Warning: this is very much not my area. I don't do micro/GE theory. I was reading a bit of this stuff over 30 years ago, and then moved on to other things. If somebody asked me: "So Nick, what was all that about?", this is what I would say. Take it in the spirit of a personal reflection/interpretation. It still puzzles me.
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.
2. They made some special assumptions that helped them explain prices from technology alone, without talking about preferences. Like: all labour is identical; all technology is linear; prices never change over time.
3. But they still couldn't explain the rate of interest. Because it's hard to explain the rate of interest if you don't want to talk about time preferences. And all the other prices depend on the rate of interest, as well as on technology. So they assumed the rate of interest was exogenous.
4. Some economists in Cambridge US made a very special assumption that let them explain the rate of interest without talking about time preferences. They assumed that there was only one good, and it could be converted back and forth between the consumption good and the capital good by waving a wand. This very special assumption meant that the price of the capital good was always the same as the price of the consumption good, and that the rate of interest was determined by the marginal product of capital.
5. You might have thought that this would make the economists in Cambridge UK happy. Because they could now explain the rate of interest without talking about preferences. But they were unhappy.
6. A lengthy debate followed. [This is a good line to remember if you are ever asked to take the minutes at a departmental meeting.]
7. Eventually it was agreed that the economists at Cambridge US had made a very special assumption. And that what they said about what determined the rate of interest wouldn't be true without some special assumption like that.
8. Everyone went back to doing what they were doing before the debate took place. Everyone forgot about the debate, and nobody could remember what it was about. Except the economists at Cambridge UK, who felt that they had won.
9. It doesn't make any sense to me either.
10. I think it was maybe about politics. The rate of interest is a touchy subject, politically.
11. I think that if you want to explain prices, including interest rates, then you really need to talk about preferences, including time-preferences, as well as technology. Unless you are willing to make some very special assumptions about technology.
A question: do economics departments actually teach capital theory nowadays? I don't mean one-good models like the Solow or AK Growth models; and I don't mean existence proofs of Arrow-Debreu General Equilibrium. I mean something in between those two extremes. I mean something vaguely like Dutch Capital Theory. What do they teach?
Worthwhile Canadian Initiative 
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:
Click to access 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.
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.