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I don't actually know what you mean by capital theory, what does a capital theory aim to explain? The marginal product of capital (like in the Ramsey model)? The price of capital? Heterogeneous capital models?

Britonomist: I'm not sure I want to be overly precise. Some sort of general (as opposed to partial) equilibrium model that explains: interest rate(s); the price(s) of capital good(s), without assuming the capital and consumption goods are the same good.

#1. if you talk about preferences, then the topic drifts naturally toward 'whose preferences', and if you're busy trying to set up a non-Marxist capital theory, this is not the road you want to walk down.

Then yeah, doesn't the Ramsey model do that? I'm not sure, in the objective function you can either consume or invest/spend income on capital, it doesn't specifically talk about goods, there is just income. It's possible to modify the model with things like money, heterogeneous agents and technology. I did really like the Ramsey model, not because I think it is realistic, but it's just nice to be able to derive all the solutions so perfectly and come up with profound implications about the determination of savings & interest etc...

Nick - when Bob Dimand and I wrote the obituary for TK Rymes that recently appeared in the Review of Income and Wealth, I spent some time reading TK's reflections on the Cambridge capital debates, and talking to Bob about them. Here's what I wrote in the obit:

Rymes’ position on the nature of capital came down on the side of Cambridge, England, as opposed to Cambridge, Massachusetts. Like Joan Robinson, he argued that capital must be seen as a heterogeneous commodity; he drew a clear distinction between primary or non-produced capital goods, and intermediate, or produced goods (Durand, 1996)....Rymes argues that: "[P]roper measures of technical change must take into account the fact that in technically progressive economies, such capital goods themselves are being produced with ever-increasing efficiency."

So I'm not sure about your (2) and (3) above - but isn't the idea of capital being a produced good part of van Rowe's Dutch capital theory?

Britonomist: "Then yeah, doesn't the Ramsey model do that?"

Emphatically No. The Ramsey model is a one-good model. It makes exactly the same very special assumption that the Solow growth model made. The price of a physical unit of the capital good is always the same as the price of a physical unit of the consumption good. We know that because: "K" appears in the production function, which only makes sense if "K" means physical units; it includes the equation Kdot + C = Y (minus dK for depreciation, if you like); r = MPK. This only would be true if you can wave a wand and convert 1 physical unit of the capital good into 1 physical unit of the consumption good and vice versa. The MC curve of newly-produced capital goods is always and everywhere horizontal at a price of 1.00 in terms of the consumption good.

Ignoring depreciation and stuff, the equilibrium condition should be: r=MPK/Pk, where Pk is the price of the capital good in terms of the consumption good numeraire. The Ramsey/Solow assumption implies MCk is always and everywhere 1.00, so Pk is always and everywhere 1.00.

(Suddenly I feel sympathy for the Cambridge UK guys, if what we are teaching as *the* theory of capital and interest is Ramsey. My crappy little Dutch Capital Theory is *much* better.)

david: anyone who has any income today may choose between current consumption and (the vector of) future consumption, depending on time preference. Their time preferences will be one of the things that affects the prices of capital goods and rates of interest in general equilibrium (except under very special assumptions). That's the road we have to walk down, Marxists or not.

Frances: I think what really matters is whether the capital good is the same good as the consumption good. In my Dutch Capital Theory model it definitely isn't. Multiple consumption goods and multiple capital goods is interesting, but not the most important thing.

TK was of course correct that technical change happens both in the production of consumption goods and in the production of capital goods. In a one-good model, where the capital good *is* the consumption good too, the rate of technical change must by definition be equal across the two sectors. But it doesn't have to be, in general. Technical change could cause the MC curve for capital goods to shift either up or down relative to the MC curve for consumption goods. Plus it's going to affect the growth rate of consumption and the rate of time preference at the margin.

O.k. TK also wrote a lot about "waiting" in the production of capital - time being both a consumption and capital good. But I couldn't quite work out his position on it.

Frances: Yep. I used to talk to TK about it a bit. I could never exactly work out his position on it. Sort of halfway between Austrians and Cambridge UK? The "waiting" bit was the Austrian bit.

Economists do the "economics" of a capitalist society without capital goods -- it's a scientific disgrace I epic proportions.

On the "Cambridge" episode let me recommend Daniel Hausman, Capital, Profits, and Prices.

Bare with me as New Classical macro is not my strong point (I got the best grades in econometrics, economic history & finance)

"This only would be true if you can wave a wand and convert 1 physical unit of the capital good into 1 physical unit of the consumption good and vice versa"

I think of Ramsey as implicitly including monetary spending without specifically modelling it. In that sense it's converting expenditure on capital to expenditure on consumption. It's no different to me than having a closed economy national income accounting identity without government: Y = C + I, Kdot is basically I, but it also includes K, which is capital assets that has a role in determining interest rates and production. That's probably not a very good explanation. I simply don't interpret Kdot as an increase in 'capital goods' specifically, but an intangible measure of investment that yields income in the production function, while C is an intangible measure of consumption that yields utility.

"if what we are teaching as *the* theory of capital and interest is Ramsey"

Oh no not at all, it's one of many models taught and only at a post-graduate level.

Greg: I would say that's an exaggeration. Some simplifying assumptions can be too simplifying for some purposes. And some do this.

What annoys me a little is when people speak as though "neoclassical model" were synonymous with "neoclassical one good model". It isn't.

Britonomist: OK.

When we write "Kdot+C=Y we can (if we wish) interpret that as an accounting statement, where we are adding the *value* of capital goods produced to the value of consumption goods produced to get the total value of goods produced.

But when we write "Y=F(K)" we *must* be interpreting that as an engineering relationship between the *physical amount* of goods produced and the *physical amount* of capital goods we have to produce them with.

If you write both together as: Kdot+C=F(K) you *must* interpret that as an engineering relation between physical units of K and C. And it embodies a very special assumption about technology that the Marginal Rate of Transformation between Kdot and C is always and everywhere minus one. No curvature on that PPF. That's why preferences don't affect Pk, given that straight line PPF.

Thought-experiment: suppose everybody joined a doomsday cult, and stopped caring about the future. What would happen to the price of assets and the rate of interest? Price of assets would fall to near zero, and rate of interest infinite. But not in this model. People just eat the machines, so the prices of machines stays the same.

Nick,

I can't recall being taught something like Dutch Capital Theory in undergrad, the closest I can think of is Fisher and inter-temporal choice in micro & finance.

Alternatively if you think of capital theory as the structure of production etc. I'd say that you would want to look at industrial organization, but the determination of the interest rate is hardly a question there.

For Macro we did have the simple model, but not anything like what you would call Dutch Capital Theory.

I think what you call Dutch Capital Theory is fragmented along several sub-fields in economics.

Also Nick & Britonomist,

"Britonomist: I'm not sure I want to be overly precise. Some sort of general (as opposed to partial) equilibrium model that explains: interest rate(s); the price(s) of capital good(s), without assuming the capital and consumption goods are the same good."

I think you might want to have a look at the first chapter of Bob Murphy's dissertation for an example of such a model, it's available here: http://consultingbyrpm.com/resumecv; he defends/explains Bohm-Bawerk's and uses a model such as the one you're suggesting.

The chapter is also published as:
Robert P. Murphy (2005). Dangers of the One Good Model: Böhm-Bawerk's Critique of the “Naïve Productivity Theory of Interest”. Journal of the History of Economic Thought,27, pp 375-382

Martin: I think you might be onto something when you say it's fragmented across sub-fields in economics.

The simple Irving Fisher diagram is very instructive, in showing how the rate of interest and the intertemporal consumption path are co-determined by preferences and technology. But it doesn't explicitly have capital goods in the model. They are in there somewhere, buried inside that intertemporal PPF.

I have skimmed the first chapter of Bob Murphy's dissertation. Yep, it looks good stuff, but it's maybe too specific on a particular issue and a particular economist (Bohm Bawerk) for what I'm talking about.

This is a good summary article:

http://www.econ.yorku.ca/~avicohen/Linked_Documents/JEP_Cohen_Harcourt.pdf

Timothy; good find. not a bad article. Underplays the importance of the role of time preferences, IMHO. (If people didn't care about *when* they got to consume stuff, the theory of capital and interest would be *massively* different. All interest rates would be 0%, for starters.) And it talks about reswitching and *the* rate of interest, ignoring the whole term-structure question.

david: anyone who has any income today may choose between current consumption and (the vector of) future consumption, depending on time preference. Their time preferences will be one of the things that affects the prices of capital goods and rates of interest in general equilibrium (except under very special assumptions). That's the road we have to walk down, Marxists or not.

Quite true. In fact their preferences for any kind of good at all, not just goods that differ in time, will affect relative prices of goods now. The difference is that economists at the time could not convince their colleagues that this doesn't matter, whereas economists today are quite willing to ignore it (for a variety of conceptual reasons). When Robinson was solemnly pronouncing that such-and-such was NOT INDEPENDENT OF THE INCOME DISTRIBUTION!!, it was really a declaration that was expected to cause metaphorically pale faces, shrieks of fear, etc.

(note that in DCT, relating the interest rate to individual time-preferences is non-trivial if you have people have different endowments of land and different individual time-preferences. Worse if their time-preference isn't constant, but changes with the rest of their basket.)

david: yep, but relating the relative price of apples to bananas to the vector of different individuals' preferences for apples and bananas and their endowments is also non-trivial (but solvable) in the same way.

There are more periods of time than there are different fruits; the future is less certain than the present because things change; there are few futures markets; technologies are replicable across time periods (unless we forget stuff or the weather changes) etc., so there are genuine differences between the economics of choice across time periods and the economics of choice across goods in one time period. But ignoring preferences, expectations, and assuming prices never change, seems like a retrograde step to me.

Having recently taken graduate-level coursework, I can say that "capital theory" is not taught, it's was all just one-good growth models. I first came upon CCC by reading the Cohen & Harcourt JEP article, and while I've tried to read more about the topic since then, it's still not clear to me what was all the fuss about.

But anyway, capital theory in neoclassical framework would be probably about dynamic general equilibrium models with multiple capital goods. Mas-Collel et al. textbook has some theory in chapter 20 ("Equilibrium and time"), although most of the examples are again just Ramsey one-good model (but there are also few paragraphs about how some properties do not generalize to multiple-good case). This approach is also nicely defended in paper by Dixit ("The accumulation of capital theory", http://www.jstor.org/stable/10.2307/2662714 ), which in turn is a review of book by Bliss ("Capital theory and the distribution of income", North-Holland, 1975).

Nick,

"But it doesn't explicitly have capital goods in the model. They are in there somewhere, buried inside that intertemporal PPF."

The only 'school(s)', who I think deal explicitly with what's inside the PPF, is the Austrian school; I think you can find it in Rothbard in Chapter 5 to 9. A claim could be made on part of the New Institutional Economics, though they're more pre-occupied with institutions and the firm and not so much with the interest rate. I say that a claim could be made, because their work can be seen as describing the capital structure without actually talking about the capital structure.

Neither is really being taught in undergrad, as far as I am ware, and the latter is probably only taught in programs that also do L&E.

For Rothbard Ch5 to Ch9: http://library.mises.org/books/Murray%20N%20Rothbard/Man,%20Economy,%20and%20State,%20with%20Power%20and%20Market.pdf

Study Guide (i.e. a quicker overview): http://mises.org/books/messtudy.pdf

"I think you might be onto something when you say it's fragmented across sub-fields in economics."

To be honest though, I think that there is a good reason for why that is the case. If you would want to write capital theory today, you'd have to integrate insights on the one hand from finance (e.g. real options etc) with what we know about the firm, competition, entrepreneurship etc, and all you would get out of it would be a microlevel explanation of Bohm-Bawerk's three causes of interest.

I wouldn't even know where to start to model something like that and what to learn to do so. To top it off, I wouldn't even know what kind of a question someone would be answering by writing out capital theory today.

It seems to me that we today have a bunch of ad hoc models to answer various small questions rather than one big model to answer all those small questions, and I can guess why.

I can be wrong though, I am reading up on it now, so clearly I think there must be something there :P.

ivansml: "But anyway, capital theory in neoclassical framework would be probably about dynamic general equilibrium models with multiple capital goods."

I think that's right. But I think you could get most of the important insights with just one capital good and one consumption good, as long as those two goods were genuinely different in production.

Though, I still think my Dutch capital model is maybe simpler and gives the most intuition with very little math (plus it does land at the same time). Start with land, and explain how the price of land and rate of interest gets determined. Then introduce an investment technology and ask how that changes the picture.

Actually, in a world where technology is improving over time, the existing stock of capital goods is *exactly* the same as (non-Dutch) land. We aren't making land any more, and we aren't making old capital goods any more. The new capital goods we are making are different from land and different from old capital goods. The fact that God made the stock of land and our ancestors made the stock of old capital goods is irrelevant.

Martin: without having read enough of the Austrians to know for sure, my sense is that the Austrians basically got it right.

The Austrians only ran into trouble if they tried to simplify by (in effect) collapsing all the future time periods into one future time period. "Waiting", for example, is multi-dimensional if there are multiple future time periods. (But there was nothing intrinsic in the Austrian approach that said they *had* to do this simplification).

In holland can firms be land?

Also, it looks like Mas-colell has a paper on the debates, where he argues they were similar to comparative statics in general equillibrium, the theorems for one good generally didn't hold for the multigood case. http://www.econ.upf.edu/~mcolell/research/art_065.pdf

Nick

I don't know about economics programs, but I really, highly recommend the stuff that John Hicks wrote between 1960 and 1980. You'd like his '73 book especially if you basically agree with the Austrian take. Jim Tobin tried to develop Fischer's theory a bit in some papers. And Fischer Black took it to its logical conclusion, albeit from a financial perspective where the past and accounting values don't matter, at all.

Edeast,

"In holland can firms be land?"

Let's say you have one firm, F1, that owns a particular input, A, that two other firms, F2 & F3, use in the production with B2 & B3 respectively, to produce two different goods, C2 & C3. When F2 buys F1 to control A and to produce more of C2, the status of the input A has changed and so has the status of B3.

In Holland firms are not land, but combinations of land are often controlled through firms, and who controls what now matters for what happens to the interest rate. Sure if transaction costs were zero, people could hold land directly, and rent out fractions etc, and there would be no firms; as transaction costs are not zero, there are firms and who controls what and in what combination matters for what happens to the interest rate.

Edeast: "In holland can firms be land?"

Some farmers own their land; others rent it. Some farmers own their own combine harvesters; others rent them (actually, they usually rent the bundle of combine harvester+labour to operate it, because it's easier to abuse a rental combine harvester than a rental car). Some farmers own their own labour and others rent it (or do a bit of both).

A firm can be owned by the people who own the land, the capital goods, or the labour. Usually they own a combination. Law firms are usually owned by the workers (or a subset of senior workers).

"Capitalism" (i.e. the firm is owned by the people who own the machines, as opposed to the people who own the land or labour) is not a very accurate description of many firms. And if I wanted to explain what determines whether farmers will own or rent land, machines, labour, I would start talking about things like moral hazard and other asymmetric information problems. It's an interesting question, but has little directly to do with capital theory, in that exactly the same questions about the price of capital goods and the rate of interest would need to be answered even if there were no asymmetric information so it didn't matter who owned them.

I find it conceptually easier to imagine firms renting all their land, machines, and labour, from the owners of land, machines, and labour.

I know I'm going to regret saying anything on this thread. Two references: Syed Ahmad's Capital in Economic Theory: Neoclassical, Cambridge and Chaos (Edward Elgar, 1991) and The New Palgrave: Capital Theory (Macmillan, 1990).

Anyways, analyzing fixed points in certain dynamical systems is not the same as "assuming prices never change". I could go on.

What I was thinking,was that an entrepreneur is like an engineer, puts together a blueprint, contracts in all the components, and they then sell the rights to their rent, like a capital good. Albeit the machine has a fairly complex production function. I've just never understood the demarcations in economics, c + i+g and tech.. , I was just wondering if firms vs capital was a meaningfull separation, and I gather from your informationassymetry it is.

It wasn't directly related to questioning the price of capital and the rate of interest. What I had in my mind was trying to determine how firms are created, and I was approacing it as a coalition, breaking off and forming a minieconomy. From, jerry green, description of the core as the set of unblocked allocations, then i got lazy and just threw out the question to see if I was going anywhere.

Edeast: "What I had in my mind was trying to determine how firms are created, and I was approacing it as a coalition, breaking off and forming a minieconomy."

Yep. I think that's similar to how Coase thought of the firm.

david: yep, but relating the relative price of apples to bananas to the vector of different individuals' preferences for apples and bananas and their endowments is also non-trivial (but solvable) in the same way.

There are more periods of time than there are different fruits; the future is less certain than the present because things change; there are few futures markets; technologies are replicable across time periods (unless we forget stuff or the weather changes) etc., so there are genuine differences between the economics of choice across time periods and the economics of choice across goods in one time period. But ignoring preferences, expectations, and assuming prices never change, seems like a retrograde step to me.

Yes. This is because we have, in orthodox modelling, permitted such variations to exist, with the assumption that many possible pathological interactions simply do not happen: all curves slope the right way, there are no crazy income effects, we can aggregate individuals into firms and firms into markets and markets into aggregate demand safely, etc. So naturally assuming that the variations don't happen at all is a step backwards.

The heterodox worry that the step forward was a step down the wrong road, of course. In a perfect world we would have some tractable model that can grasp the entire artifice of preferences, expectations, and uncertainty without having all these kludges - or at least some manner of rigorous surety that piecemeal models can actually add up without hiding adverse interactions.

Martin, firms exist to overcome transaction costs,? Whatever those are. Does the same go for capital, because things dont't magically assemble each period. Anyways thanks guys, my internet is shit.

Robert:

1. Suppose people didn't care about *when* they consumed. I.e. no rate of time-preference proper, no diminishing marginal utility of consumption, so they simply want to maximise their total consumption regardless of when it occurs. Any (risk-free real) loans would always be at 0% interest.

2. Suppose (at the opposite extreme) people didn't care about their future consumption at all. Any asset that couldn't be immediately converted into immediate consumption would be worthless. There would be zero saving and investment (more precisely, both would go as far negative as is physically possible), and the implied rate of interest would be infinite.

If we then observe an argument between two groups of economists about what determines asset prices and interest rates, where neither of their models talks about the role of time preferences in determining the current price of existing assets and the current rate of interest, it does seem a little bizarre.

Nick Rowe,

"it does seem a little bizarre"

It all very much does. Capital theory seems to be a bubble of abstract theory and so it's not surprising that Mark Blaug was so uncomplimentary about things like the Cambridge capital controversy. I initially thought he was being unfair, but your summary makes me suspect otherwise...

I'll stop talking I swear, I read the wiki. Just in the dutch example there aren't transaction costs. A machine, is a machine, is a tulip.

Edeast,

"Martin, firms exist to overcome transaction costs,? Whatever those are. Does the same go for capital, because things dont't magically assemble each period. Anyways thanks guys, my internet is shit."

Nick posted a very good link explaining it all (http://en.wikipedia.org/wiki/Theory_of_the_firm).

To answer your question directly: transaction costs are the costs of exchange, and firms are basically ways to substitute command and control for exchange; firms exist because it is sometimes cheaper to have command & control instead of exchange. From this definition you'll also see that in a world with no exchange, i.e. Robinson Crusoe on his island, there still would be capital and capital goods, but that there would be no firm.

Though when there is exchange, it is perfectly possible that capital exists because there are transaction costs. To give you one example: when looking for a place to live, you can either look around your self and collect data and try to come in touch with different homeowners or landlords, or you can go to an agency or an agent who have/has already invested the "time and the money" to do so for you.

"There is a well-known propensity of individuals to dislike what they
don't or can't understand. This book, as well as the writings of the
other Cambridge economists, makes perfectly clear that they do not
understand neoclassical capital theory.... Thus, the appropriateness
of the marginal-productivity theory as a theory of distribution of
income among factors is completely unrelated to any of the controversies
concerning double switching, savings behavior, or the aggregation of
capital.

Yet it appears that it is the confused attempt to discredit the marginal
productivity interpretation of the interest rate which imbues the topics
of capital theory with their ideological interest to the devotees of
Cambridge (U.K.) doctrine."

-- Joseph Stiglitz, JPE, 1974.

Edeast: Yep. My Dutch example totally ignored transactions costs. All (most?) capital theory ignores transactions costs too. Because transactions costs affect (or can affect) all transactions, not just those having a time-dimension. So we duck that question, if we can, to try to keep it simple. But we can't duck transactions costs if we want to understand why firms exist and why they look like they do.

Most transactions costs come down to asymmetric information. The seller (or buyer) knows something the buyer (or seller) doesn't. The seller knows whether his used car is a lemon. The worker knows whether he's working or slacking off. The buyer of life insurance knows whether he is healthy or not. Stuff like that.

Edeast,

"I'll stop talking I swear, I read the wiki. Just in the dutch example there aren't transaction costs. A machine, is a machine, is a tulip."

Yes, that's why I said that writing capital theory today and going further beyond Nick's example would result in very little additional reward:

"If you would want to write capital theory today, you'd have to integrate insights on the one hand from finance (e.g. real options etc) with what we know about the firm, competition, entrepreneurship etc, and all you would get out of it would be a microlevel explanation of Bohm-Bawerk's three causes of interest."

The answer and the main points of what Nick said would remain pretty much the same as far as I can see, but you would know a little bit more about it all.

I don't see really to what question "capital theory" would be the answer, that isn't already answered by some subfield in economics.

Take this in the least offensive possible way, Nick, but I'm pretty sure you're completely wrong.

Cambridge UK took issue with the neoclassical treatment of capital: it's measurement, aggregation, and the concept of the MPC. The MPC is circular because the $ measure of capital is determined partly by the rate of profit, but the rate of profit is supposed to reflect the $ of capital being used. Piero Sraffa assumed neoclassical concepts like equilibrium in 'Production of Commodities' to take on neoclassical economics on its own logic. He came to several conclusions including but not limited to reswitching, The most important point I take away from it is that you must know the distribution of profits and wages before prices can be calculated.

UnlearningEcon,

I am pretty sure that you can find in Fisher (1930) that it's the value of the future income from that capital that determines the value of the capital. The marginal increase in the value of future income then determines the marginal increase in the value of capital.

This point: "The most important point I take away from it is that you must know the distribution of profits and wages before prices can be calculated."

is therefore shared by the mainstream/neoclassicals/etc.

@Chris Auld,

I guess Stiglitz thought Samuleson and Solow also failed to understand their own models, seeing as they themselves conceded the major points.

@Martin

And the value of the future income depends on the rate of profit, no?

'is therefore shared by the mainstream/neoclassicals/etc.'

Care to elaborate? I know there are considerations like this in monpolistic models, but as far as I'm aware income is determined by marginal productivites.

Unlearning: that wasn't at all offensive.

"The MPC is circular because the $ measure of capital is determined partly by the rate of profit, but the rate of profit is supposed to reflect the $ of capital being used."

I basically agree with what you are saying there. But I want to restate it in my own words, because what you said wasn't as clear as it could have been, and (some) people (on my side) really do need to understand this point.

Consider the statement "the rate of interest is equal to and determined by the marginal product of capital". (Let's ignore depreciation to keep it simple.) That statement is only true in a simple-one good model where the capital good is the same as the consumption good so that the price of one unit of the capital good is always equal to the price of one unit of the consumption good.

The correct statement would be: "the rate of interest is equal to [I did not say "and is determined by"] the marginal product of capital divided by the price of capital (in terms of the output good)".

So even if you know the MPK, you can't solve for the rate of interest unless you know the price of capital (Pk). We need an additional equation before we can use this correct statement to determine the rate of interest. What could that additional equation be?

1. If you make the very special assumption of a one-good model, where you can convert the capital good into the consumption good or vice versa by waving a wand, then Pk=1. But that is a very special assumption.

2. You talk about people's preferences. In particular, you talk about their time-preferences. Will people be willing to own the current stock of capital goods at the price Pk? If I buy one unit of the capital good I consume Pk fewer units of the consumption good today, but MPK(t+1) more units of the consumption good next period, and MPK(t+2) more units the period after that, etc. An equilibrium for Pk would be where at the margin people are just indifferent between the extra consumption today and the stream of extra consumption in future periods. And that depends on their time preferences.

Unlearning; YES. If neoclassical economists didn't talk about time preference then (except under very special assumptions so there's basically only one good) neoclassical theory of interest would be...not circular precisely, but....what's the right word for being an equation short of a solution?....let's just say "total crap". But (good) neoclassical theory does talk about time preference. So it isn't total crap.

Please please please read my Dutch Capital Theory post, which makes this point very simply.

"The most important point I take away from it is that you must know the distribution of profits and wages before prices can be calculated."

That point is (sort of) correct too. Again I need to restate it. Prices and the distribution of income are determined simultaneously. Each depends on the other. You need to know: technology; preferences; and endowments too (who owns what), if you want to explain prices. (Except in special cases like identical homothetic preferences). If the people who like cricket own a lot of land and the people who like soccer own a little land, then cricketers will get high wages and soccer players will get low wages.


Is it possible to reformulate exchange rate models, which have consumption goods plus contingent assets/arrow securities, by just declaring those securities to be capital?

Even advanced labour market models generally talk about how excessively high wages and search 'frictions' create unemployment, which is inconsistent with the idea that wages and profits can vary a la Sraffa. I just don't think economists would be comfortable with the statement 'income distribution is largely determined by political power,' but if I'm wrong then great.

Also, you said on Ryan Murphy's post that neoclassical critics don't realise the centrality of preferences. I think this is important - have you seen this essay where two economists (you possibly know Varoufakis from his commentary on the EZ crisis) identify neoclassical economics a being a methodological core consisting of 3 main components: preferences, individualism and equilibration. If you have time:

http://www.paecon.net/PAEReview/issue38/ArnspergerVaroufakis38.htm

I have problems with preferences. In an aggregative model like Sraffa's, you'd have to aggregate preferences which leads to well known problems such as the Sonnenschein Mantel Debreu theorem, which as I expect you know, states that aggregated preferences don't display properties similar to individual preferences without incredibly restrictive assumptions:

http://en.wikipedia.org/wiki/Sonnenschein–Mantel–Debreu_theorem

So how do we invoke preferences? I accept there is a constraint on production based on whether people actually want what is produced, but I don't see why it's impossible to add this to a model like Sraffa's.

On (2), firstly I would generally reject the idea of an representative agent who decides between capital and consumption; I'd prefer to split into capitalists and workers (and bankers and the government). But even ignoring this, your formulation of an equilibrium is merely an equilibrium for the price of capital - it does not deal with the fundamental problems of measuring and aggregating capital (.e.g brooms versus blast furnaces). Sraffa's dated labour inputs creates a level of consistency here by giving us the value of what was required to produce the capital in question.

Obviously parts of this debate would collapse into arguments about microfoundations and the Lucas Critique. I have noticed mainstream and heterodox debates tend to gravitate towards a few key issues.

UnlearningEcon,

"And the value of the future income depends on the rate of profit, no?"

If you mean the rate of interest, then yes. I was basically thinking of Fisher (1930 p.15): "The value of any property, or rights to wealth, is its value as a source of income and is found by discounting that expected income.".

The question then is basically how do you find the rate of interest.

I. If income expected income is fixed, Fisher (1930 p.72) states that the rate of interest is that value that clears the market for lending and borrowing. Lending and borrowing is used to change "the shape" of the "income stream" to maximize "total desirability". The shape of the income stream, is what Fisher means by when certain income is received; total desirability is utility.

Fisher (1930 p.72):

"Through the alterations in the income streams produced by loans or sales, the marginal degrees of impatience for all individuals in the market are brought into equality with each other and with the market rate of interest.

This condition B is equivalent to another, namely, that each individual exchanges present against future income, or vice versa, at the market rate of interest up to the point of the maximum total desirability of the forms of income available to him."

If you've read Nick's "Dutch Capital Theory", you'll recognize this. The assumption is also the same, the rate of interest is that rate that clears the market (implicit here, but explicit in Fisher is that there is no default etc.).

Fisher and Nick are also way more accurate than me, as they both do emphasize that: "the determination of each can be accomplished only with the determination of all the rest." Fisher (1930 p.73).

II. If expected income is not fixed, but actors have the choice out of various income streams with different time-shapes, then you get I guess what Sraffa meant with the perceived "circularity".

Fisher (1930 p.85):

"At first sight it may appear to those not familiar with the mathematics of simultaneous equations and variables that the reasoning is circular; the rate of interest depends on individual rates of impatience; these rates of impatience depend on the time shapes of individual income streams; and the choice of these time shapes of income streams depends, as we have just seen, on the rate of interest itself.

It is perfectly true that, in this statement, the rate of interest depends in part on a chain of factors which finally depend in part on the rate of interest. Yet this chain is not the vicious circle it seems, for the last step in the circle is not the inverse of the first."

The interest rate is still the one that clears the market,

Fisher (1930 p.86):

"This mathematical principle of determinateness applies in our present problem. Real examples of circular reasoning in the theory of interest are common enough, but the dependence, above stated, of interest on the range of options and the dependence of the choice among them on interest is not a case in point, for this last determining condition is not derivable from the others".

The interest rate "is determined so as (1) to make the most of opportunities to invest, (2) to make the best adjustment for impatience and (3) to clear the market and repay debts." (Fisher 1930 p.88)

You can find Fisher (1930) here if you're interested: http://files.libertyfund.org/files/1416/Fisher_0219.pdf

UnlearningEcon,

If you walk through Fisher (1930), you'll find that:

1. You don't need aggregate preferences, you just need to solve for the interest rate to clear the market. No aggregation necessary there.

2. Aggregating capital is easy now, as it is equal to the discounted value of (expected) income, and you can add up money.

Britonomist: Hmm. Dunno. Probably not, because those securities don't get "produced" in quite the same way.

Unlearning: Let me give you a very brief overview of Walrasian/Arrow-Debreu General Equilibrium theory.

There are individual consumers, who each have endowments (of labour, land, and the existing capital goods they own today). And they have preferences, defined over the current and future consumption goods. Their endowments can all be different, and their preferences can all be different. We don't need to aggregate preferences (unless we are math-challenged like me, or we want to tell a simple version of the story). Individuals sell/rent their endowments and use the proceeds to buy current and future consumption goods. They maximise utility taking prices as given. The rates of interest are just (intertemporal) prices. The "taking prices as given" bit is where the assumption of competition (as opposed to monopoly/monopsony) comes in.

There are individual firms that have a technology that lets them transform some goods into other goods (maybe at the same or at different times). They maximise profits taking prices as given. The profits, if any, go to the individuals who own shares in the firms.

The equilibrium price vector (which includes interest rates) is where the sum of the individual quantities demanded equal the sum of the individual quantities supplied for every single good.

Another way of describing the equilibrium is with a lot of equations like MUa/MUb = Pa/Pb = MPLb/MPLa. The ratio of the Marginal Utility of apples to bananas equals the price ratio equals the ratio of the Marginal Products of Labour in producing bananas to apples. And those same ratios are equal for every individual consumer and firm. For all pairs of goods, including future goods. For all types of labour, and land, and machines, etc.

And there's a whole little math-econ industry which checks the conditions under which an equilibrium exists (basically, you can't have increasing returns to scale, which makes sense, because if you did then you would get monopoly anyway).

The S-M-D theorem says that the result may look rather different from the case where all individuals are the same. OK. If that's what happens then that's what happens. Even if it is unfortunate for math-challenged economists like me, who really want to get a simple intuitive understanding.

Is there "political power" in that model? No. The distribution of income in that model, just like everything else, depends on: endowments; technology; and preferences. If you happen to own something (like your particular skills) that can be used to make something that other people really want, especially rich people, then you will be rich. If not, you won't.

Take that model. Now simplify it. Assume there is only one type of labour. Ignore land. Assume fixed coefficient linear technology. Cross your fingers (or keep tweaking the assumption about preferences) and hope a steady state exists where prices never change over time. Now throw away the preferences. You've got Sraffa. (I might have forgotten something.) But the rate of interest (or the real wage rate) is now indeterminate, and must be assumed exogenous. Because you have thrown away the assumption about time preference.

Unlearning: "On (2), firstly I would generally reject the idea of an representative agent who decides between capital and consumption;.."

Yep. The representative agent analysis will only exist under very special assumptions (identical homothetic preferences, IIRC). But it doesn't really matter (unless you want to keep it simple). The B.MU(C(t+1))/MU(C(t))=1/(1+r) equilibrium condition will still hold for every individual, even if they have different consumption streams. (Except for credit-rationed individuals, of course).

" it does not deal with the fundamental problems of measuring and aggregating capital (.e.g brooms versus blast furnaces)"

We don't need to aggregate capital.

I see Martin can type (or think, or both) quicker than me. I wonder if we are saying the same thing?

I think Martin and I are saying the same thing.

P.s. as Martin says, you can aggregate different capital goods by value if you want to. But why would you ever want to? just don't ever stick the *value* of capital in a production function!. You only ever stick the physical quantities of capital goods in production functions. That was where Cambridge US got sloppy. Production functions are what the engineers know, not what the accountants know.

Yes, I think we're saying the same; mostly because Fisher and you both think in terms of a simplified GE model.

The result is that of which is to look at the problem as an arbitrarily long list of equations, that is as arbitrary as the number of actors and you try to find the value for the "interest rate" that is consistent with all of them.

The economics comes in when you write the equations in terms of preferences, technology and endowments.

"just don't ever stick the *value* of capital in a production function!"

So - just don´t do what pretty much every micro and macro economist are doing.

We can't aggregate labour either. Or land. Except by value. But then we can't stick aggregate value of labour or land in a production function either. Blast furnaces and broomsticks, brain surgeons and buskers, bitumen mines and beaches.

Theoretically this isn't a problem. Empirically it is a problem.

nemi: it's OK to do it if you cross your fingers.

"Walrasian/Arrow-Debreu General Equilibrium theory"

No such thing exists. In particular, Walras's part V model (1954, Jaffe translation) is overdetermined and, thus, logically inconsistent in general if one takes endowments of capital goods as given.

A problem exists in relating financial capital to capital goods. Many above just ignore the existence of this problem.

I am OK with a two good model, in which there is K, L going into, say, 2 production functions, with C and K going out of each.

I am a lot less OK with the following assumptions:

1) we gain utility only from C, and not from holding K.
2) There is no risk
3) There are no credit constraints

It seems to me that risk tolerance dwarfs time preference as a determinant of equilibrium rates, and that the demand for more wealth by the wealthy is endless, while most everyone else, who isn't wealthy, engages in rudimentary buffer stock savings for insurance purposes that have little to do with time preference.

"1. Some economists in Cambridge UK wanted to explain prices without talking about preferences. I don't know why they didn't want to talk about preferences."

This must refer to Sraffa, and I don't believe it's right, since it ignores the difference between value(s) and price(s). This is from Sraffa's introduction to Ricardo's Principles:


"The idea of an ‘invariable measure’ has for Ricardo its necessary complement in that of ‘absolute value’. This concept appears in the Principles at first (in ed. 1) as ‘absolute value’1 and later (in ed. 3) as ‘real value’,2 it comes out from time to time in his letters,3 and takes more definite shape in his last paper on ‘Absolute Value and Exchangeable Value’. In one of his drafts for that paper he writes: ‘No one can doubt that it would be a great desideratum in political Economy to have such a measure of absolute value in order to enable us to know[,] when commodities altered in exchangeable value[,] in which the alteration in value had taken place’.4 In another draft he explains what he means by a test of whether a commodity has altered in value: ‘I may be asked what I mean by the word value, and by what criterion I would judge whether a commodity had or had not changed its value. I answer, I know no other criterion of a thing being dear or cheap but by the sacrifices of labour made to obtain it.’5 And elsewhere he writes: ‘To me it appears a contradiction to say a thing has increased in natural6 value while it continues to be produced under precisely the same circumstances as before.’7

Ricardo starts (in ed. 1 of the Principles) by applying the concept to the problem of two commodities which have changed in relative value as a result of a change in the difficulty of production: absolute value is then the criterion for deciding in which of the two the real change has occurred. He ends (in his last paper on value) by bringing this criterion to bear upon another problem, namely the distinction between two causes of changes in exchangeable value: for, ‘difficulty or facility of production is not absolutely the only cause of variation in value[,] there is one other, the rise or fall of wages’, since commodities cannot ‘be produced and brought to market in precisely the same time’.8 Absolute value, however, reflects only the first type of change and is not affected by the latter. As Ricardo says with reference to a commodity which changes in price owing to a rise of wages: ‘If the measure was perfect it ought not to vary at all’.1 After one of the numerical examples with which in a letter of 1823 he illustrates this deviation, he comments as follows: ‘The two commodities change in relative value....Can it be said that theproportions of capital we employ are in any way altered? or the proportion of labour? certainly not, nothing has altered but the rate of distribution between employer and employed...—this and this only is the reason why they alter in relative value’; and he concludes: ‘The fact is there is not any measure of absolute value which can in any degree be deemed an accurate one.’2 Accordingly he falls back on his admittedly imperfect standard as giving the least ‘deviation from truth’.3

In this attempt to extend the application of absolute value to the second problem (that of distinguishing the two sorts of changes in exchangeable values) Ricardo was confronted with this dilemma: whereas the former application presupposes an exact proportionality between relative and absolute value, the latter implies a variable deviation of exchangeable from absolute value for each individual commodity. This contradiction Ricardo never completely succeeded in resolving, as is apparent from his last paper.

There is another respect in which his last paper on value reverts to a position similar to that of edition 1. The effects on value of different proportions or durabilities of capital can be looked upon from two distinct aspects. First, that of occasioning a difference in the relative values of two commodities which are produced by equal quantities of labour. Second, that of the effect which a rise of wages has in producing a change in their relative value. In edition 1 the second aspect is the one exclusively considered: whenever different proportions or durabilities of capital are mentioned in connection with value, Ricardo always speaks in terms of the effect of a rise of wages. The first aspect creeps into the later editions: once into edition 2 and a few times into edition 3, usually as incidental to discussion of variations in value, and probably as a result of argument with his opponents, particularly Torrens and Malthus, who looked at the problem from this angle.1 But while in edition 3 Ricardo sometimes refers to different proportions or durabilities of capital as causing differences in relative values, the effect of a rise in wages remains in the forefront, and it is upon this aspect that attention is focused in the paper on ‘Absolute Value and Exchangeable Value’.

This preoccupation with the effect of a change in wages arose from his approach to the problem of value which, as we have seen, was dominated by his theory of profits. The ‘principal problem in Political Economy’ was in his view the division of the national product between classes2 and in the course of that investigation he was troubled by the fact that the size of this product appears to change when the division changes. Even though nothing has occurred to change the magnitude of the aggregate, there may be apparent changes due solely to change in measurement, owing to the fact that measurement is in terms of value and relative values have been altered as a result of a change in the division between wages and profits. This is particularly evident in the extreme case where the aggregate is composed of the same commodities in the same quantities, and yet its magnitude will appear to have changed as measured in value.

Thus the problem of value which interested Ricardo was how to find a measure of value which would be invariant to changes in the division of the product; for, if a rise or fall of wages by itself brought about a change in the magnitude of the social product, it would be hard to determine accurately the effect on profits. (This was, of course, the same problem as has been mentioned earlier3 in connection with Ricardo’s corn-ratio theory of profits.) On the other hand, Ricardo was not interested for its own sake in the problem of why two commodities produced by the same quantities of labour are not of the same exchangeable value. He was concerned with it only in so far as thereby relative values are affected by changes in wages. The two points of view of difference and of change are closely linked together; yet the search for an invariable measure of value, which is so much at the centre of Ricardo’s system, arises exclusively from the second and would have no counterpart in an investigation of the first.

This function of the theory of value of making it possible, in the face of changes in distribution, to measure changes in the magnitude of aggregates of commodities of different kinds or, what is even more important, to ascertain its constancy, appears once more in connection with the measurement of the quantity of capital. With reference to the theory of Torrens (‘that commodities are valuable according to the value of the capital employed on their production, and the time for which it is so employed’) Ricardo says in the letter to McCulloch of 21 Aug. 1823: ‘I would ask what means you have of ascertaining the equal value of capitals?... These capitals are not the same in kind [if they were, he points out in an earlier draft, ‘their proportional quantities would indicate their proportional values’1 ]... and if they themselves are produced in unequal times they are subject to the same fluctuations as other commodities. Till you have fixed the criterion by which we are to ascertain value, you can say nothing of equal capitals’; for, as he says in another draft of this letter, ‘the means of ascertaining their equality or variation of value is the very thing in dispute.’2"

Now if "the ‘principal problem in Political Economy’ ...[was] the division of the national product between classes", profit as marginal product of capital wouldn't appeal to someone who held the views quoted above.

So Sraffa as a neo-Ricardian wanted to undermine the marginal product theory and fulfill Ricardo's program of finding an alternative theory of value both for the technical purpose of having a standard numeraire and the political economic (yes, there used to be such a thing, but we're beyond it now, of course) program of justifying a pattern of distribution. This would be particularly important if it is possible that "measurement is in terms of value and relative values have been altered as a result of a change in the division between wages and profits" and the justification reasoning is circular.

Sraffa succeeded in his program in a sense, but the usefulness and relevance of this positive part is unclear. The attack on marginal theory was both successful and relevant.

The key problem is that marginal product is undefined because the value of capital is undefined for this use. Such definitions are circular, and attempts to define it run into insoluble problems. Capital is also multivalued, so which value do you use and why? Re-switching isn't the main problem, but it's symptomatic. For instance there's also the problem of externalities (the spell checker votes for paternalistic extermination here. Seems a bit extreme).

Capital is the luminiferous aether of economics. It's hard not to believe that some of the enthusiasm for marginal product theory is owing to its political implications for income distribution.

"At first sight it may appear to those not familiar with the mathematics of simultaneous equations and variables that the reasoning is circular; the rate of interest depends on individual rates of impatience; these rates of impatience depend on the time shapes of individual income streams; and the choice of these time shapes of income streams depends, as we have just seen, on the rate of interest itself."

If you add risk, uncertainty I would agree, though risk and uncertainty often dominate as they do now in US and German treasury bonds. So you can define the value of capital as the NPV from applying this interest rate to the income stream (ignoring risk). Now, however defining this income stream as the marginal product of this capital value IS circular. The income stream doesn't depend on the value of capital; It defines it (for this purpose).

nick: How do you type with your fingers crossed?

@Peter N:

Am I misreading/misundertanding, or are the Ricardo and Saffra you describe attempting to define value as an objective/intrinsic property of an object, and not a subjective relationship between objects and people? If so, why does anyone care what they think? Isn't it obvious to everyone that that project is silly?

@Alex:

If you object to that definition of "value," then by all means, continue to use the word to mean a subjective relationship, and we can pick a different word to stand in for the objective property of embodied social labor. Whether the laws of motion of a capitalist economy are better described by the former or the latter is an empirical question, so there's no sense getting all stopped up over definitions.

@ Alex

I think that was exactly the project of Sraffa--to formulate some objectivist theory of economic value (and relatedly, of production) foundationally based on "physical real costs" as opposed to marginalism's subjective preferences or utilities. That project ended up bringing Sraffa close-ish to Marxists and Ricardian socialists in terms of political economy (capitalist exploitation of labour and all that), which is really the only reason anyone cares about it. (see e.g. Sen's nice article in JEL 2003 on Sraffa). Sraffa's work is often elegant, but yes It does seem pretty silly when you step back and look at the big picture.

@ As an antidote, here's an Austrian view from Robert Murphy, no uncritical admirer of Sraffa's theories.

"Having said this, I still urge the serious student of Austrian capital and interest theory to peruse Sraffa's work. Sraffa's neo-Ricardian[2] disciples were not completely misguided in their attacks on the neoclassical mainstream in the Cambridge capital controversy. They were perfectly correct to criticize the orthodox justification of interest payments as a "return to the marginal product of capital." Outside the neoclassical world of economies with one good, there is no such thing as a "stock" of capital; instead, there are various quantities of heterogeneous capital goods. One can only compute an aggregate total of "capital" by first knowing the interest rate at which to capitalize the present discounted value of the heterogeneous goods. As Sraffa himself explains:

'…in general the use of the term 'cost of production' has been avoided in this work, as well as the term 'capital' in its quantitative connotation, at the cost of tiresome circumlocution. This is because these terms have come to be inseparably linked with the supposition that they stand for quantities that can be measured independently of, and prior to, the determination of the prices of the products. (Witness the 'real costs' of Marshall and the 'quantity of capital' which is implied in the marginal productivity theory.) Since to achieve freedom from such presuppositions has been one of the aims of this work, avoidance of the terms seemed the only way of not prejudicing the issue. (9)
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. To offer a proper defense of interest payments, one must turn to a theory of interest (such as the theories offered by Austrian economists) that does not view interest as the marginal product of capital.'" http://mises.org/daily/1486


This is pretty clear about the real issue marginal productivity - It's "the conventional, mainstream justification of the capitalists' income". Ricardo would obviously have hated it.

The basic result above doesn't depend on things like objective value, or reswitching.

rsj: "I am a lot less OK with the following assumptions:

1) we gain utility only from C, and not from holding K.
2) There is no risk
3) There are no credit constraints"

Risk gets handled, in a way, in Arrow-Debreu. By redefining goods as state-contingent dated goods. The problem then is the assumption of complete markets.

But here's the wider issue: think of all the problems in GE theory. Now add some additional problems (one type of labour, steady state, rate of interest not explained at all). You've got the problems of Neo-Ricardian theory.

Peter N: "The key problem is that marginal product is undefined because the value of capital is undefined for this use. Such definitions are circular, and attempts to define it run into insoluble problems."

Read my response to Unlearning, where I have already dealt with this old chestnut. Or maybe re-read my Dutch Capital Theory post, only more slowly this time.

Robert: BTW. Let me remind you of a comment you left on my Dutch Capital Theory post:

"Consider an economy growing at a constant rate of growth with steady state prices. Two processes are operating, according to the above assumptions. In one, each acre of land is used to produce a yearly output of an unchanged acre of land and 4 tons of wheat. In the other a tons of wheat are used to produce an acre of land. Assuming a (competitive) uniform rate of profit, prices are described by two equations. The first is P(1 + r) = P + 4. The second is a(1 + r) = P. These are two equations in two unknowns. (As stated in the post, the first equation can be used to find a third unknown, the rent of land, in terms of the original unknowns.) There is only one economically meaningful solution. One need not talk about intertemporal preferences at all."

Your answer was identical to the Cambridge US solution. Yes, if you assume a very special technology that is equivalent to assuming a one-good model, then you can determine the rate of interest independently of preferences. I'm not sure if you saw where I explain this more fully in my later comment:

"I am a bit surprised that Robert didn't fire back with a quick counter: if the first process stops being used, there is zero consumption today, so MU(C(t)) probably becomes extremely high; and if the second process stops being used, growth will stop. But Robert could easily have handled that second case by simply assuming his second process was reversible, so growth could go negative if people suddenly get very impatient.

Let's put some numbers on it:

Assume 1 acre of land produces 4 tons of wheat per year. Assume 40 tons of wheat can be used to produce 1 acre of new land, and that this process is reversible. It follows immediately that the MC of land is 40 tons of wheat. The MC curve is flat, in both the positive and negative quadrants, so P=MC=40, regardless of preferences. And since the rent on land is 4, it follows immediately that the rate of interest (measured in wheat) is 10%, regardless of preferences.

In other words, if we do make a strong simplifying assumption about technology, we can determine the rate of interest from technology alone, regardless of preferences.

But, what Robert has done is reinvented "American (i.e. Solow-Samuelson, and certainly not Fisher) Capital Theory". Just redefine units so that we measure land in fortieths of an acre, and one unit of output is equivalent to one ton of wheat or one unit of land (i.e. capital). C+I=Y=4K where I=dK/dt. This is the "AK Growth Model", where "A" is 4 (Robert calls A "a").

With units defined that way, and with that technology, the rate of interest is equal to and determined by the marginal product of land (i.e. capital).

It was EXACTLY that same simplifying assumption that caused the whole Cambridge-Cambridge Capital controversy. It's a one-good model, where the capital good and the consumption good are exactly the same. (More generally, where the capital/labour ratio for the consumption good is always the same as the capital/labour ratio for the investment good, or in Marxian language, they have the same "organic composition of capital")."

Do you get my point here?

nick: You said:


Read my response to Unlearning, where I have already dealt with this old chestnut. Or maybe re-read my Dutch Capital Theory post, only more slowly this time."

I assume you mean this response.

"1. You don't need aggregate preferences, you just need to solve for the interest rate to clear the market. No aggregation necessary there.

2. Aggregating capital is easy now, as it is equal to the discounted value of (expected) income, and you can add up money."

. I agree with you the method works. This shouldn't be a surprise since I wrote higher up:

" So you can define the value of capital as the NPV from applying this interest rate to the income stream (ignoring risk). Now, however defining this income stream as the marginal product of this capital value IS circular. The income stream doesn't depend on the value of capital; It defines it (for this purpose)."

In this case, it's a question of implied causation, and a very important one. If you use marginal productivity a guide to division of profits the implication is that the value of the capital produces the return. That's different from saying the value is the discounted sum of the net return by definition. That's not causation. You're defining an accounting identity. I vaguely seem to remember you had an opinion about reasoning from accounting identities.

It's also an arbitrary choice among price to buy, price to sell, distress sale price, book value, liquidation value, NPV of net earnings, NPV of gross earnings, NPV of EBITDA, NPV of dividends, market capitalization, price as a takeover target. These are all legitimate definitions of value for various purposes. Moreover there isn't complete agreement as to which value to use in all circumstance (like EDITDA or GAAP earnings). In addition some industries have specialized, even bizarre accounting rules. For instance a movie rarely makes a net profit (Return of the Jedi grossed $475 million with 0$ net to date), a band can have a record go platinum and end up owing the company, you may not enjoy being a limited partner,... REITs, banks, insurance companies, conglomerates, utilities, private capital outfits like Bain... - all these have peculiar ideas about profit.

This is an Austrian view:

" One can only compute an aggregate total of "capital" by first knowing the interest rate at which to capitalize the present discounted value of the heterogeneous goods. As Sraffa himself explains:

'…in general the use of the term 'cost of production' has been avoided in this work, as well as the term 'capital' in its quantitative connotation, at the cost of tiresome circumlocution. This is because these terms have come to be inseparably linked with the supposition that they stand for quantities that can be measured independently of, and prior to, the determination of the prices of the products. (Witness the 'real costs' of Marshall and the 'quantity of capital' which is implied in the marginal productivity theory."

Of course Fetter would say it should be the present discounted value of the earnings, since there's no presumption of any intent or desire to liquidate, though, of course, if the liquidation value of your company greatly exceeds the earnings value, you're likely to get a call from Carl Icahn you won't like.

This comment is about multi-good models.

Let A and B be square matrices expressing the technique in use. Each column of A shows the inputs used up in the corresponding industry in a year. Each column of B shows the outputs produced. Since B is not necessarily the identity matrix, this is a model of joint production. That is, this model includes fixed capital (such as, long lived machinery) and land in some sense. (One might think of A as including real wages. Wages are treated like feed for livestock.)

Let p be a row vector of prices, with some chosen numeraire, and let r be the rate of profits. What prices are consistent with smooth reproduction of the economy in the year under observation? The answer is found by solving the following system of equations for relative prices and the rate of profits:
p A (1 + r) = p B
When does this system have a solution? It is meaningless to talk about each industry here having the same "organic composition of capital" prior to and independently of the solution prices and rate of profits. Rowe is simply confused.

A question, perhaps of interest to John Von Neumann, is when are the matrices square in a wider model in which many more processes are available for production. He found it useful to assume constant returns to scale and abstract from the existence of land. It works out that smooth reproduction with a constant rate of growth is possible with square matrices when the rate of profits and the rate of growth are equal. And, in looking at smooth reproduction, one will find a certain multi-good vector of commodities being reproduced at a constant rate, so to speak.

One can ask other questions about this model. What sort of social conventions must exist for rules of thumb for savings and consumption patterns to be consistent with smooth reproduction? What institutions (e.g., conventions on retained earnings for corporations) would be consistent with smooth reproduction? In addressing these questions, one might discuss requirements for the use of commodities and non-commodities. I don't see that one must insist that requirements for use can only be discussed by bringing in mythical and non-existent utility functions.

Sraffa had two broad critiques of neoclassical theory. One was an internal critique. It has been shown that rigorous neoclassical price theory does not necessarily imply the stories that economists tell in teaching and applied work. Equilibrium prices are not indices of relative scarcity. The other was an external critique. Sraffa provided the elements for another theory of value and distribution, a re-discovered classical theory purged of certain weaknesses and also brought forward by Leontief and by Von Neumann.

Let p be a row vector of prices, with some chosen numeraire, and let r be the rate of profits.

But profits very greatly among industries, the number of "commodities' are infinite (as new commodities keep being invented), and the transformation function is both non-deterministic and non-linear.

As an example of the difficulties of production, look at the software industry (which did not exist in Sraffa's time). There are many failed software projects, delayed software projects, and projects which fail to deliver code as expected. Construction has similar problems -- anyone who has hired a building contractor is familiar with delays, work not being completed to spec, etc. Or look at sales. Sometimes the salesmen succeeds in selling and sometimes they fail. Or marketing/advertising/public relations industries. Etc.

By the way, each of the above industries has very different profit rates, possibly because they have different degrees of monopoly power, different barriers to entry/exit, and different risks, but really all we know is that some industries earn a high rate of profit routinely while others (such as airlines) have negative earnings.

http://www.bea.gov/scb/pdf/2010/08%20August/0810_domestic.pdf


Risk gets handled, in a way, in Arrow-Debreu.

That's a bit like hitting a fly with a hammer. Arrow-Debreu takes all transactions out of time. No one goes shopping, they all take delivery of goods based on pre-negotiated contracts. Therefore no one needs money and there is no such thing as monetary exchange (or monetary policy). It's also an excessively complicated model that is a bad way of looking at how an economy works. And it doesn't solve the problem of risk.

I think you can't talk about money without talking about credit constraints, and you can't talk about credit constraints without talking about risk (e.g. that the loan will not be repaid). Without credit constraints, no one would want to hold money (they would hold bonds instead). They hold money because they cannot instantly and frictionlessly sell whatever portion of their endowments that they would want to sell, or they cannot instantly and costlessly borrow.

I don't understand how one can talk about an economy with money without making risk and credit constraints the heart of the analysis.

Peter N,

"If you add risk, uncertainty I would agree, though risk and uncertainty often dominate as they do now in US and German treasury bonds. So you can define the value of capital as the NPV from applying this interest rate to the income stream (ignoring risk). Now, however defining this income stream as the marginal product of this capital value IS circular. The income stream doesn't depend on the value of capital; It defines it (for this purpose)."

Fisher does add risk later on in his third approximation; I just showed the first two briefly.

I do recommend however reading Fisher (1930) if you believe the absence of risk to mean that it is circular: http://files.libertyfund.org/files/1416/Fisher_0219.pdf

rsj,

"I don't understand how one can talk about an economy with money without making risk and credit constraints the heart of the analysis."

Well you have to start the analysis somewhere. To best illustrate what risk and credit constraints do, is to first assume that these are absent. It's therefore not so much that it is not talked about, it is just to understand it some other ground needs to be covered first.

For example, I derive utility from my copy of Samuelson (1977 [1947]) because I like to read it. I however also derive utility from drinking coffee, sometimes I also use my copy of Samuelson (1977 [1947]) to store my coffee on it as I do not want to put it on the couch lest it tips over.

A first model of me reading on the couch would explain the role of Samuelson (1977 [1947]) as a book to read. Now you're perfectly right to add that I also drink coffee and that I should not talk about reading on the couch without drinking coffee; so I add drinking coffee and we have a second model that explains the role of Samuelson (1977 [1947]) also as a place to store my cup of coffee.

If we did not assume the absence of coffee, and you would see me on the couch drinking coffee you'd be led to assume that the sole reason for Samuelson (1977 [1947]) would be as a place to store my coffee on. The existence of coffee also makes it a store of coffee, but that's not its only role; this explanatory strategy guards us against such mistakes.

In the case of money, we have a first model where money is purely a medium of exchange and we use it in transactions. In a second model, we can add risk and we find that apart from a transaction balance there is now also a precautionary demand for money. If we skipped the first step, it would be possible, but much more difficult to see that there is also a transaction demand for money.

Peter N: "I assume you mean this response"

No, that was Martin's response. The names are below the comments on this blog. This was my response

Robert: there are two ways to approach preferences:

1. You can ask "Suppose the economy is in Sraffa's equilibrium. What would people's preferences have to be to make this work?"

2. Or you can ask "Suppose people have the preferences that they do. What happens in the economy?"

The second way makes sense to me.

We don't know which goods will be produced, until we know people's preferences. We don't know if the economy will be growing with positive investment, or declining with negative investment.

Again: suppose people didn't care at all about when they consumed stuff. Then all (real safe) rates of interest would be 0%. Suppose people didn't care at all about future consumption, they only cared about present consumption. Then all interest rates would be infinite.

You can't talk about interest rates and investment without talking about preferences.

The search for a unique stable static solution may have failed but that doesn't mean it was silly. Multivalued, not necessarily stable, dynamic solutions may be more elegant in some aspects, but they are more complex, and they do undermine any given solution as true, just, or obligatory.

Here are a couple of things I want to point out:

In what world does the marginal product of capital NOT have a substantial influence on rates of interest in a world with preferences? Assume I'm a guy with a lot of cash, I might lend the money.

If I were this guy, I'd consider the oppurtunity cost of lending, one opportunity cost is the foregone income I could recieve from investing .
Assume both lending and investing are equally risky, if I could make a larger expected return from investing, I'd invest instead. Therefore, in this situation the return from lending must at least be equal to the expected return on investment.
If investment is more risky than lending, then the interest rate I demand from lending would be the expected rate of return on investment minus a risk premium. The interest rate would therefore still vary with the expected rate of return on investment.
The expected rate of return on investment is weighted average of /net/ company profits.
The weighted average of net company profits after investment corresponds to the marginal product of its internal investment.
Almost all investment funds go to expanding capital, including intangible things like knowledge capital.
Therefore the marginal product of capital strongly influences interest rates.
Where is the flaw?

anon: the marginal product of capital is, per the 'marginal', dependent on the (God help me) quantity of capital that already exists. Thus you might see changes to the general productiveness of capital as showing up in the inframarginal product but not the marginal product.

"the marginal product of capital is, per the 'marginal', dependent on the (God help me) quantity of capital that already exists."

Obviously.

"Thus you might see changes to the general productiveness of capital as showing up in the inframarginal product but not the marginal product."

Huh? I don't care about the general productiveness of capital and I don't even know what the 'inframarginal product' is, I care about my return on my investment = I care about how much additional profit investment funds for a firm produces = I care about how much additional profit acquiring more capital produces = I care about the marginal product of capital

Martin @6:57,

No, I would ask "Why is there a transaction demand for money?" The answer is because of credit constraints. Without credit constraints, there would be no transaction demand for money -- no would hold money, they would instantly and costlessly borrow it as needed, hold it for zero time, and make their transaction. Therefore the economy-wide money *stock* would be zero (the flow would be large). Once you add frictions and transaction costs, there is a demand to hold something that does not pay interest provided that the loss of interest income is less than the transaction fees you would pay if you always needed to sell or borrow in order to obtain money prior to making a purchase. Then you get a demand for money balances, purely due to credit constraints and transaction costs.

The precautionary savings demand is for bonds, not money per se.

@anon

Huh? I don't care about the general productiveness of capital and I don't even know what the 'inframarginal product' is, I care about my return on my investment = I care about how much additional profit investment funds for a firm produces = I care about how much additional profit acquiring more capital produces = I care about the marginal product of capital

The point is that given preferences, it's easy to construct a world in which the (general) productivity of capital has no influence on the marginal productivity, and where the marginal productivity of capital is determined by time preferences alone. In which case you wouldn't really get anywhere with "the interest rate should be influenced by the marginal product of capital" because they are actually both determined by the same things.

rsj,

Could you define what you mean by a credit constraint?

Or let me ask you a different question, in a society of N individuals, where N is very large, how does the absence of credit constraints solve the problem of the double coincidence of wants?

Or to put it differently: if you have a butcher, a baker, and a candlestick-maker, what good does it do the candlestick-maker if the baker promises bread in exchange for candles if the candlestick-maker wants meat? It seems to me that the candlestick-maker still needs to look for a butcher in want of bread.

There is no credit constraint, the candlestick-maker accepts the promise, but money would make things considerably easier.

"The point is that given preferences, it's easy to construct a world in which... the marginal productivity of capital is determined by time preferences alone."

Uh, no?

anon: it's both (except in special cases). Interest rates depend on: intertemporal preferences; and intertemporal production possibilities. IIRC Irving Fisher found a nice way of putting it into words, which I think Martin quotes somewhere above. But "the marginal (physical) product of capital" is only one of the things that appears on the intertemporal production possibilities side -- there's also the trade-off (at the margin) between producing capital goods vs producing consumption goods. And all these things are co-determined in equilibrium, rather than there being one-way causation.

(I've ignored expectations in the above, which I really didn't ought to have done. And the influence of monetary policy is a whole other issue that gets ignored, and shouldn't be in a fuller treatment.)

Lord: "The search for a unique stable static solution may have failed but that doesn't mean it was silly."

Fair point. Maybe I was too hard on the Sraffian enterprise.

But take 3 extremely simple examples of the Sraffian production matrix Robert talks about (in all cases assume labour is the numeraire):

1. one unit of labour produces one unit of wheat next year. We know Pw=1+r, but we can't solve for Pw and r. We can solve for both if we include preferences.

2. one unit of labour plus one unit of land produces one unit of wheat this year. We know 1+Pl=Pw, but we can't solve for Pl and Pw. We can solve for both if we include preferences.

3. one unit of labour produces one unit of mutton plus one unit of wool this year. We know Pm+Pw=1, but we can't solve for Pm and Pw. We can solve for both if we include preferences.

"anon: it's both (except in special cases). Interest rates depend on: intertemporal preferences; and intertemporal production possibilities."

I agree, but inter-temporal preferences don't change much invariant to risk, the only things that change is risk and marginal products, therefore it makes sense to think of variation in mpc explaining much of the variation in real or natural interest rates.

anon: Hmmm. Fair point.

But it's not just changes in the schedules of marginal physical products of capital. Changes in technology of producing new capital goods matter too. In fact, since it's often hard to figure out new ways of using existing capital goods, I would say it's changes in the technology of producing new capital goods that's what matters most. (Hmmm, I think I just repeated TK Rymes' point?)

And, you can't say exactly how changes in technology will affect interest rates without knowing the shape of preferences.

"Changes in technology of producing new capital goods matter too."

To me that is equivalent to changes in the mpc.

Maybe I'm confused, what real world implication is Cambridge UK objecting to?

Could you define what you mean by a credit constraint?

Not being able to instantly and costlessly borrow as much as you want at the risk-free rate.

Now that sounds absurd, but that is exactly the assumption required to get the euler equation Nick cited. Notice that there is only one rate there, r, which is the rate at which you borrow and the rate at which you lend.

As soon as the rate that you pay when you borrow differs from the rate that you receive when you lend, you need to include both rates in the euler equation. And as soon as you cannot borrow as much as you want but need a certain type of collateral, then wealth enters into the euler equation. And as soon as you add transaction costs, then income enters. Etc.

Or let me ask you a different question, in a society of N individuals, where N is very large, how does the absence of credit constraints solve the problem of the double coincidence of wants?

If you have a double coincidence of wants problem, you must have credit constraints. It's inconsistent to pretend that you have one problem but not the other.

If you would never have any problem selling your labor, then banks would be willing to lend against your labor and wouldn't demand other collateral. It is because you may not be able to find a buyer for your labor at the same time that the loan is due to be repaid that banks wont lend against it or demand a premium if they do. The *size* of the premium is determined both by the likelihood that you may not be able to find a buyer and by preferences, but the existence of the premium is fundamentally due to you not being able to find a buyer at the right time -- double coincidents of wants.

Similarly, if whenever you wanted to buy a good A, but had only good B to sell, you could costlessly borrow to buy good A and then repay the loan when you sold good B to someone else. That means that you have no double coincidence of wants problems if you have no credit constraints.

So credit constraints are flip-sides of coincidence of want problems. I would say that both are consequences of the fact that buyers and sellers must find each other via a costly search, the outcome of which is uncertain.

You cannot talk about an economy without credit constraints and assume that there is a demand to hold money. You can try to get around that by sticking money into the utility function, but that is poor micro foundations.

rsj,

in what unit would such a loan be? Bread? Candles? Meat?

If our baker wants candles, from our candlestick-maker, he could borrow meat and pay, but the problem would now be for the baker to find someone to sell him meat in exchange for bread. That however only shifts the problem from the baker to the candlestick-maker to find a butcher in want of bread.

Wouldn't holding money make things substantially easier for all parties involved?

This:

"That however only shifts the problem from the baker to the candlestick-maker to find a butcher in want of bread."

should of course read:

"That however only shifts the problem from the candlestick-maker to the baker to find a butcher in want of bread."

anon: "To me that is equivalent to changes in the mpc."

I think we need to be picky on terminology here.

Marginal Product of Labour is the extra output per extra worker and equals the rental on a worker.

Marginal Product of Land is the extra output per acre of land and equals the rental on an acre of land.

Marginal Product of Capital is the extra output per extra machine and equals the rental on a machine.

What you are calling "mpc" you should be calling the Marginal Rate of Transformation between Present consumption and future consumption, and it equals 1 + the real interest rate.

Only in the special case where one unit of consumption can always be transformed into one machine (and vice versa) is 1+MPK the same as the Marginal Rate of Transformation.

E.g. suppose the technology for transforming consumption into machines were non-linear (which it probably is, since some inputs have a comparative advantage at producing machines and other inputs have a comparative advantage at producing consumption goods). Then the MC and price of a machine (in terms of the consumption good) will vary according to the level of investment in new machines.

"Maybe I'm confused, what real world implication is Cambridge UK objecting to?"

Suppose e.g. the rate of interest fell because of a change in preferences, or demographics. Then (if the technology for transforming consumption into machines were non-linear) the price of machines would rise. So the Value of the total stock of machines would rise, even if the stock of machines didn't. So an econometrician who estimated a production function using the total *value* of the stock of machines would falsely think that the stock of machines had increased.

(Actually, *many* Cambridge UK guys are themselves confused. They think this proves that neoclassical theory of the rate of interest is "circular" or logically incoherent. It doesn't. It just means they are forgetting preferences.)

Martin,

The unit doesn't matter. I want to buy good A and I have good B to sell. If I sell good B before good A, I lend out the proceeds immediately. If I buy good A before I sell good B, I borrow the proceeds immediately.

With many buyers as and sellers, odds are high that for everyone finding a buyer, someone else is finding a seller, so no one needs to hold money. The demand for money is reduced when there is a bond market that effectively allows for netting. This is particularly true as the number of actors grows. If every actor is immediately lending out money whenever they receive it, and everyone borrows whenever they spend, then the quantity of money needed is very small. The demand for money balances is also small.

So think of in terms of limits. In the limit as credit constraints --> 0, the demand for money balances --> 0 as well. You cannot talk about a demand for money balances in the absence of credit constraints, or credit constraints in the absence of a demand for money balances.


anon: it's actually easier to explain the point using land. Suppose an econometrician were estimating a production function Wheat = F(Land). And suppose he used the market value of all land as a proxy for land. Now suppose time preference halves, so the rate of interest halves, and the price of land doubles. The econometrician would falsely conclude that land productivity had halved.

The only difference between land and capital is that (Holland aside) the MC curve for new land is vertical at zero, and the MC curve for new machines isn't. But it probably slopes up, at least in the short run. Only if the MC curve for new machines were horizontal could we ignore this effect (called a "Price Wicksell effect").

rsj,

I have difficulty seeing what the claim is that you make; I see roughly two claims.

Claim I

from above I read:

"Therefore no one needs money and there is no such thing as monetary exchange (or monetary policy). It's also an excessively complicated model that is a bad way of looking at how an economy works. And it doesn't solve the problem of risk.

I think you can't talk about money without talking about credit constraints, and you can't talk about credit constraints without talking about risk (e.g. that the loan will not be repaid)."

I interpret this as:

Claim I. Money only exists because of credit constraints.

The world of the butcher, the baker and the candlestick-maker is a very simple example of a world without credit constraints where nonetheless it is still necessary to solve the problem of the double coincidence of wants.

I think it is pretty clear from that world that credit constraints are not a sufficient reason for money; take the credit constraint away and you still are left with the problem of the double coincidence of wants. Perhaps, I am wrong, so could you show me in this particular case how the double coincidence of wants is solved without money?

As I see it you have two options: 1. the costs of solving it are very small or 2. you need to hold something that many people want.

Claim II

Alternatively though, I see that above, you've stated as much that the demand for money can also arise out of transaction costs:

"Then you get a demand for money balances, purely due to credit constraints and transaction costs."

"They hold money because they cannot instantly and frictionlessly sell whatever portion of their endowments that they would want to sell, or they cannot instantly and costlessly borrow."

Claim II: the transaction demand for money is due to either credit constraints or due to transaction costs

What I don't understand now, is why you would argue that the sole cause for the transaction demand are credit constraints i.e. claim I? Do you, or do you agree with me when I say that you can talk about money without credit constraints?

Martin, I would call transaction costs that arise from coverting bonds to money or money to bonds as credit constraints as well. I don't see the difference between paying a $10 fee whenever I want to borrow $1000 and paying an extra 1% interest.

Rsj,

I have basically two questions:

1. Which claim do you subscribe to have made both?
2. How do you solve the problem of the double coincidence of wants?

The answer to the first seems to be that you subscribe to claim I: money exists only because of credit constraints.

The answer to the second seems a bit fuzzy to me, could you elaborate on how bonds solve the problem in the world of the butcher, the baker and the candlestick-maker?

The baker wants candles, the candlestick-maker wants meat. Does the baker issue a bond in bread to the candlestick-maker, and the candlestick-maker then goes looking for a butcher in want of bread? Or how does this setup work?

This:

"Which claim do you subscribe to have made both?"

should read:

"Which claim do you subscribe as you seem to have made both?"

Let me defend neoclassical economists. Rowe is just as accurate in describing neoclassical price theory and the arguments of, for example, Samuelson, Solow, and Burmeister as he is in describing the arguments of "Cambridge UK guys" (to include Joan Robinson). I don't understand what he thinks the point is of spouting poppycock.

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