissful or even willful ignorance.

One of the problems in the economics of search is that you need to form some sort of estimate of the probability that search will be successful. And how can you know that probability before you've done a thorough search and found out what proportion of rocks contain gold? It's a bit like that in deciding what to read. You won't know if it was worth reading until after you've read it. But there are far more things that might be worth reading than you can possibly read. So you follow various rules of thumb that seem to have worked for you in the past. You read a new book by an author whose previous books you had read and liked. You follow the recommendations of other readers who have read and liked the same books as you. But rules of thumb like this can be self-replicating. You can get stuck in a genre. There must be some very good authors out there that nobody reads simply because nobody reads them. And different circles read different authors simply because different circles read different authors. Search equilibria may be path-dependent.

I didn't take a gap year between school and university. I took a gap year in the middle of my PhD program, when I should have been writing my thesis. I didn't tell anyone I was taking a gap year. It's hard to monitor what PhD students are doing when they have finished their courses.

Probably like most, my gap year was a wasted year, when looked at ex-post, and even ex-ante, from the perspective of what was good for my career. I should have spent the time sticking to my knitting and banging out three money/macro essays for a quick thesis. But I needed to do it.

When I told Ian Steedman (he was visiting Carleton in the 1980's) how I had spent my gap year he could articulate my reasons and how I felt at the time better than I could. It was partly just sheer curiosity and looking for something new, because maybe the economics I had learned might not be the whole story, even in broad outline, and had probably left a lot of interesting stuff out. And it was partly inspired by taking David Laidler's History of Thought class. But it was also an almost existential self-doubt, when you wonder if everything you think you know and identify yourself as believing might be totally wrong. And I had vaguely heard about those economists who thought that economics had taken the wrong path in 1871. And they weren't just saying that post 1871 economics needed improvement, or wasn't a perfect fit empirically (so what else is new?); they were saying that post-1871 economics was logically flawed. That was an existential challenge.

So I gathered up my courage and started reading, more or less at random. It had to be more or less at random, because the very nature of the problem was that I might be stuck in a path-dependent search equilibrium reading the same genre as all the people I knew, and I couldn't trust any guide, even if I knew one.

Eventually I abandoned my search and went back to writing my thesis. I didn't abandon my search because I became certain that the critics were wrong, though my search did eventually increase my subjective probability they were following a path that would lead nowhere very interesting. There was always the possibility that I would find gold if I just looked under the next rock, or dug deeper under a rock I had already looked at. But I was running into diminishing expected returns, and there was an opportunity cost to my search as well. Not just writing my thesis, but spending the time reading about asymmetric information or thinking about doing macroeconomics with imperfect competition seemed more valuable alternative uses. Time spent searching in one area has an opportunity cost. It wasn't a waste of time, because I did learn stuff. And it forced me to think through stuff that I thought I understood so I could understand it better than I did before. But it didn't seem worthwhile on the margin to continue any further.

The 1871 revolution in economics (Jevons, Menger, Walras,.. and Marshall, when classical economics became neoclassical economics) is usually called the marginal revolution. Which makes it sound rather trivial. Calculus wasn't exactly new in 1871, and if someone is choosing something to maximise something then looking at first derivatives (which is what things like marginal utility and marginal product are) seems sort of obvious. What was revolutionary about 1871 was the subjectivist revolution. Thinking about margins mattered only because thinking about margins made it possible to think about goods having subjective value. Otherwise you are stuck wondering why water should be worth less per gram than diamonds, when we would prefer living with no diamonds than dieing of thirst wearing diamonds. Water has higher total utility but lower marginal utility.

Goods don't have value; people value goods. It doesn't matter how much labour or other resources were used in the past to produce this good; if nobody wants it now or is expected to want it in future, it has no value. Why is the labour of a skilled soccer player worth more than the labour of a skilled cricket player, when both had to practice equally hard to create those rare skills? Because people prefer watching soccer to watching cricket. You cannot separate the theory of distribution from the theory of value, and both value and distribution depend on preferences. Is labour even a cost of production? Not if that labour is spent doing something that, at the margin, I find enjoyable, like fixing my car. Thinking about economics like that was a revolution.

If people were all converted by some millennial cult and suddenly stopped caring about the future, and only cared about the present, then the prices of all assets, both real and financial, that could not be physically converted into goods that created immediate pleasure, would immediately drop to zero. Nobody would pay anything for any future benefits those assets might create. Both saving and investment would go as far negative as is physically possible. You simply cannot talk about capital and interest without talking about people's subjective preferences for future goods.

Right now there is a stock of capital goods of many different types. And if markets are competitive those capital goods, like all the different types of labour and different types of land, either individually or in combination with other resources, are earning rents equal to their value marginal products. (Or marginal revenue products if markets are imperfectly competitive.) And people have expectations about the streams of rents those assets will earn in future. And asking how much we value those assets is to ask how much we value those streams of future rents. And the answer, in part, is inherently subjective. How much do we value the expectation of those future streams of goods that the expectation of those future streams of rents will let us buy? And our subjective evaluations of those future goods will in part determine the current price of capital goods, which influences the current production of new capital goods, which will influence the future stocks and the future value marginal products of capital goods. So, if we are rational, our expectations of streams of future rents will take into account the current and likely future production of capital goods.

I just don't see how you can talk about value, capital, and interest, without talking about people's subjective preferences for current and future goods and people's subjective expectations about the future. Far from leading economics down a fundamentally flawed and logically incoherent path, the 1871 subjectivist revolution seems to me to be an essential pre-requisite of any coherent understanding of value, capital, and interest.

How do people form their subjective expectations about the future? Good question. But we can't duck it by ignoring those subjective expectations. They matter. If everybody expected that all capital goods would fall apart tomorrow, or they thought that people would suddenly stop wanting the particular goods those particular capital goods could produce, the current prices of those capital goods would drop to zero. Unless you could eat the capital goods now.

It was over 30 years ago now, my memory is not good, and it was a random search, and so I can't remember what I read and didn't read, or read part of and abandoned. And I didn't understand some of what I tried to read and understand. I abandoned Sraffa's book, which isn't exactly user-friendly, because he just jumps right into the algebra. My attempt to understand his quest for Ricardo's invariable measure of value was a bit like an atheist trying to understand the quest for the Holy Grail. Not just "Why are you looking?", but "If you did find it, how would you know you had found it?" and "what would you do with it if you did find it?"

I'm pretty sure I understand why "The rate of interest is determined by the marginal product of capital" is wrong, except under very special assumptions. But a simple Irving Fisher diagram is sufficient to show that that is wrong. Or a simple model where there is no capital and no investment and only consumption loans tells you it can't be generally right. Or a model where there is only land that produces wheat and wheat is measured in tons and land is measured in acres so the marginal product of land has the units tons per year per acre which can't possibly be equal to the rate of interest, which has the units per year, and how you need to talk about people's preferences between wheat today and the stream of future wheat an acre of land can give you to determine the price of land in terms of wheat and thus the implied rate of return on buying land.

A few years later Luigi Pasinetti lent me one of his papers which, IIRC, had a pure consumption economy with no capital where the rate of interest was determined by people's subjective preferences for future vs current consumption. His paper seemed right to me. It was simple and clear. And it was consistent with my prior beliefs. But it was the only such paper I remember from those who think 1871 was a mistake, and it was a paper that seemed to be saying that 1871 wasn't a mistake, because it showed that subjective preferences matter??

My gap year was a very confusing year. I still can't really figure out what it was all about. Apart from the occasional flashback, I have moved on, because other things seem more worthwhile. But I really did try to listen, and understand.

Addendum: I was reading through the Wikipedia for Luigi Pasinetti, just to refresh my memory and see what I might have missed. It's a very good Wikipedia, which someone has clearly taken the time to do well.

Some notes:

1. There's a typo in equation 1.1 or 1.5. The X should be Y or vice versa. (No big deal. Just to show I was paying attention and understanding what I read.)

2. Consider these two sentences:

"At the same time, prices though of course not equal to, are exactly proportional to the quantity of labour embodied in each commodity. This is a perfectly clear labour theory of value."

The first sentence is missing an absolutely crucial three words, and that omission is the only thing that makes it appear that the second sentence follows from the first. Those three words are :"at the margin". Because it is certainly not true in Ricardo's model that prices are proportional to the average quantities of labour embodied in each commodity. The total exchange value of wheat produced, divided by the total quantity of labour used to produce it, is greater (in Ricardo's model, and as presented in the Wiki) than the total exchange value of gold produced divided by the total quantity of labour used to produce it.

We normally interpret the labour theory of value to be about average, not marginal, quantities of embodied labour. In which case the labour theory of value is false in the Ricardian model.

If instead we interpret the labour theory of value to be a statement about the marginal quantity of labour embodied (the extra amount of labour needed to produce one extra ton of wheat) then the labour theory of value is also true in the neoclassical theory. Because the quantity of socially necessary labour embodied at the margin is just the reciprocal of the marginal product of labour. If that's how you define the labour theory of value, then the labour theory of value is true in neoclassical models. It's true for each and every different type of labour. And the land theory of value is true too. And the oil theory of value is true too. And the screwdriver theory of value is true too.

Gimme a break guys. We figured this all out in 1871.

Then my ADD kicked in again.

The best paper I read in my gap year was Herbert Gintis and Samuel Bowles "Structure and Practice in the Labour Theory of Value" (abstract, full article gated). Two Marxists (at least I thought they were sort of, at the time). They start out by laying out clearly and simply several devastating arguments against the labour theory of value. All the arguments I had previously heard of, and maybe a couple I hadn't. By this time they really had my full attention and massive amounts of credibility. "I have no idea where they are going with this, and how they can possibly escape like Houdini and still say there's some validity to the labour theory of value; but I sure do want to listen to what they say!" And I was handsomely rewarded by a presentation of what would later be called the "efficiency wage theory of unemployment".

There is some gold out there.

Comments

[Ryan]

The way this post starts out, it nearly implies that your gap year occurred in 1871. I know you always make jokes about your being old, but this is ridiculous! ;)

Great post. I really enjoyed it.

[Nick Rowe]

Thanks Ryan! I was going to call it "1871 and all that", but then I thought that only old Brits might get the joke.

[Nathan Tankus]

"Goods don't have value; people value goods. It doesn't matter how much labour or other resources were used in the past to produce this good; if nobody wants it now or is expected to want it in future, it has no value. Why is the labour of a skilled soccer player worth more than the labour of a skilled cricket player, when both had to practice equally hard to create those rare skills? Because people prefer watching soccer to watching cricket. You cannot separate the theory of distribution from the theory of value, and both value and distribution depend on preferences. Is labour even a cost of production? Not if that labour is spent doing something that, at the margin, I find enjoyable, like fixing my car. Thinking about economics like that was a revolution."

um.... that's why it's called "socially necessary labor time" not "random labor somebody just starts to do time"

In the first couple chapters of Capital Marx sets out pretty clearly that items only have value in a society (in the case marx examined, simple commodity production societies )through the particular social relations that items are produced and distributed in that society (production and exchange). This is very basic and certainly wasn't discovered by the subjective marginalists.

[Nick Rowe]

Nathan: but once you add the "socially necessary" bit, and unpack it, and follow it where it leads, it leads right away from the labour theory of value. If some goods were "socially necessary", even if they embodied no labour, and even if we had forgotten or were unable to reproduce them, would they still have value? And the answer is "yes", if they have positive marginal utility. And even if we can reproduce them, it is equally true to say that the value of diamonds determines how much labour we will expend at the margin to find an additional diamond, rather than the reverse. Would people spend so many days digging for an extra diamond if we didn't value them as much as we do?

[Nathan Tankus]

@Nick: so? Marx never actually called his theory a labor theory of value. that's an application of critics and enthusiasts alike.

you can analyze those goods in a framework that isn't marginal utility theory. You're also making a dig at Marx for essentially not having the logical method that you had. Marx starts at what he sees as the beginning and goes out from there. he never got close to finishing capital. not to mention that major important works weren't published until the sixties and seventies. even more recently too. the first draft to volume three is finally being published in English next year!

[Greg Ransom]

The word "subjective" used above is a multiple pun -- the word is used to do all sorts of DIFFERENT work, related by not the same.

Example, the logic of marginal valuation gets the label "subjective" but that logic is itself inter-personally & universally valid, and you can explicate it in the universally shared language of math. But individual perceptual judgments of local opportunity spaces in unique places and times is NOT inter-personal & universal.

But we use the word "subjective" for both of this. Ie the word subjective is equivalent to a _pun_.

If you want to make progress in this domain of problems, you have to punt the word "subjective" and replace it with clear articulations of the different issues at hand.

[Greg Ransom]

Note well that the revolution of 1871 applied the logic of relational valuation at the margin successfully only to consumption goods.

And the hints at how to apply that logic to production goods thru time found in Jevons & Bohm-Bawerk did not fall successfully to conquest by mathematics.

There is an interesting yet unwritten history of how folks attempted to successfully extend and complete the revolution of 1871 into production goods which took place from the 1920s to the 1940s.

The result was a huge fault line which opened up in marginalist economics -- Hayek's program to extend and complete the 1871 revolution into capital goods led to the work of Harrod and then Solow (see Hicks on this) which constituted essentially a giant retreat & FAIL for marginalist capital theory involving more than one capital good, ie involve the real sort of environment in which real production goods get their value.

What Hayek & others sensed in the 1920s -- that Bohm-Bawerk's "Average Period of Production" would fail as a cheat stand in for marginalism applied to multiple production goods across time proved out in further research across the next few decades.

So the first thing we need to reckon with is the fact that marginalism fails in the domain of multiple production goods by the standards of formal system building and proof dominant among economists in the 1950s.

So this formal/object type of "subjectivism" comes into play in thinking about the valuation of multiple production goods across time BEFORE the non-objective/formal aspect of 'subjective" expectations comes into the picture.

[Nick Rowe]

Nathan: "Marx never actually called his theory a labor theory of value. that's an application of critics and enthusiasts alike."

Hmmm. Interesting. I didn't know that.

Yep, if Marx had lived longer, and had started writing later, he might well have written something very different. But we work with what we have. And sometimes I do come across people who are *sort of* Marxists, who have nevertheless come to grips *in some sense* with 1871 (and also maybe methodological individualism). And they are very interesting writers. Jon Elster? Herb Gintis (or is it Sam Bowles, or both, because I get the two muddled)? But they are *very* different from other Marxists who haven't come to grips with 1871.

Greg: OK. There are preferences, and there are beliefs. And I called both "subjective", even though preferences and beliefs are not really the same. But for my purposes here, both matter for value theory.

[Greg Ransom]

The fact that the problem of 'imputation" re production goods is insolvable formally both for the individual and within an equilibrium construct does nothing to obviate the fact that people are chosers between future focused alternatives at the margin, ie this fact does nothing to make objective cost theories true.

[Nathan Tankus]

@Nick Rowe: I see we are still following down the narrative that those who reject marginal subjective utility theory don't understand it.

[Ed Seedhouse]

It's good to see you pointing out that nothing has any inherent value, but that as you say, people value things. Good start.

But you didn't seem to take what seems to be the next step and point out that different people value the same things differently. Or is that what you mean by "utility"? If so it would have been nice if you'd explained that.

So there's a problem with money as a measure of value. Physical objects don't generally change their lengths randomly so we can define a "centimeter" and everyone can more or less agree that a given stick is x centimeters long and it works fine until we get down to the quantum level.

But how do you define the value of money when the thing you are measuring varies from person to person?

I think that Chartalism is the only sensible explanation of why fiat money has value as a medium of exchange. Can you point out the fallacy of Chartalism (assuming you think there is one, which you seem to)?

But of course if Chartalism is right isn't Neoliberal economics pretty much wrong by definition?

[Ed Seedhouse]

Forgot to mention that the "labour theory of value" is, I agree, obviously wrong. Labour produces goods and services which people value or don't value. If you are smart you produce stuff that lots of people value, but just producing something doesn't make it valuable unless other people want it and are willing to give up something of value for it.

Take Emily Carr's paintings (just to be patriotic I will ignore poor old Vincent). Lots of labour went into them but no one valued them much until well after she died. Now people value them in the hundreds of thousands. Without her labour they would not exist, but how did her labour produce the value we place on them today?

[JKH]

“Calculus wasn't exactly new in 1871”

Yeah – like in the 1600’s?

http://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy

Why so long for economics to use it?

Did neoclassical economics over-compensate for the late start?

[Nick Rowe]

Greg: so what's wrong with the model I sketched out above, which does not assume a single capital good? (It's hardly new or original). Are you saying a competent mathematician couldn't build and solve that model, with say 2 capital goods? The only really tricky bit mathematically is taking into account rational expectations of future rents. If you assumed static expectations instead, it's not that much harder than a single period model. Time preference gives you the relationship between rents and capital goods prices.

Even with perfect foresight/RE, it's no different from an Irving Fisher diagram with lots more dimensions to the PPF.

[Greg Ransom]

"Greg: OK. There are preferences, and there are beliefs. And I called both "subjective", even though preferences and beliefs are not really the same. But for my purposes here, both matter for value theory."

Yes, both matter for economic explanation, but their explanatory role is very different, and the "belief/desire" model falsifies the causal role of rival & constantly adapting alternative judgments about current environments and the unfolding of physical and relative price relation across time.

[Nick Rowe]

Ed: "But you didn't seem to take what seems to be the next step and point out that different people value the same things differently. Or is that what you mean by "utility"? If so it would have been nice if you'd explained that."

I take it for granted that different people value things differently. But if you and I both eat apples and bananas, even if you and I have different preferences, it will still be true that the ratio of my marginal utilities for apples to bananas MUa/MUb will be equal to your ratio. That's because both our ratios will be equal to the price ratio. I.e.

[MUa/MUb]Nick = Pa/Pb = [MUa/MUb]Ed

"I think that Chartalism is the only sensible explanation of why fiat money has value as a medium of exchange. Can you point out the fallacy of Chartalism (assuming you think there is one, which you seem to)?"

See my old post.

"But of course if Chartalism is right isn't Neoliberal economics pretty much wrong by definition?"

No. I can imagine a Neoliberal who thinks that fiat money only has value because of state power to tax. They probably exist too. Maybe some gold bugs fit the description.

[Nick Rowe]

JKH: "Why so long for economics to use it?"

Good question. I don't know the answer (though I *think* some might have used it in some applications before 1871). You need a real historian of thought to answer that one. Or try to.

[Greg Ransom]

Nick, here is one way to think about or get a grip in two very different things that most economists fail to distinguish between.

"Information" as a construct built out of intersubjective/object 'givens' in a model is a very different thing from unique rival understandings of the significance of unique never to be exactly repeated local environments and relative price conditions.

There are two ways to think about Hayek's knowledge problem applied to production and consumption goods thru time -- both of them called "subjective" perspectives by economists.

The first way attempts to come up with a math construct which purely formally 'coordinates' the relations between sets of 'given' information provided in different "agents" in the form of probability distributions.

The second way considers how individual judgments of local conditions and relative prices must constantly evolve and adapt through learning, working as a bottom up causal mechanism to create some degree of constantly adjusting plan coordination across time involving every changing production processes and consumption plans.

If you get the distinction you get that there are two radically different ways to conceive "subjectivism" as an explanatory program in economic science, the first of them non-causal and causally non-explanatory -- misleading even to the point of leading countless economist to misapprehend what is just a model and what is the real work, mistaking a toy math construct for "the economy" (see for a similar critique Milton Friedman's review of Abba Lerner's _The Economics of Control_).

[Nick Rowe]

Ed: I like the Emily Carr example. But you might be amused by an earlier example, also Canadian. De Quincy ("Confessions of an English Opium Eater" guy) was an early precursor of subjectivist value theory. He said that the value of a musical snuff box in Birmingham(?) is determined by labour needed to make it. But the value of the same musical snuff box, *in a canoe in the middle of Lake Superior(?)* (the wildest place he could imagine) is determined by subjective value of those in the canoe.

[Frances Woolley]

Nick, enjoyed this post, must remember to forward it to David Laidler ;-)

It seems to me that where econ is going right now is trying to explain where preferences come from - whether that's neuro economics, behavioural economics, or evolutionary economics. Are we at the verge of a paradigm shift, where we no longer accept that it's impossible to look inside people's heads, read their minds, and know how/why they value things?

[Nick Rowe]

Frances: Oh God, this is just between you and me and the internet. For God's sake nobody show it to David!

Yep, I think that's what some people are trying to do, and I wish them luck! That's all I can do. I have no idea if they will succeed, or what the answer will look like. I think the big question will be: what sort of feedback there is from the rest of the economy to preferences? That's what might lead to a big paradigm shift. We know there's almost certainly some feedback. Hey, just think of diamonds and deBeers and engagement rings!

[Michael]

Nick, you ask: "what's wrong with the model I sketched out above, which does not assume a single capital good?"

In your model is their a uniform rate of profit on the capital goods? One of the responses to the 1960s debate was to use the Arrow-Debreu model which can handle heterogeneous capital goods. But heterogeneous capital goods are not substitutable and thus the notion of a long run equilibrium is lost. There is no uniform rate of profit is this approach. Have you solved that problem?

For those interested in another point of view, Matias Vernengo provides some useful comments here:

The capital debates: A brief introduction

Microfoundations and the capital debates

And, perhaps it should be pointed out that the prices in Sraffa's 1960 model are simply long-run equilibrium prices-of-production, the book does not have a labor theory of value. Even Marshall thought that long run equilibrium prices were determined by production cost; utility determined only short-run price in Marshall.

[Will]

"But the value of the same musical snuff box, *in a canoe in the middle of Lake Superior(?)* (the wildest place he could imagine) is determined by subjective value of those in the canoe."

That's actually pretty close to Ricardo's story:

"There are some commodities, the value of which is determined by their scarcity alone. No labour can increase the quantity of such goods, and therefore their value cannot be lowered by an increased supply. Some rare statues and pictures, scarce books and coins, wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity, are all of this description. Their value is wholly independent of the quantity of labour originally necessary to produce them, and varies with the varying wealth and inclinations of those who are desirous to possess them." (from the fifth paragraph of his Principles)

Ricardo does seem to want to express scarcity values in labor terms, as he succeeds in doing for rent and interest. But can't find a way. The American economist Henry Carey actually thought he had found a way in the 1840s: he said that the higher value of scarce or monopoly goods resulted from the "wasted" labor of all who worked to get possession and failed -- Tom Hanks's paycheck would be a measure of myriad failed actors' labor. A rather charming theory, though not the most convincing.

[Mike Sproul]

"I can imagine a Neoliberal who thinks that fiat money only has value because of state power to tax."

Correction: because the state that issued the money has ASSETS, one of which is its power to tax

[Nick Rowe]

Michael: lets take an even simpler example. Instead of two types of capital good, let there be two types of land. Clay land only grows wheat, and earns $10 per acre per year rent. Sandy land only grows veggies, and earns $5 per acre per year rent. I don't know what the price of land will be, without knowing people's time preference. But I do know that the price of clay land will be double the price of sandy land, (assuming people expect rents and land prices to stay the same). So the two types of land will have the same rate of return. Simple arbitrage. Everybody would want to sell clay and buy sandy if sandy gave a higher rate of return.

Now let's change the assumptions slightly. You can clear more forest to create more land. Which means that "land" is now economically equivalent to "capital". Does it change my story? No. Unless it changes people's expectations of the paths of future rents and land prices, which it may. But the (expected) rates of return on clay and sandy land will still be equal. By simple arbitrage.

"Even Marshall thought that long run equilibrium prices were determined by production cost; utility determined only short-run price in Marshall."

Notice those "..." before Marshall's name, in my post ;-)

[Nick Rowe]

Will: It does sound very similar. I wonder if Ricardo or de Quincey came first? Hmmm. I think Ricardo did.

You sound like you know history of economic thought. Do you want to take a crack at JKH's question above?

Mike: OK! But you can imagine a Neoliberal who thinks that fiat money can only have value according to the state's power to tax, and who doesn't like that fact, and so doesn't want there to be fiat money.

[Greg Ransom]

Hayek's landmark work in mind/brain learning theory (see UCLA neuroscientist Joaquin Fuster on Hayek's global brain theory) give us no reason to believe that science will be able to reduce each individuals constantly evolving unique judgments and theory laden perspective on thing to a formula usable as some sort of causal theory of "preferences" which can be plugged into economic "models" using fake model of "science" demanded by professors teaching economics in the top 30 economics departments.

[Greg Ransom]

Why should anyone expect there would be a "science" of this?

Why should anyone think there needs to be a science of this?

"I think the big question will be: what sort of feedback there is from the rest of the economy to preferences? That's what might lead to a big paradigm shift. We know there's almost certainly some feedback. Hey, just think of diamonds and deBeers and engagement rings!"

Hayek addresses this issue in his famous 1937 & 1945 essays on knowledge and learning.

Becuase of his background in neuroscience & the history of scientific explanation in the social domain Hayek indicates although he has identified learning in the context of changing local conditions and relative prices as the core explanatory mechanism in economic science, there is no reason to believe that further investigation of this topic will lead to very much more than all sorts of particular facts & insights about a process that is either already familiar to everyone who participates in the market or who which is fairly well understood by most economists.

There is a margin for better understanding and more complete understanding, but no reason of any kind to image paradigm smashing advance, for anyone who doesn't have a false understanding of the role of the "rationality" assumption in economics.

[Greg Ransom]

Let me recommend Mirowski's terrific More Heat Than Light on math/physics and classical vs neoclassical economics.

Mirowski is as much a conspiracy theorists & imaginative writer as he is an historican of economic thought -- but you can't but learn and have your understanding expanded by this wonderful book.

[Greg Ransom]

Note well that different treatments of capital theory (vis vi classical/neoclasical) in light of different models for
math & physics stand at the core of Mirowski's classic More Heat Than Light

[Donald A. Coffin]

Nick, this is a brilliant post. I suspect the phenomenon of a "gap year" is fairly common (in my case, it was four years, that I spent outside academia, working in local government, and learning more about how labor markets actually worked than anything I had done before). And your unpacking of marginalisn (and Pasinetti's value theory) seems to me to be absolutely correct.

[Determinant]

Nick:

Very nice piece on marginalism.

All that Patrick, myself and anybody else with engineering backgrounds have to add is that when you have a margin and an original function, you cannot generate a logically consistent solution that instantaneously optimizes the outcome at every single time point.

This is basic calculus. It's really easy to deal with when you add in Laplace Transformations to linearize everything back into simple algebra.

The combination of the function and its derivative creates lag.

It is my contention, easily derived, that savings and investment form a pair and therefore a function to logically and consistently describe production, consumption, savings and investment is a second-order equation, with direct counterparts to acceleration, velocity and position.

It follows from this that in response to any sort of shock, you will have a transitory response that won't be optimal for some period of time. Change the savings/investment characteristic by any amount and you will change the response too.

Seen in this light its is readily and utterly apparent WHY economic fluctuations exist, why they are hard to control and why we so readily and often observe sub-optimal behaviour like unemployment, low savings or low investment.

[Patrick]

Hey Determinant, don't drag me into this. Apart from having nothing intelligent to add to Nick's (as always) thought provoking post, I'm in the middle of my gap year. :)

[david]

@Determinant

Yep. Hence the use of Arrow securities and Samuelsonian unique-goods-across-time to squash all of the future into static analysis. In Samuelson-land, any goods with different prices are different goods, even if they are only separated by different positions in time (and price evolution over time).

[Will]

Nick:

JKH's question is tough. As far as I know, no economist before the 1840s or so uses math beyond basic arithmetic. The answer as to why could have to do with the mathematical literacy of the people who became economists (remember there were no academic posts in the subject prior to Malthus, and most of the heavy hitters were wealthy autodidacts), or the scope of early economists' inquiry (preoccupation with aggregates, monetary issues, and tax and trade policy). I'm not sure either of these explanations suffices, though. Utility theory wasn't remotely new in 1871, only the mathematical exposition was. So maybe the calculus is originally a winning sales pitch? I do agree with JKH that economists have overcompensated.

[rsj]

Instead of two types of capital good, let there be two types of land. Clay land only grows wheat, and earns $10 per acre per year rent. Sandy land only grows veggies, and earns $5 per acre per year rent. I

OK, let's say that over the last 3 years, sandy land earned, per acre:

$5, $4, $3

And that over the last 3 years, clay land earned, per acre:

$3, $4, $5

What is the relative price of sandy land to clay land? Ask 10 people, and you will get 10 answers. But investment is a lot more like this than it is like the fixed ratio story. People disagree even on what future risk free interest rates will be, and they disagree on what inflation will be. The republicans, for example, are sure that hyperinflation is around the corner. How much more would they disagree on the relative price of sandy and clay land?

[Nick Rowe]

Donald: thanks!

Determinant: that's not at all obvious to me. Are you assuming some sort of information lag, or inertia, or something? And when you talk of "optimal", are you defining that subject to that same information lag, inertia, or whatever?

Will: OK. Makes sense to me. Economists were a bunch of artsie amateurs who didn't know any math, so didn't use any. I too agree that economics has gone overboard. But I might just be biased, because I'm no good at math myself.

rsj: let me suggest an even harder question:

There are two types of used sports cars: Mazda MX6's and Ford Probes. Nobody knows how long they will last, and how well they will work in future, and how much they will cost to repair, etc. Different people have different opinions. Different people have different preferences. Etc. What determines the relative prices of MX6s and Probes?

We don't even have any numbers. How can you possibly put anything so crude as a number on the sheer beauty of the MX6's lines?

And yet the market does put a number on it. And all we can really usefully say is that the prices of the two cars will be determined by the whole distribution of preferences and beliefs and endowments of various potential owners, and by the distribution of the existing stocks of the two cars. And that the preferences and beliefs of the marginal buyer, who, at the equilibrium price differential, is indifferent between buying the prettier MX6 or the cheaper Probe, is what are crucial. (Though you need to know everyone else's preferences and beliefs before you can figure out who that marginal buyer is).

I expect if you put everyone's preferences and beliefs about MX6 and probes into a computer simulation it might spit out some sort of answer. If you could ever figure out what those preferences and beliefs were.

There is no fundamental difference between the theory of capital and interest and the theory of used car prices.

[nemi]

Of course e.g. Smith, Ricardo and Marx understood the notion of subjective value and expectations. They, however, did not believe that people could be viewed as selfish calculating machines.

Neither did Marschall. From the first version of Principles:

“Attempts have been made to construct an abstract science with regard to the actions of an ‘economic man’ who is under no ethical influences and who pursues pecuniary gain warily and energetically, but mechanically and selfishly. But they have not been successful . . .”

… and went on to talk about how a real economy would be completely dysfunctional if people actually acted that way (due to e.g. incomplete contracts). In Marshalls view, as far as I understood it, people act more in the form of rule of thumbs than according to some first order derivative of their utility function.

Marschalls principles is a thousend times better than any micro text that i currently seen in use.

You can read it here:
[link here good find NR]

[JKH]

Is marginal utility a concrete steppes manifestation?

Same question for calculus.

[BenP]

"Otherwise you are stuck wondering why water should be worth less per gram than diamonds"

Here's Adam Smith: "The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it"

Marx: "Diamonds are of very rare occurrence on the earth’s surface, and hence their discovery costs, on an average, a great deal of labour time...If we could succeed at a small expenditure of labour, in converting carbon into diamonds, their value might fall below that of bricks."

Looks like you did leave a lot of interesting stuff out.

[Edmund]

Nothing material to add, but I'd like to this say to all: if you're unfamiliar with Herbert Gintis, do yourself a favor and Google Scholar some of his work. I can't think of another contemporary economist who has done more interesting work in as wide a field as he, nor with less BS. Even when he's considering ideas or policies he's clearly partial to, no prisoners are taken.

[Alex Godofsky]

BenP: but what if diamonds were very rare but also very easy to find - say all of the diamonds in the world started out just lying on the ground? You would predict that their value would be low, but in reality it would probably be high.

[Nathan Tankus]

"ince labour-time is the intrinsic measure of value, why use another extraneous standard as well? Why is exchange-value transformed into price? Why is the value of all commodities computed in terms of an exclusive commodity, which thus becomes the adequate expression of exchange-value, i.e., money? This was the problem which Gray had to solve. But instead of solving it, he assumed that commodities could be directly compared with one another as products of social labour. But they are only comparable as the things they are. Commodities are the direct products of isolated independent individual kinds of labour, and through their alienation in the course of individual exchange they must prove that they are general social labour, in other words, on the basis of commodity production, labour becomes social labour only as a result of the universal alienation of individual kinds of labour. But as Gray presupposes that the labour-time contained in commodities is immediately social labour-time, he presupposes that it is communal labour-time or labour-time of directly associated individuals."

- http://www.marxists.org/archive/marx/works/1859/critique-pol-economy/ch02b.htm

re individual labor needing to be transformed into social labor through exchange ie sale.

[Jed Harris]

There's an un-gated PDF of the Gintis and Bowles paper: [link here good find Jed NR]

For some reason it doesn't show up in Google or Google Scholar. You have to go to Gintis' pub list on his web site and there it is. Either Google is excluding it for some reason (agreement with publishers?) or they are falling down on the job. Either way, symptom of something wrong.

I too would like Determinant to unpack his (?) interesting but opaque comment about lags. It sounds like they are intrinsic but I don't know enough to see why.

[Ed Seedhouse]

"Can you point out the fallacy of Chartalism (assuming you think there is one, which you seem to)?"

See my old post."

I read it carefully before and have read it again, just to be sure (thanks for the link). I don't see that it refutes Chartalism. You merely point out that other mechanisms have an effect on the value of a fiat currency, and I will concede that they do. But that doesn't mean that the fact that government taxation must be paid in the fiat currency also gives value to that currency. I don't see how this affects the point the chartalists make. Heck, the very act of saying (and enforcing) that all currency transactions in the country must be made in the fiat currency must also give some value to the currency on it's own. The enforcement the chartalist choose is taxation, which seems the most practical way to do it to me. I mean it beats armed currency police patrolling every square foot of land in the country making sure you only use the fiat currency.

I would enjoy being proved wrong, though.

""But of course if Chartalism is right isn't Neoliberal economics pretty much wrong by definition?"

No. I can imagine a Neoliberal who thinks that fiat money only has value because of state power to tax."

Then is Steve Keene wrong when he asserts that the Neoliberal model does not consider money? If Keen is right then sure a neoliberal economist can still stick with his model that ignores currency and it's effects even if he agrees with chartalism, but it seems rather pointless to do that since it will have no effect on his model of the economy.

However I'll agree that I overstated my case here. If Keene is right then it makes neoliberal economics largely irrelevant. Yet as a chess player I know that any plan, even a bad one, beats no plan every time, and similarly I suppose any model, even a bad one, beats no model. Krugman seems to be able to make reasonable predictions with that model that actually come true, more or less, but then he seems to be somewhat aware of it's weaknesses and use it as a tool rather than a religion.

[Philo]

What do you mean by ‘subjective’? My guess is: to be subjective, a function must be *relative to a person* and *psychological*.

But then note that total utility, not just marginal utility, is subjective. On the other hand, first derivatives exist for many functions that no one would consider “subjective.” Thus I don’t understand your statement: “Thinking about margins [i.e., first derivatives] mattered only because thinking about margins made it possible to think about goods having subjective value.” Total value is just as subjective as marginal value; the value to me of the (several gallons of) water I use today and the value to me of the last drop I use are equally subjective (because they are psychological and relative).

Also, I would take issue with: “Goods don't have value; people value goods.” Individuals’ utility functions are more basic, but on that basis goods *do* attain value.

Historical question: People must have discussed the water-diamonds paradox long before 1871. What was the best prior account of it that anyone gave? (It’s hard for me to believe that no one figured it out before 1871.)

[Nick Rowe]

Philo: "Historical question: People must have discussed the water-diamonds paradox long before 1871. What was the best prior account of it that anyone gave? (It’s hard for me to believe that no one figured it out before 1871.)"

Yep. See the quotes from Adam Smith and Marx in BenP's comment above.

Basically, since economists couldn't see any relation between the total utility and total value of water and diamonds, they figured values had to be determined by labour/cost of production, and have nothing to do with utility. Once they figured out that it was *marginal* utitility that mattered, they could see the relation between utility and value.

BenP: you missed the point. See my response to Philo above.

Philo: "But then note that total utility, not just marginal utility, is subjective. On the other hand, first derivatives exist for many functions that no one would consider “subjective.”"

Agreed. But once economists started looking at *marginal* utility, they could see the relation between utility and value.

Alex: Yep. Good thought-experiment.

It would be easier for us to explain it by drawing a supply curve and demand curve. The height of the supply curve is related to *marginal* amount of labour needed (or marginal amount of any other scarce resource needed) to produce one extra diamond. And the height of the demand curve is related to marginal utility. And the two curves together co-determine the price and quantity of diamonds. 1871/ECON1000.

My students tell me that some PoliSci and Soc profs are still teaching the labour theory of value as though it was *the* theory of value. It's not quite as bad as science departments still teaching creationism, but close.

Edmund: I fully endorse reading more Herb Gintis. I spent a happy afternoon once reading his Amazon book reviews! (I wonder if he still considers himself a "Marxist"? Not that it really matters. Things move on. Old categories shouldn't remain applicable in a progressive discipline. You keep some old stuff and ditch other old stuff for better.)

Ed: "Then is Steve Keene wrong when he asserts that the Neoliberal model does not consider money?"

I don't *think* that Steve Keene would have said that. He *might* have used the word "neoclassical" instead of "neoliberal" (very different things). But that is wandering waaay off-topic.

[Nick Rowe]

Nathan: that passage of Marx you quoted (which I read 3 times, to no avail) reminds me of one of the reasons I so dislike Marx. That poncy Continental obscurantism. Pity he didn't go to England much earlier in his life. Gimme Smith, Ricardo, Malthus (or Darwin, for that matter) any day. They want to be understood. And you can understand them.

[Nick Rowe]

JKH: I think MU and calculus are unrelated to concrete steppes. Neither pro or con.

nemi: "Marschalls principles is a thousend times better than any micro text that i currently seen in use."

I'm trying to remember (Will or someone else may know the answer): wasn't Marshall's Principles in fact used as the main (intro?) text in UK universities for decades? Or am I muddled with JS Mill's Principles?

[Will]

Nick: I've read that Mill's book was the standard text in the UK until around the turn of the century, and then Marshall's text supplanted it until macroeconomics had to be added.

[Alex1]

BenP:
"The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it"

That doesnt make the slightest sense to me and I am unsure what I am missing. It seems to me like a definition that is true ex post by definition, not any substantive "theory" of value. Another way to say that is "the cost of something is what you have to give up for it". But the same way that opportunity cost in itself cannot explain prices, the sentence above doesnt explain how much toil and trouble you are willing to accept and how much toil is too much toil for the good in question.

But generally I see Marx's point about the diamond-water paradox but I actually think it doesnt adres the real historical criticism of the LTV. The way i understood it the problem of the LTV is not that it can't explain value per-se (it can by definition if strongly formulated) but that it runs into trouble explaining exchange. The simple formulation of the argument: in a world of purely objective value (regardless whether it derives from labour or magical spirits or whatever), no reasonable person will want to exchange a good for less than its objective value. Thus, exchange can only happen in the form of exchanges of goods or bundles of goods with the same objective value. But then, why would exchange happen? It seems rather pointless. And even if we would posit that exchange would start, why would it ever stop? In that sense I always understood Ricardo's comparative advantage as a roundabout way of explaining exchange using "toil and trouble", but to me it still doesnt quite explain why people actually trade stuff. We could mavbe justify it with assymetric information about objective value, which means that all trade would happen because people are stupid to put it bluntly, which seems cynical enough for me to accept it. But still, I'm not sure whether it would be a very potent way of explaining the last 200 years of economic history. So ultimately, to explain sustained exchange, you have to reason that people have different preferences, thus valuing goods differently, leading us to where we started.

Another issue i keep having is with taxation. If a good is traded based on an objective value (whether its labour or whatever) and we would imagine the govt putting on it a sales tax, no matter how low, wouldnt it mean that no reasonable person would buy the good, because it is forcefully being sold above what it is objectively worth? (On this one i am actually quite sure I must be missing something, but I dont know what)

But back to the diamond water paradox. If we reformulate it into the gold water paradox its easier to see why Marx probably still isnt quite right.
Look at that graph I found really quickly in the internets: (now I'll be getting Ron Paul ads for the rest of my life...)
[link here NR]
Are you telling me the toil of finding/making gold tripled in five years?

[Alex1]

Also, I really cant use HTML

[Fixed (I think) NR]

[Nick Rowe]

Michael: (if you are still reading). I have now looked at your two links. They recapitulate the 're-switching' controversy.

Here's my take.

If you are deciding whether to undertake an investment project, or which investment project to undertake, you do an NPV calculation, to see if NPV is positive (or which has the highest NPV).

For an n-period investment project, ***if you assume the rate of interest must stay constant over time***, the n-period NPV equation means you are solving an n-degree polynomial equation. And an n-degree polynomial in general has up to n different solutions.

But there's something called the term structure of interest rates. You cannot just assume that interest rates will stay constant over time, which is equivalent to assuming that the term structure of interest rates is always perfectly flat. If there are n time periods, there are n-1 different 1-period interest rates.

If there are just 2 time periods, today and tomorrow, then there is one rate of interest and the saving/investment decision has just one time dimension. But if there are three time periods, today, tomorrow, and the day after, then there are two different interest rates (between today and tomorrow and between tomorrow and the day after) and you can't assume they are the same and you need to break down the future into tomorrow and the day after.

Simple version: assume there is 1 consumption good and 2 time periods. "Capital/saving/investment" has one dimension. Assume there is 1 good and 3 time periods. "Capital/saving/investment" has 2 dimensions. If we save and invest more today, we have to ask ourselves: "is this particular investment going to give us more consumption tomorrow? or the day after tomorrow? or a bit of both?" And the answer matters. People don't just care about "the future". They care about their consumption in each and every future period. You can't assume a flat yield curve.

[Nick Rowe]

More generally, if there are n goods, and t time periods, then there are (up to) n(t-1) different saving/investment decisions. "If I consume fewer eggs today, will I get more apples in 42 days from now?" You have an n.t dimensional Irving Fisher diagram. Capital/saving/investment decisions are not 1-dimensional. "Are swallows scarce?" "Do you mean the African or the European swallow?"

[Nick Rowe]

Will: thanks. That means my memory is not so bad, after all. Both Mill's and Marshall's Principles were used as texts.

[Nick Rowe]

BTW: Determinant, Patrick, or anyone who is mathematically competent. Is this right:

"0=a + bx+ cx^2 + dx^3 +.....+ ex^n is an n-degree polynomial equation, and, in general, it has up to n different solutions for x."

Am I using the right words? Is what I said right? What should I be saying?

[JL]

Frances said : "It seems to me that where econ is going right now is trying to explain where preferences come from - whether that's neuro economics, behavioural economics, or evolutionary economics. Are we at the verge of a paradigm shift, where we no longer accept that it's impossible to look inside people's heads, read their minds, and know how/why they value things? "

What about sociology, anthropology, history? Preferences are often inscribed in social and cultural contexts and these disciplines know a lot about this. The economics of social networks would be a good place to start moving towards some sort of bridge in the social sciences, no?

[Nick Rowe]

Alex1: "Are you telling me the toil of finding/making gold tripled in five years?"

Yes, I would say that is true, *at the margin*. ;-) But causation runs the other way from what a defender of the LTV would argue. The trebling of the price of gold caused people to treble the amount of labour they would find it profitable to spend, at the margin, to find an extra ounce of gold.

But your point still remains valid, of course.

[Nick Rowe]

Nick's dictionary: "Capital is scarce" = "People are not indifferent about when they get to consume stuff"

Take the example where storage of consumption goods is costly, and people would prefer to consume an extra apple next year than consume an extra apple now, so the real rate of interest (deflated by the rate of inflation on apple prices) is negative. (Because all the boomers are planning to retire next year, so there will be fewer people picking apples, for example.)

Can we say that "capital is scarce" in this economy? God only knows. But we can if we define it my way.

And I can also explain *why* real interest rates might be negative.

[W. Peden]

Nick Rowe,

"Yep, if Marx had lived longer, and had started writing later, he might well have written something very different."

I don't think so. Marx could have lived a hundred years and wouldn't have finished Capital. The last 16 years or so of his life feature almost no new work on economics. Some would attribute that to ill-health, but actually Marx was intellectually very active in his later life, learning several languages, studying Russian economic statistics, learning agronomical chemistry, studying anthropology, contributing original works of political philosophy, and a return to some of the themes of The German Ideology regarding pre-historical and post-revolutionary society. What he did NOT do was finish Capital or make any significant headway in that direction. Engels had nothing to go on for Vol. II and III apart from manuscripts from 1864 to 1867. As Gary North put it, Marx "short-circuited" as far as economics goes and would never finish a book after Vol. I.

It's unclear what exactly made Marx abandon economics, but perhaps significantly the manuscript of Vol. III of Capital ends two paragraphs after he begins (and this is in Vol. III!!!) to define 'class', a concept of some importance in Marxian economics. In other words, he finally came under pressure to justify his class analysis of society, and broke down at the prospect.

(Sraffa wouldn't have broken down, because whatever you think about Sraffa, he was the kind of academic who wouldn't quit a project when he started it. He's the Michael Myers of economics: no matter how much pain a topic involves, he keeps stalking on, introducing more idealisations and more labrynthine mathematics. I think that's part of the whole Sraffa mystique.)

[Determinant]

BTW: Determinant, Patrick, or anyone who is mathematically competent. Is this right:

"0=a + bx+ cx^2 + dx^3 +.....+ ex^n is an n-degree polynomial equation, and, in general, it has up to n different solutions for x."

Am I using the right words? Is what I said right? What should I be saying?"

Yes, that is precisely right, though conventionally you write the highest power first. In a differential equation you write the highest derivative first, hence d^2(x)/(dx)^2.... is a second-order differential.

Determinant: that's not at all obvious to me. Are you assuming some sort of information lag, or inertia, or something? And when you talk of "optimal", are you defining that subject to that same information lag, inertia, or whatever?

The lag can be thought of as inertia, and its a property of the system we live in. It's because we have savings and investments across time periods. Savings and investments are based on legally-enforced contracts with real penalties if they are not honoured.

A system described by a second-order differential equation (as a system with savings and investment is, note that I did not say that they are equal) must have a time lag for its output, consumption, to reach a new stable level after the initial shock. This behaviour must occur in order for the system to remain consistent with its own properties and description, contract-based savings and investment. Savings and investment are storage elements, if you will, for production.

A system cannot immediately fly to a new, optimal level unless somehow the actor(s) in it break their own contracts. But you can't break contracts without penalty so people in general don't, further people make contracts so that they can plan, co-ordinate and achieve their desired goals in the first place. This is a trade-off or iron law, you can't have savings and investment contracts without observing some sort of sub-optimal behaviour part of the time and you can't have economic co-ordination and planning (by firms, individuals, whatever) without contracts to get that higher state of development in the first place.

What happens when you "shock" the system I described is that you get a "ring" or circulation between savings, production and investment such that Y (Consumption) != Y(Production) for a time. It's transitory (economists' favourite) to the long-run solution.

But Savings and Investment can themselves change. Because some contract default happens, the long-term values of S, I and C can change and permanently lower themselves. It doesn't matter what the transitory response is, the long-term response, the forced response, itself changes and lowers. Therefore the long-run is changing and getting grimmer, regardless of what the short-term or transitory response is. This is how Keynes could logically say that in the long-run we are all dead.

[W. Peden]

Nick Rowe,

"No. I can imagine a Neoliberal who thinks that fiat money only has value because of state power to tax."

Charles Goodhart probably gets classified as a neoliberal by many (of course, 'neoliberal' is about as useful a term as 'socialist', if left undefined; I can imagine two different people describing Goodhart as neoliberal and a socialist respectively!) but I recall reading a review by him of a Chartalist book and he seemd enthusiastic about Chartalism but suggested that it was spoilt by the endogenous money/non-neutrality of money stuff.

Though it's interesting how people tend to fall down into consistent patterns on these things e.g. I struggle to think of any libertarian Keynesians or social democrat monetarists or democratic socialist supply-siders, yet there's nothing inconsistent about these positions, suggesting that beliefs in both politics and economics have other underlying reasons like views concerning epistemology.

[Will]

Nick: Strangely, it is much easier to find old editions of Mill (both for sale and in library collections), and they are much cheaper than old editions of Marshall. This may be because of the large number of editions that Mill made, in contrast to Marshall, who (like Marx) failed to deliver on the promised follow-up. On the other hand, maybe Marshall is just more sought-after.

[Alex Godofsky]

Determinant: we observe 'instantaneous' changes in both prices and quantities all the time. Neither is well-described by systems of differential equations.

Prices: at micro scales we observe both financial asset prices and retail goods prices update in discrete increments. e.g. Amazon can cut the price of a book by a dollar instantly; they don't have to let it adjust continuously. At macro scales we see asset prices act like stochastic processes. We don't see them act like solutions to a (non-stochastic) system of differential equations.

Quantities: we also see quantities adjust in discrete increments, e.g. my house can burn down (in fact a non-negligible fraction of an entire region's housing stock can burn down overnight).

(btw, I'm also from an engineering background, but I think your attempts to treat economic systems like physical systems don't work very well. Physical systems don't have intelligent agents.)

[Determinant]

Sticky prices at the macro level, Alex? At the micro level, price changes are in transactions not limited by contract. Sure, spot prices change, but futures contracts don't, that's the point. Loans are a prime example of inter-temporal contracts which may or may not be a good idea, depending on how the future works out.

"Physical systems don't have intelligent agents."

Don't tell that to systems engineers or programmers.

"Quantities: we also see quantities adjust in discrete increments, e.g. my house can burn down (in fact a non-negligible fraction of an entire region's housing stock can burn down overnight)."

Right, and the region's economic output goes into a tailspin, existing investment contracts are defaulted on, you get reduced output.

What you are describing is a production shock. But what happens to consumption? People live off their savings and consumption is higher than production for a while. That's what I mean about storage elements.

[Greg Ransom]

This is what I'm talking about when I talk about the false picture of individual perceptions, judgments and changes in understanding which dominates the thinking of most economists and which is built into the belief/desire model of mental causation / categorization -- a model with hopeless pathologies (See Alex Rosenberg's work in the philosphy of economics on this topic).

Nick writes,

"I expect if you put everyone's preferences and beliefs about MX6 and probes into a computer simulation it might spit out some sort of answer. If you could ever figure out what those preferences and beliefs were."

[Greg Ransom]

Friedman used Marshall's book into the 1960s -- Hayek's "Use of Knowledge" paper and Marshall was 1st year graduate price theory at Chicago as taught by Friedman.

[W. Peden]

Greg Ransom,

Wouldn't have thought of you as an Alexander Rosenberg fan, given how embedded folk psychology is into the work of von Hayek and von Mises.

[Determinant]

@Alex

I'm not strictly treating economics as a physical system; I just note that any system which has two storage elements, in this case savings & investment, has to be modelled by a second-order equation to be complete and because of the storage, we get consumption out of synch with production.

With contract-based savings and investment, something has to give when a shock comes along, either contracts get broken, consumption is not optimal or both. Either way, there is a penalty. There's no free lunch and you can't instantaneously fly to perfection after a shock.

[Greg Ransom]

Not only a Rosenberg fan, a Rosenberg student. Rosenberg is the last 'post-positivist' standing and it's fascinating seeing Rosenberg move from a crude Mill/Hume model of 'science' buttressed by Kimian metaphysics to a where he is now -- hanging by a thread holding on to prediction as the sole criterion of 'science' & the theoretical posits of particle physics as the only entities existing in his ontology.

I disagree with Rosenberg on the nature of science, mind, learning, categorization, and language -- I'm a Wittgensteinian, a Hayekian, a Darwinian, a Kuhnian & a Larry Wright guys while Rosenberg is an a Mill/Nagel/Quine/Lewis/Hempel/Hume/Davidson guy who knows he's lost his footing, has been knocked off his "post-positivist" perch and is now flailing arms and legs to hold onto something, anything as the foundation for his scientistic metaphysics and epistemology.

I can't think of a better why to challenge your own understanding of thing that to challenge it against one of the bightest mind in philisophy working out the whatever possibilities are left in the scientistic project which the tradition of my own project directly challenges and has been taking on for the last 140 years (ie since Carl took in Mill's empiricism & German historicism).

[Greg Ransom]

Hayek took a Wittgensteinian turn in the 1950s, under the influence of Peter, Polanyi and the later Wittgenstein, moving toward an embodied and evolving unarticulated rules picture of shared ways of going on together, eg in language use or in moral rules, etc.

And Hayek long understood Popper's point about the theory ladden nature of explanation.

Then look at Hayek on the role of tacit local knowledge and learning in economic science and his attack on "givens" in model building -- it becomes clear that Hayek was focused on personal perceptions and changes in understanding on the part of individuals in a way that Cannot be captured in the "givens" of folk psychology, ie universally "given" belief and desire tokens of universal types of the sort that we could look down upon from a zgod's eye view as part of a "given" set of belief and desire types and tokens which coukd be assigned as univocal entities in any head at any place across time and place.

The belief and desired, mental state talk of Hayek's "Scientism" peppers simply does not have a place in Hayek's causal science of economics with learning in local environments and changing relative prices as the causal mechansim.

[W. Peden]

Greg Ransom,

I quite agree, except for Kuhn, whose main virtue in my view is being the most clear great deductivist philosopher of science and therefore the go-to in order to see the flaws of that approach: reject the idea that we have reason to believe that it is probable that it will rain in the Sahara tomorrow than that it will rain in Scotland tomorrow, throw in some confusion about incommensurability (a problem on which Kuhn never settled) and you end up losing any reason to believe that we know more about the world through science than Ptolemy.

I'm not aware of anything worthwhile in Kuhn that cannot be obtained by relaxing the assumption in standard diachronic ontological reductionism (by which I mean the view that science over time describes the same world) that science is always cumulative i.e. that theories always in some sense contain their predecessors as true within a certain domain. Kuhn was right to point out the historical fact that this was true, but tied himself up in all kinds of knots because he was still too much influenced by the likes of Popper.

(Oddly enough, the first two essays I ever wrote in the philosophy of economics was criticising Rosenberg, precisely for the reason you give: he expressed clearly and persuasively many points which I'd heard from people in general about economics.)

[Nick Rowe]

Determinant: thanks. One last question on that topic. Suppose my constants (A, B, C, etc) switch sign s times. (By that I mean that if A is negative, B is positive, C is negative D is positive, and all the others are either positive or zero, then s=3). Does that mean there are s different solutions for x? I think it does, but I'm not sure. I can't prove it, but it feels roughly right intuitively.

(This is all about the "re-switching controversy".)

If I have a contract to deliver to you 100 tons of wheat next year, and when next year arrives something changes (either for me or for you), so it is now optimal for me to deliver only 80 tons to you, we can always do a side deal in which I buy back 20 tons from you, and so only deliver 80 tons net.

[Nick Rowe]

Oh. I *think* I am only looking at positive solutions for x.

[W. Peden]

A question re: Sraffa - is it true, as Screpanti and Zamagni assert, that Sraffa's theory falls to pieces once the assumption of constant returns to scale is relaxed?

[Determinant]

On sign switching: no, off the top of my head that doesn't matter. What does matter is that a polynomial of degree n will have n solutions. For instance a quadratic equation of degree 2 has two solutions.

If I have a contract to deliver to you 100 tons of wheat next year, and when next year arrives something changes (either for me or for you), so it is now optimal for me to deliver only 80 tons to you, we can always do a side deal in which I buy back 20 tons from you, and so only deliver 80 tons net.

Ah, but what happens to the deals I made with that 100 tonnes of wheat, to turn it into 150 tonnes of bread? My customers won't let me off the hook, so I won't let you off the hook. We may be able to do a deal, but that is not guaranteed. In fact you signed a contract, you defaulted, and I can sue you for damages. How can I rely on you in the future when you jilted me in the past? Now you have a miserable reputation as a wheat merchant and I'm going to the guy who has a better one. I guess that employee you have will have to be laid off.

[Alex Godofsky]

Determinant:
Don't tell that to systems engineers or programmers.

Cute, but when programmers have to account for intelligent agents they use the appropriate techniques from game theory, just like economists - these are not the sort of techniques you'd ever use to model e.g. the flow over an airfoil.

I'm wandering off-topic here, but what I'm reacting to is the general direction you seem to approach these topics from (e.g. monetary policy as a control system) across multiple comment threads.

I'm not strictly treating economics as a physical system; I just note that any system which has two storage elements, in this case savings & investment, has to be modelled by a second-order equation to be complete and because of the storage, we get consumption out of synch with production.

With contract-based savings and investment, something has to give when a shock comes along, either contracts get broken, consumption is not optimal or both. Either way, there is a penalty. There's no free lunch and you can't instantaneously fly to perfection after a shock.

It depends on whether the contracts are contingent on future events, and whether you are talking about ex ante or ex post optimality.

[Nick Rowe]

Determinant: OK, that answer was off the top of your head, so I won't hold you to it. But consider this example:

0 = -1 + X + X^2 + X^3 + X^4 +....+ X^n

Let's restrict attention to solutions where X is positive (for economics, not math reasons).

No matter how big n is, that equation only has one solution for X, doesn't it? (And there's only one sign switch).

Or am I muddled?

[Nick Rowe]

W Peden: If "does not fall to pieces" means "can predict relative prices based on technology alone", then Sraffa's system seems to need:

1. A real rate of interest or real wage assumed exogenous
2. Perfect foresight/steady state equilibrium where nothing ever changes
3. Only one type of labour
4. No other inputs like land or any natural resources
5. Perfect competition
6. Other assumptions I might have forgotten
7. Constant returns to scale (otherwise marginal and average products aren't equal, and both change when preferences change and the distribution of demand changes).

I think constant returns to scale is the least of our worries.

[Nick Rowe]

8. No joint products like wool and mutton. Or new MX6 cars and used MX6 cars. (If you build 1 new MX6 you also build a 1 year old MX6 1 year later, and a 2 year old MX6 2 years later...and they aren't perfect substitutes, and you need preferences to predict the relative prices of new and used MX6's, just like wool and mutton.)

[W. Peden]

The weird thing is that Screpanti and Zamagni make a point of rejecting any theory which relies on unrealistic assumptions (their reason for rejecting general equilibrium analysis and New Classical economics) yet they're hardened Sraffians and explicitly state that his theory relies on unrealistic assumptions. I can't imagine why they would hold unrealistic assumptions against the theories they dislike, yet not do the same for Sraffa.

[Determinant]

Determinant: OK, that answer was off the top of your head, so I won't hold you to it. But consider this example:

0 = -1 + X + X^2 + X^3 + X^4 +....+ X^n

Let's restrict attention to solutions where X is positive (for economics, not math reasons).

No matter how big n is, that equation only has one solution for X, doesn't it? (And there's only one sign switch).

Or am I muddled?

I don't know if it's muddled, but I have never heard of a theorem asserting it. There are n roots to that equation, but some of them will be complex (involve imaginary numbers like 3+2i). You cannot say, analytically, how many will be real roots, positive roots, negative roots or complex roots. I don't know of any theorem or method which lets you do that.

[Greg Ransom]

W. Peden -- we just read Kuhn differently.

i studied Kuhn with Larry Wright, and read it through the lens of Hayek, Popper & Wittgenstein etc.

See Wright's Teleological Explanation for some hints at an alternative picture of explanation.

[Greg Ransom]

W. Peden -- don't see that you are avoiding the muddles that Kuhn identifies in standard talk of "the same world" across alternwtive conceptual schemes.

If you read him carefully Kuhn is not contradictory or incoherent. It's just hard stuff to develop a vocabulary to talk about.

The key thing in Kuhn is his anti-foundationalist and his anti-justificatory framework -- it is this attack on justification and foundations which Hayek makes against the philosophical tradition which has given us so much if the content of modern economics -- a philosophical tradition which demands the Scientism found in Schumpeter, Samuelson, Friedman, Lipsey, -- the math "model" and quantitative verification paradigm.

It's why economics is psupeudo-science -- it's the bogus epistemology, stupid. The pseudo-scientific demand for foundations and justifications inherited from philosophy can be traced directly to the failed and non-explanatory research program of 'mainstream' economics -- just as you can identify the source of the rejection of Boettke's 'mainline' economic science in the bogus and failed philosophical requires for "knowledge" demanded by the professors,controlling the top 20 graduate programs in economics, along with the guild journals of the AEA and a handful of departments.

[Nick Rowe]

Determinant: "There are n roots to that equation, but some of them will be complex (involve imaginary numbers like 3+2i)."

Aha! (-1)^0.5 had totally forgotten about imaginary numbers!

You see, "X" here is going to be 1/(1+r), where r must be a real number between -1 and + infinity, and X must be a real number between 0 and + infinity.

My "theorem" (proof by iterated assertion) still feels good to me, if we restrict attention to positive real solutions.

W. Peden: " I can't imagine why they would hold unrealistic assumptions against the theories they dislike, yet not do the same for Sraffa."

That has always seemed weird to me too. I can understand (say) fundamentalist Keynesians disliking neoclassical economics for all of its restrictive assumptions, but the Neo-Ricardian models seem to have all the same restrictive assumptions of neoclassical micro, and then a load more on top of that. Our kettle's got nothing compared to their pot!

That was what was underlying my bit in my "loanable funds" post. Start with Walrasian/Arrow-Debreu GE theory, make some very special assumptions, delete the preferences, and say "Oh look! The rate of interest cannot be determined in the model, so it must reflect...whatever"

[K]

Nick,

"Does that mean there are s different solutions for x?"

As you already said, there are n solutions (not necessarily distinct, and not necessarily real).

"Oh. I *think* I am only looking at positive solutions for x."

If we consider polynomials that don't necessarily have n real roots, it seems unlikely that there is any straightforward relationships between the number of sign switches and number of positive roots. Imagine that an n-th order polynomial has n positive, real roots. Now change the 0-th coefficient a_0 (the constant term), thereby shifting the polynomial up or down. If n is even, then for any positive value of a_0, there will be no negative roots. But as you increase a_0 above zero you will lose two roots every time a minimum of the polynomial shifts above the x-axis. But you aren't changing the way the coefficients oscillate. You are just keeping them constant, except for the last one which you are increasing uniformly starting from zero. (You can make a similar argument for odd polynomials, except to make sure that initially positive roots stay positive, you have to keep a_0 negative, and make it more negative thus bringing the *maxima* of the polynomial below the x-axis.)

"No matter how big n is, that equation only has one solution for X, doesn't it?"

I think that's right. There can only be one positive root. If a_0 was 0 instead of -1, the biggest root would be zero. Since the coefficient of a^n is positive, the polynomial is going to +infinity on the right. So if you make a_0 negative you shift the whole thing down and you get one positive root (but you could also be losing negative roots). But lets assume you still have n-1 negative roots. What could bring one of them to the other side? If we take the first derivative of the polynomial, then c_0 goes away, and we can apply a similar argument to the roots of that polynomial, i.e. the extrema of the original polynomial. If c_1 is made negative, then one extremum must move to x>0. Which, if c_0 is high enough, *could* mean that there are two positive roots. But it doesn't look to me like a negative c_1 and a positive c_0 requires it. I do sense some intuition for *some kind* of oscillation of the parameters producing positive roots, but not sure. What is behind your intuition?

[Nick Rowe]

K: "What is behind your intuition?"

I see curves. (Said in hoarse creepy voice). Curves, all stacked on top of one another, and added up vertically to one big curve. X on the horizontal axis, and Y on the vertical. And each curve reflects one of the terms in the polynomial. And the ones with positive signs slope up, and keep on getting steeper, and the ones with negative signs slope down, and keep on getting steeper down. And the ones with higher powers start out small and don't do much when X is small, but as X gets bigger they come to more and more dominate.

Maybe it should be: will have up to s positive real roots??

I don't know K. Thanks for trying to help me on this.

[K]

Nick,

"I see curves. (Said in hoarse creepy voice)"

:-)))

Exactly. And if all the coefficients are positive, then all terms go up from zero on the right and there can be no positive roots. But, if you make a_0 negative, you get one positive root (for Determinant).

I don't have the paper, but apparently there exists a proof (D.C. Kurtz 92) that if all a_i are positive and a_i^2 -4a_{i-1}a_{i+1} > 0 then all the roots are real (and therefore also negative - see above). Now if you take all the coefficients of the odd powers and make them negative then you mirror the function left to right around the y-axis. So now you have a sufficient condition for n *positive* real roots, which does indeed involve alternating signs of a_i. I don't think oscillation is a necessary condition to get n positive roots (will try to provide example later), but still, your intuition is pretty damn good.

[Nick Rowe]

Thanks K!

[Min]

Nick Rowe: "But if you and I both eat apples and bananas, even if you and I have different preferences, it will still be true that the ratio of my marginal utilities for apples to bananas MUa/MUb will be equal to your ratio. That's because both our ratios will be equal to the price ratio. I.e.

"[MUa/MUb]Nick = Pa/Pb = [MUa/MUb]Ed"

Par'n my iggerance, but. . . .

Let's say that I am hungry and I will eat an apple if I have to, but I really like bananas, which I do not at the moment have. In fact, if I had 5 apples I would gladly trade them for 1 banana. As it turns out, I only have 1 apple, which I am prepared to eat, faute de mieux. You feel exactly the opposite. You would gladly trade 5 bananas for 1 apple, which you do not have. But you have only 1 banana, which you are prepared to eat, if need be.

Fortunately, you and I trade 1 banana for 1 apple, making us both happier. That makes Pa/Pb = 1. How can we claim that the ratios of our marginal utilities are equal, and equal to 1? (Before, after, or during the trade?)

Thanks. :)

[Nick Rowe]

Min: "[MUa/MUb]Nick = Pa/Pb = [MUa/MUb]Ed" is only true in equilibrium where we are able to buy and sell as much as we want at prices we take as given. (It won't work if either of us has monopoly or monopsony power, and can influence prices by buying more or less.

[Nick Rowe]

Lemme give you the intuition. Suppose Pa/Pb=1, to keep it simple. If I get to the supermarket checkout and find my MUa>MUb I would put 1 banana back and pick up 1 extra apple, and increase my total checkout utility. If I find my MUa

[W. Peden]

Greg Ransom,

It is very hard to create a faithful interpretation of Kuhn that is not contradictory, philosophically dubious, historically unworkable and plain barmy at times. For starters-

(1) Are paradigms strictly incommensurable or just hard to compare? Kuhn's analogy of paradigm-shifts as comparable to gestalt-shifts suggests the former and it is needed for the hard-nosed incommensurability required to deny the possibility of knowing whether or not science has more truth-content over time, but this makes it unclear how we can do history of science. On the other hand, Kuhn seems to reject hard-nosed incommensurability when he says that historians of science CAN observe data in the same way as persons in different paradigms, so incommensurability becomes a difficulty rather than an impossibility, but then it's unclear why we can't compare the virtues of different theories in different paradigms.

(2) Just what DID Kuhn mean by "different worlds"? I'm not convinced that he knew.

(3) The actual history of science rarely follows a Kuhnian pattern. "Revolutions" like the Copernican revolution took over a hundred years. And the distinction between revolutionary science and normal science is rarely clear: was Kepler a revolutionary or an ultra-conservative? Was Copernicus, for that matter? Kuhnian history needs the distinction to be sharp; fortunately, history of science as such does not.

(4) At the end of the day, Kuhn's theory of scientific "progress", logically implied by his other philosophical beliefs, is that we know no more today about physics or economics than Ptolemy or William Petty. There would be absolutely no basis to say that Hayek's theories are any closer to the truth than Aristotle's. Comparisons of Aristotle's labour theory of value with modern marginal utility theory would be just so much babbling. (The reductio ad absurdum applies to Karl Popper as well.)

So Kuhn DID identify muddles. And he jumped right into them. In constrast, I think the proper reaction to the reductio ad absurdum above is to say "There's something wrong here!", and the dogma of the conceptual scheme is a perfectly good place to start. If the map says that you're at the bottom of the Atlantic Ocean and you're a good map-reader, then there's probably something wrong with the map.

[W. Peden]

Nick Rowe,

There's a well-established practice in the rhetoric of science where one accuses one's opponent of methodological errors or being outright pseudo-scientists. Sometimes it's legitimate and sometimes it's not.

What puzzles me is when, for example, a Neo-Ricardian says "Bah! Neoclassical economics is just a bunch of maths and unrealistic assumptions. Why can't economists be more empirical?"

Heterodox economists don't have to be that way: say what you like about the Austrian School or evolutionary economists, but they have an admirable habit of practicing what they preach as far as methodology goes.

[Min]

JKH: "Why so long for economics to use {calculus}?

"Did neoclassical economics over-compensate for the late start?"

Will: "As far as I know, no economist before the 1840s or so uses math beyond basic arithmetic."

Daniel Bernoulli, 18th century. :)

[Min]

Nick Rowe: "There are two types of used sports cars: Mazda MX6's and Ford Probes. Nobody knows how long they will last, and how well they will work in future, and how much they will cost to repair, etc. Different people have different opinions. Different people have different preferences. Etc. What determines the relative prices of MX6s and Probes?"

Advertising!

(Sorry, I couldn't resist. ;))

[Min]

Nick Rowe: "[MUa/MUb]Nick = Pa/Pb = [MUa/MUb]Ed" is only true in equilibrium where we are able to buy and sell as much as we want at prices we take as given."

IOW, we are able to buy and sell until we reach indifference at the given prices? We have no budget constraints?

Thanks. :)

[Greg Ransom]

re Kuhn -- W. Peden this requires a long conversation which can't take place here.

The conversation might start with my rejection of your notion of "truth content".

[Jean]

To count the number of real positive roots of a general polynomial, you need Sturm theorem.
http://en.m.wikipedia.org/wiki/Sturm's_theorem

But it is a bit too general. Peron-Froebenius theory is more useful to discuss Sraffa's work

[Nick Rowe]

Min: "IOW, we are able to buy and sell until we reach indifference at the given prices? We have no budget constraints?"

Nope. Simple example: apples and bananas cost $1 each, and I have $10 to spend. So I buy 10 bits of fruit. But will it be 6 apples and 4 bananas, or 5 each, or....what? Answer: whatever combo gives me MUa/Pa=MUb/Pb.