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 
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.
Click to access 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.