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Nick Rowe's misconceptions about Sraffians II

As promised here are my additional responses to Nick Rowe’s assumptions (here) on the Sraffian or Cambridge UK side of the capital debates. I had agreed to comment also on assumptions 3 and 4, which stated that:

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.
Before we get to why Sraffa argued that the rate of interest is exogenously determined by the monetary authority, let me discuss the neoclassical assumptions behind Nick’s proposition. I would argue that point 3 is exactly in reverse, that is, it is impossible (not hard) to explain the rate of interest on the basis of subjective preferences.

Böhm-Bawerk famously argued that there are three conditions for the determination of the rate of interest, namely: (1) the differences between wants and provision in different periods of time; (2) the systematic underestimation of future wants and the means available to satisfy them; and (3) the technical superiority of present compared with future goods of the same quality and quantity. The first two are related to subjective preferences, and are behind the supply of savings or abstinence from consumption, while the third is related to productivity. With both thriftiness and productivity one gets a version of the neoclassical loanable funds theory of the natural rate of interest.*

Note that the subjective basis for the determination of the rate of interest is incredibly shaky. The marginalist approach suggests that there is a positive rate of time preference, that is people prefer to consume now rather than latter, and are willing to part with consumption now in order to get more at some future date. That is why there must be a positive rate of interest to convince consumers to postpone the immediate fruition of pleasure. Yet it is far from clear that the positive time preference precedes the positive rate of interest. It seems rather more logical to assume that given a positive rate of interest some people might be willing to postpone consumption. The neoclassical subjective analysis is no more than a tautology with very dubious assumptions about causality, to say the least. It is hard to see why one could base a theory of interest on such uncertain foundations.

Remember that classical authors were very skeptical of subjective individual behavior. They actually referred to social utility when they talked about preferences. In that sense, Sraffa, not only thought that the foundations for subjective theories were unsound, but also from a methodological point of view were not particularly relevant. Interest rates were not positive because some individual preferred things now rather than latter, but they had an institutional foundation, associated to the fact that certain social groups could extract a surplus from society as a whole.

What about the productivity part of the marginalist/neoclassical argument? That’s the part that the capital debates disqualified, as was accepted by no other than Paul Samuelson. I’m not going to discuss the whole issue again, but it suffices to say that there is no logical way to determine the quantity of capital independently of the rate of interest, which implies circular reasoning.

Sraffa had determined very early in his investigation of the determination of relative prices, as early as his first equations in 1927 (with the help of Ramsey) that he could solve the system of simultaneous equations simply with the technical coefficients of production and an exogenous rate of interest (see DeVivo, 2003; subscription required). Sraffa after several changes and developments of his basic equations eventually settled (by the 1940s) on the notion that the rate of profit was determined exogenously by the monetary rate of interest (a proposition not unlike that of certain classical authors, in particular Thomas Tooke, and similar to Keynes idea of a conventional normal rate of interest in the General Theory), in the famous paragraph 44 of PCMC.

Note that classical authors for the most part assumed that the real wage was the exogenously determined distributive variable. The reasons for why Sraffa settled with a monetary theory of distribution require a different post. However, it should be clear that the exogenous rate of interest is not an arbitrary assumption as Nick suggests, but is required for the logical solution of the system of simultaneous equations (which demand the rate of profit to be determined independently of relative prices, something that the marginalist theory is unable to do in a system with a uniform rate of profit). Finally, the important part of the exogeneity of the rate of interest, besides the fact that it fits the historical/institutional framework of the capitalist economies that we live in, where central banks actually do determine the rate of interest, is that institutions play a role in the classical-Keynesian theory of distribution. As noted above, it is class and power that are behind a positive rate of interest and not you aunt's preferences for chocolate cake tomorrow.

Regarding point 4, there is an incredible confusion in the comment by Nick. Sraffa’s system never assumes any aggregate production or a one good economy. There is a composite commodity in the construction of the standard commodity and system, but production is a circular process. Even if it has similar properties as the Ricardian corn model, it is actually composed of several commodities. It is in fact the neoclassical theory, including the disaggregate Walrasian (in its Arrow-Debreu version) model, that requires a one commodity world to bring about the equilibrium of investment (the demand for a quantity of capital) to full employment savings. It is the marginalist theory of the natural rate of interest that lacks any logical foundation.

* Irving Fisher was critical of the limitations of Böhm-Bawerk’s theory even within the neoclassical paradigm. For the debate between them see Avi Cohen (2011).


  1. Matias: thanks for writing this, and thanks for the civil tone in which you write it.

    Sorry for the delay in responding. Two reasons:
    1. A busy start to the term.
    2. I find this a bit depressing. I thought we might be making some progress towards a common understanding, even if they were baby steps. Now I see we aren't. I too think you misunderstand neoclassical theories of interest. Two solitudes, and all that.

    Let me change the subject a little (in my next comment, I just want to check that this comment works).

    1. Busy myself, will try to catch up with all the back and forth this weekend. Thanks for your comments and replies.

  2. OK. It works.

    This is slightly off-topic. But it might help me interpret Sraffa. Which is on-topic.

    I was never at all sure if I understood his quest for the "invariable measure of value". (It comes across a bit like the quest for the Holy Grail to an atheist: "If you found the HG, how would you know you had found it; and what would you do with it if you did find it?")

    So tell me if you think I am right or wrong on this:

    1.Sraffa wrote PCMC in part (large part?) because he was searching for the invariable measure of value (IMV)?

    2. The IMV is a good (or more likely a bundle of goods) such that: if all prices (and wages) are measured in terms of the IMV, then, if the rate of profit/interest changes, but the output of each and every good stays the same, and the per-unit inputs and outputs all stay the same, and if rates of profit/interest are the same across sectors, (have I missed anything?) then:

    2.1 The value of total output will stay the same?
    2.2 Equivalently, if you put total wage income on one axis, and total profit/interest income on the other axis, the curve showing the trade-off between those two types of income would be a straight line with a slope of minus one?

    3. Only by fluke (except in a one-good model) would the IMV be a single good; it will almost always be a bundle of goods (composite commodity)?

    4. Only by fluke (except in a very simple model where production processes never take more than two periods between labour input and final output then you start again from scratch) would the IMV bundle contain only two goods??

    5. Sraffa proved the IMV exists?

    6. Sraffa showed how to find the IMV?

    7. What did he want to use it for, once he had found it??

    8. Conjecture: Is the whole point of PCMC in fact not to "explain" prices but an exercise in how to find the IMV?

    1. "Sraffa wrote PCMC in part (large part?) because he was searching for the invariable measure of value (IMV)?"

      Didn't Matias debunk this in Part I? I quote Sraffa which was quoted by Matias in Part I:

      "I am sorry to have kept your MS so long - and with so little result. The fact is that your opening sentence is for me an obstacle which I am unable to get over. You write: 'It is a basic proposition of the Sraffa theory that prices are determined exclusively by the physical requirements of production and the social wage-profit division with consumers demand playing a purely passive role.' Never have I said this: certainly not in the two places to which you refer in your note 2. Nothing, in my view, could be more suicidal than to make such a statement. You are asking me to put my head on the block so that the first fool who comes along can cut it off neatly. Whatever you do, please do not represent me as saying such a thing."

      Clearly demand matters to Sraffa. And, hence, preferences matter. And if preferences matter there is no timeless, invariable Holy Grail of value.

      I have a bit of experience arguing with people on this point and I will say this: although it seems doubtful that Sraffa believed in the Grail, certain Marxists have taken over his argument as justification that the Grail (Labour Theory of Value) should be sought. That's on them. The above quote indicates that Sraffa did NOT think this. And we are 100% sure that the other Cambridgers, like Robinson, did not think in these terms. (Robinson used to talk about "snob prices" and all that and she explicitly refuted the Holy Grail labour theory of value as "metaphysics").

      But I don't blame you for thinking that this might be the case because this debate rages today. Some people like their Grail. Although you shouldn't chalk that up as a failure of the heterodox because I think that marginal utility theory (and, indeed, the whole research program) is just as much of a Holy Grail in that "utility" becomes the sought after "essence of Truth", but the neoclassicals hide their metaphysics in indifference curves.

    2. A few replies. On (1): Sraffa was not looking for an absolute measure of value. He was just trying to determine relative prices with objective data (taking preferences as given). His 1927 system of simultaneous equations (for which Ramsey confirmed there was a solution, and form the basis of ch. 1 of PCMC) preceded his understanding of Ricardo, and the question of value. In fact, the theory of value is simply the device that Marx and Ricardo used because they did not have simultaneous equations. The search for an absolute measure of value plays no role in Sraffa, but he did show with the Standard System that one can determine in Ricardian fashion the rate of profit (the ratio of profits measured as the physical amount of several commodities to the means of production also measured as bunch of commodities) independently of relative prices.

      On (2): Yes Sraffa's prices equations take outputs as given.

    3. The quote from Sraffa seems typically eliptical. "I have said no such thing". Totally true, but reading the book and he has built a model within the surplus tradition that gives scant reference to demand, excepting that he is assuming that the effective demand is there.

  3. On "social utility" vs "individual utility":

    I thought the whole point of the literature on "public goods" was that goods which have social utility but don't have (much) individual utility don't get produced because they don't get priced properly in a market economy in which people only pay for goods which give them individual utility?

    On time-preference. I am going to repeat my two thought-experiments:

    1. Suppose, just suppose, that people had different preferences to what they have today. Nobody cared at all about *when* they consumed goods. All they cared about is consuming the largest number of apples (and bananas, etc.) regardless of when they consumed them. In such a world, all (safe real) interest rates on all goods would be 0%. Nobody would offer to pay 101 apples next year in return for 100 apples this year, and if anyone did make that offer, every single person with any apples would want to accept it. And the market price of any (safe) asset, real or financial, would equal the undiscounted sum of the payoffs to owning that asset.

    2. Suppose, just suppose, that nobody cared at all about their future consumption. They all wanted the maximum possible consumption today, never mind tomorrow. In such a world, all (safe real) interest rates on all goods would be infinite. Nobody would offer to pay 1 apple today in exchange for 100 apples next year, and if anyone did make that offer, every person who expected to have 100 apples next year would want to accept it. And the market price for any asset, real or finanancial, which could not be converted into consumption today would be zero. All future returns would be worthless.

    1. I don't think what Matias is referring to as "social utility" has anything to do with public goods. Matias isn't talking about the government providing roads, he's talking -- in an institutionalist mood -- about the social character of preferences.

      Matias talks about this in terms of "use values" -- a term I disagree with -- but what he's getting at is that society must find things desirable in order for them to be produced. In doing so he is stressing the social character of these desires: as individuals we are not atoms and our preferences rely on what others prefer. When a Nike runner becomes fashionable and is desired by others it price may rise significantly and yet this very price rise might, due to fashion, cause other people to desire it even more.

      I quote Matias from Part I:

      "These preferences are not the subjective preferences of individuals, about which nothing scientific can be said, since there are no regularities and they can change for irrational and circumstantial reasons.

      The utility that society attaches to a particular good, say a car, however, can be taken as given at a particular point in time. The reasons are not only directly connected to objective characteristics, like the fact that a car is a means of transportation or negatively that they worsen environmental conditions, but also that cars socially may be a source of status, as Veblen later suggested. In other words, preferences (and demand) are socially determined and taken as given for the determination of relative prices, but there is a role for historical and institutional analysis in understanding why and how demand and preferences change over time."

      What Matias is trying to show, I think, is that a Sraffian would say that demand and hence preferences matter, but that this demand cannot be analysed through a marginal utility analysis because preferences in society -- as every social scientist except economists realise -- are determined reflectively. Think of the child that doesn't want the ball until the other child has it -- then it becomes the most desired object in the child's universe (an early manifestation of invidious consumption).

    2. I'll risk an opinion, even though I'm just an amateur in these matters.

      Perhaps the difficulty with "social utility" vs "individual utility" is related to the terminology.

      If I am reading Vernengo properly:

      "social utility" = classicals' use value
      "individual utility" = marginalists' ordinal utility

      In the previous post Vernengo offered an example that seems to relate to the literature on "public goods" you mentioned:

      "Smith in his discussion of the diamond/water paradox (Wealth of Nations, Book I, ch. IV) argues that things with a high use value often have little or no exchange value, since things that are not costly to produce will command no price, even if they are useful."

      Marginalists solve the paradox by saying that water is abundant (nobody would pay anything for a good that's readily available for free), while diamonds are scarce and the difference in price reflects this relative scarcity.

      However, note that the scarcity of diamonds is partially overcome through production, which is costly. Water, at the other hand, is abundant, therefore, it is not costly to produce.

      Unless I am missing something deeper, I'd say the two explanations seem compatible.


      Regarding time-preference and your first thought experiment:

      By hypothesis in your experiment:

      (1) people are indifferent between consuming 1 apple today and consuming 1 apple in a year's time. But,
      (2) they do prefer more apples to less.

      I offer 101 apples today in exchange for 100 in a year's time. Because of (2) people take up my offer.

      Here the positive interest rate offered (r = 1%) induces people to lend their apples to me, even though they do not have a positive rate of time preference (because, by hypothesis, they are indifferent between consuming an apple today and in a year's time).

      Like Vernengo said: "Yet it is far from clear that the positive time preference precedes the positive rate of interest". In this thought experiment, I believe, it didn't precede the positive rate of interest.


      I hope this makes sense.

    3. On the literature on public goods, note that social utility is an aggregation of individual utility. Classical authors did not formalize, and didn't think you should formalize or aggregate, social utility. The same way class conflict is not formalized. It is a matter for historical/institutional analysis. Say, why did tea consumption, which started as an import for the upper classes, became the national drink (I prefer beer even warm) of the English people. On your example, it is far from clear that interest would be 0% with no differences in preferences. If you need to survive, and for that must produce, and you don't own the means of production, borrowing at a positive rate of interest, which allows the lender to subtract a part of your production (surplus), might be the only option, irrespective of preferences. The question about causality is central in this issue. And subjective theories cannot prove that the preference (for more tomorrow) are prior to the rate of interest. Of course with a positive rate of interest (if it is prior) then you might choose to postpone consumption. The intertemporal preference is the result of the rate of interest, NOT its cause.

  4. On aggregating labour and capital (and land):

    The services of different types of labour, the services of different types of capital goods, and the services of different types of land, are used, sometimes in combination, to produce different goods.

    If you can't (always) aggregate the services of broomsticks and blast furnaces (which I agree you can't), how can you (always) aggregate the services of bartenders and brain surgeons, and how can you (always) aggregate the services of beaches and bauxite mines?

    1. There are well known aggregation problems, and index theory is a complex subject. But Sraffa does not aggregate capital (means of production) because he is dealing with the Physiocratic notion of a circular flow of production. My point here was just that there is no big deal in assuming a uniform kind of labor, since different kinds of labor (with different productivities) can be reduced to a single type.

    2. Matias: "My point here was just that there is no big deal in assuming a uniform kind of labor, since different kinds of labor (with different productivities) can be reduced to a single type."

      If two bartenders could perform brain surgery as well as one brain surgeon, and if one brain surgeon could serve drinks as well as two bartenders, then we could aggregate labour (just count brain surgeons as equivalent to two bartenders).

      If a thousand broomsticks could make iron as well as one blast furnace, and if one blast furnace could sweep floors as well as a thousand broomsticks, then we could aggregate capital (just count blast furnaces as equivalent to a thousand broomsticks).

      Both assumptions are equally plausible/implausible.

    3. I don't think both are equally implausible - and I would extend that to land with different fertility. The issue of aggregating labour of differing productivity is a different problem of measurement than aggregrating capital. In aggregating labour there is a practical problem which more or less easily resolved. In aggregating capital the problem is with the means of measurement itself because it can only be aggregated using price and profit is component of that price.

      So Sraffa, in part, is about looking at the unit of measurement.

      But there again I am not an economist I'm only in the economy.

    4. Nick, not really all you need is to have in mind that there is a common thing to the bartender and the brain surgeon, they perform human labor. Mind you in Sraffa's equations in no place does labor directly appears, only wages. SpiritSkill, no Sraffa was not searching a unit of measurement at all. His 1927 equations that form the basis of the book (in the preface he says he showed them to Keynes 1928) have nothing to do with measure of value. Just determination of prices with objective (cost) data, for given technology and state of preferences.

  5. Neoclassical theories of capital and interest do not have to, and do not always, aggregate capital into a one good model. Nor do they have to, and nor do they always, assume homothetic preferences so they can aggregate preferences. These are simplifying assumptions which some neoclassical models sometimes make.

    The very simple 2-period Irving Fisher diagram to my mind gives the simplest and clearest picture of neoclassical theories of interest rates. In that diagram, the rate of interest is determined in equilibrium by preferences and technology (and endowments). At that equilibrium, one plus the rate of interest will equal the Marginal Rate of substitution between present and future consumption and will equal the Marginal Rate of Transformation between present and future consumption. We cannot say that MRT determines r (or vice versa), or MRS determines r (or vice versa). All three are co-determined simultaneously.

    And there is no reason why you can't expand that diagram to add as many different goods as you like, as many different time periods as you like, and as many different individuals (with non-homothetic and different preferences) as you like. (You just need n-dimensional paper).

    1. Yes, but even the disaggregated Arrow-Debreu model must have in neoclassical theory (as in classical-Keynesian theory) an equilibrium between savings and investment. In classical-Keynesian theory the equilibration is done by the multiplier (variations of income) and does not imply full employment. In neoclassical theory it is the rate of interest that does the equilibration (the natural rate must be part of theory) and you get full utilization of capital. And the neoclassical theory requires then an aggregate measure of capital.

  6. On monetary theories of the rate of interest:

    The Bank of Canada sets the rate of interest (well, it sets *a* rate of interest). But it doesn't set it where it feels like it. It sets it where it think it needs to to keep inflation at the 2% target. And what determines where that would be? (Please let me assume Canada is a financially closed economy to keep this simple, though of course I know it isn't). It's where Consumption demand plus investment demand plus government demand for newly-produced goods equals the "supply" of newly-produced goods. Where Cd+Id+Gd=Ys. We can rearrange that to read: where Id=Ys-Cd-Gd. And we can re-write that as: where Id=Sd (where Sd means desired national saving).

    In other words, the Bank of Canada tries to set the rate of interest equal to what the loanable funds theory would predict. And the loanable funds theory is just another way of looking at the Irving Fisher diagram.

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    2. I'll just point out a slight internal inconsistency.

      "But it doesn't set it where it feels like it."

      " It sets it where it think it needs to to keep inflation at the 2% target."

      The latter statement relies on the idea that the CB actually knows what rate will produce a 2% inflation rate. This implies that there is some "true" position that can be grasped (through reading sheep entrails?). But ultimately this is a subjective decision -- as Greenspan showed in the 90s when he went against the grain of NAIRU and won.

      Given that this IS subjective and based on the judgement of individuals, I would say that the interest rate is ultimately determined based on the feelings of the central bankers. This is why the joke about how ten economists come to ten different conclusions exists -- it is also why the markets try their best to understand the psychology of the resident central banker.

      It's only the economist that is fooled into thinking that the CB has a perfect crystal ball -- or, at least, assumes so in his models.

      Even if central bankers do use loanable funds models to set the rate (I doubt this, Greenspan claimed to use the ten year treasury yield -- and I even doubt this) it is nothing but a tautology. If you don't believe in a natural rate of interest or a NAIRU you'll believe that the central bankers are just making rather wishy-washy judgements and then backing them up with nonsense -- like a soothsayer or a palm-reader. Me? I think that interest rates are determined politically and I think they're better off for it.

    3. I know the Bank of Canada doesn't have a crystal ball. And so does the Bank of Canada. They use a New Keynesian model, plus their own judgement, to set a rate of interest. Their New Keynesian model is a natural rate model. Their judgement is based on a belief in natural rate models. They do not hit their 2% inflation target exactly every year, but they have hit it almost exactly on average. That would be a massive fluke if their model and judgement were totally wrong.

    4. It's not a massive fluke. Canada's policy is to maintain an artificially high unemployment rate. I assume that they justify this through their NK maodels through some unusually high NAIRU. But regardless of the stories they tell themselves, the tactics are obvious: they keep wage bargaining (the real source of inflation in modern economies) in check by keeping the unemployment rate at a level that keeps workers slightly uncomfortable.

      My guess would be that they're being overly zealous. They could probably get a fair boost in growth with a very low rise in inflation if they tried. And if the government worked closely with the unions they may be able to get a boost in growth with no rise in inflation at all.

      But as I said, no matter what stories you tell yourselves through your models, the onus of decision lies with the central bankers. If they really believe in their models and adhere to them to the letter -- I doubt they do -- then they are merely hiding from themselves what they are really doing.

      Father, forgive them, for they know not what they do. (Luke 23:34)

    5. BTW occasionally perceptive central bankers see this when economic models are used to justify extreme policy positions:

      This is when their strings are truly being pulled by politicians and this often doesn't last. Once the extremists are out of government the fog descends once more.

    6. Yep, there are limits to what the Bank of Canada or the Fed can do (and even more to what the central bank of Brazil and Argentina, peripheral countries, can do), but I disagree that it is a natural limit, and that the 2% inflation target is somehow connected to that optimal output. The main limit in the US and Canada is political, and that's why Ron Paul and several Republicans are against QE and the policy by the Fed of maintaining low interest rates (not discussing here whether this would be enough to the get the economy going, which in the absence of fiscal policy I don't it can). In peripheral countries international financial markets impose further limitations.

    7. Note that the definition of a "peripheral country" is a country which needs to import some important resource, can't do so by force of arms, and therefore needs access to "international financial markets". (If you can do fine with autarky, you don't *care* about international financial markets.)

      By this definition the US is a peripheral country now that we have forgotten how to win wars and are dependent on imported oil.

  7. Matias: "Regarding point 4, there is an incredible confusion in the comment by Nick. Sraffa’s system never assumes any aggregate production or a one good economy."

    I think you misread me there. I never said Sraffa assumed that. I said some economists in Cambridge *US* assumed that.

    1. Okay. Sorry about that. But who do you have in mind?

    2. Matias: "But who do you have in mind?"

      ??? I still think you are misreading me. I have in mind those Cambridge US economists, like Solow, who the Cambridge UK economists criticised for doing this.

      As in this extremely short version of the Cambridge US vs Cambridge UK debate:

      Cambridge US: "C+I=Y=F(K,L), r=MPK"

      Cambridge UK: "That's wrong!"

    3. Oops. Sorry. Sure in this case the whole thing is different, and the only thing I would add is that Cambridge UK authors would suggest that r=MPK is not always true. Only in the case of a nil rate of profit, or when all sectors have the same capital to output ratio, that would be the case.

  8. 1. Sraffa explicitly states that propositions about the Standard Commodity are not central propositions of his book.
    "Whilst the central propositions had taken shape in the late 1920's, particular points, such as the Standard commodity ... were worked out in the 'thirties and early 'forties."

    2. Rowe does not correctly state the conditions that Ricardo's invariable measure of satisfy. In addition to an (incorrectly stated) condition on distribution, the invariable measure is supposed to be used to look at changes in technology. Anyways, neither 2.1 nor 2.2 hold when Standard commodity is used as numeraire.

    5. Sraffa proved the opposite, that no (possibly composite) commodity bundle could serve as an invariable measure.

    8. This conjecture is false.

    Matias is not the first in the tradition of Keynes to refer to a "conventional" normal rate of interest. I do not read this as a subjective theory.

    I do not read Matias' remarks about social utility as being about public goods.

    I wouldn't mind a clarification of Matias's comment about Arrow-Debreu. In an Arrow-Debreu equilibrium, agents must be willing to hold the produced capital goods. This is a stock equilibrium. In a multi-good world, a belief that such an equilibrium is stable is without logical foundation. Garegnani has written quite a bit on this.

    Sraffa never aggregates different types of land. Building on, say, Ian Steedman, I can critique neoclassical theory from a Sraffian standpoint just as well with disaggregated labor as with aggregated labor.

    The one-commodity neoclassical Solow model cannot get away without intertemporal preferences on savings. The rate of interest in the long run position is related to the rate of growth. But an insightful neoclassical would bring in intertemporal preferences to explain the ratio of capital to labor.

    I suppose it is good that long-established demonstrations of the failure of neoclassical theory continue to be discuss while still teach such nonsense.

    1. Robert: I confess I would have a little bit more confidence in your ability to distinguish sense from nonsense in capital theory if you hadn't left a comment on my "Dutch capital Theory" post where you made exactly the same assumption to solve for the rate of interest that Cambridge UK criticised Cambridge US for making.

    2. This comment has been removed by the author.

  9. "you made exactly the same assumption to solve for the rate of interest that Cambridge UK criticised Cambridge US for making."

    Rowe's statement is incorrect. My comment illustrated the chapter II, Section 4 model in Sraffa's book. In some sense, I made no assumptions, but just drew out the logical consequences of Rowe's post.

    Anyway, my main point at the moment is not to respond to Rowe's unwillingness to acknowledge his mistaken conjecture on the role of an invariable measure of value in Sraffa's book.

    It is to point out an earlier exposition of mine demonstrating the errors in neoclassical intuition in which I assumed heterogeneous labor. See here:
    Above, I should have acknowledged Metcalfe and Steedman, not just Steedman.

    1. Robert: "Rowe's statement is incorrect."

      Are you able to *explain why* you believe my statement is incorrect? Or are you only able to cite chapter and verse of some authority to try to snow-job and bulldoze any disagreement?

      If (say) 40 tons of wheat can be used to create one acre of new land, which produces (say) 4 tons of wheat per year (with no labour), then the rate of interest on wheat will be 10% per year, and is determined by the Marginal Product of (1 ton of wheat's worth) of Capital. That is exactly your example (with the numbers 40 and 4 added for illustration), and that is exactly the thing that Cambridge US said, that Cambridge UK objected to.

      Again, do you actually understand all the very many things you are reading? Because you are coming across as a paper tiger.

    2. That's not what the UK school objected to. They objected to the model when you add labour and a variety of techniques. The whole point was that there was no smooth substitution of capital-intensive techniques for labour-intensive when the interest rate falls due to reswitching between the two.

      This is very basic stuff. I'm tempted to quote Nick Rowe on Nick Rowe:

      "Again, do you actually understand all the very many things you are reading? Because you are coming across as a paper tiger."

      I mean, this stuff is on Wikipedia...

  10. TheIllusionist: "That's not what the UK school objected to."

    You mean Cambridge UK was not objecting to the statement: "the rate of interest is determined by the marginal product of capital"?

    OK, if you are right about that, then I have indeed totally misunderstood at least part of the Cambridge UK position. But *I* would object to that statement, even if Cambridge UK didn't.

    1. You gave an example and said that was what Cambridge UK objected to. That example couldn't be further away from the model Cambridge UK were critiquing. In fact, it looks like a model that might have been set up by Sraffa in the 20s to demonstrate own rates of interest.

    2. Start with a standard Cambridge US model.

      C + dK/dt = A.K^B.L^(1-B)

      (I'm not sure if that's clear. That's supposed to be a Cobb-Douglas production function on the right hand side, and dK/dt is investment, and I have ignored depreciation for simplicity.)

      Let us simplify the model by assuming an extreme case in which B=1 (so labour drops out). Let us measure consumption C in tons of wheat. Let us measure land K in fortieths of an acre. Assume A=0.1 . And you have the model that Robert put forward (with my numbers added for illustration).

      I have an awful feeling you might be right when you say Sraffa set up models like that in the 20's to demonstrate own rates of interest. If so, it would be a bit like saying "the rate of profit in producing chickens will be greater than the rate of profit in producing cattle, because chickens multiply faster than cattle." No. All it would mean (if there really were no other inputs required) is that the price of chickens will be falling relative to the price of cattle.

  11. Nick,
    You say that the interest rate is a result of preferences and technology. But for that to be true, you need a set of preferences that creates a positive sloped curve of savings function of the interest rate and a downward sloped function of investment or capital intensity choice of technique function of te interest rate. To do that, you're assuming that the interest rate is exogenous (ie, agents are price takers) and then, when both functions are logically derived, you determine the interest rate of equilibrium.

    But to have a downward sloping curve of investment one should have a technology that makes you want to have more capital intensive techniques with lower interest rates, and this is only possible within a whole set of neutral wicksell effect techniques, which means equal capital intensity between branches of production, and, you may notice, this is a very, very unreal condition.

    When you have non-neutral wicksell effect, you get that the profit/wage curve is convex or concave. In the case that it is concave, the demand of investment as a function of the interest rate is upward sloping. If that's so, how can you say that there is even an equilibrium? And even if there is, how can you say it's convergent? Well that's the reverse deepening point.

    But, you may say, if there are more techniques, you could go from a less capital intensive to a more capital intensive with a lower interest rate. What reswitchning means is that this can't be done. At different rates you will choose a capital intensive technique or a labour intensive technique. This, in the investment curve perspective, is an arbitrary jump from one point to another.

    Now, what do you mean with "the interest rate is a result of preferences and technology", when you have an upward sloping investment curve with jumps everywhere? Here, the whole theory of interest rates as a result of technology and preference falls down, and that's the whole point of the theory. It's very ironic to use the preference theory in a capital debate issue. Also, all the natural rate fashion falls apart. Only with one good economy (Solow) you get well behaved curves.

    And no, neowalrasian equilibrium is a very different type of equilibrium that doesn't have the tendency to unify the rates of profit and that, because of this, it cannot be a model of gravitation towards natural prices, and it's a model that needs an auctioneer setting the prices before the transactions start, and includes perfect foresight, rational expectation and other issues. This wasn't what the classics (Marshall, Wicksell) thought it would be an equilibrium. But they relied on aggregate capital. With dissagregate capital, the system cannot be solved in gravitation unless you "force it" to be solved.

    1. Genaro: I understand why it matters whether the Intertemporal Production Possibilities Frontier is concave or convex, (and whether Intertemporal Indifference Curves are concave or convex), but I don't understand why it matters whether the total profit income/total wage income curve (what's the proper name for that curve?) is concave or convex.

      Think of the Irving Fisher diagram, with today's consumption on the horizontal axis and tomorrow's consumption on the vertical axis. Draw an intertemporal PPF that is concave to the origin, and an intertemporal Indifference curve that is convex to the origin. One plus the rate of interest is determined by the slopes of those two curves where they kiss. (We can add more time periods, more consumption goods, and more people, just by adding dimensions.)

      Increasing Returns to Scale may mean there's no competitive equilibrium (which stands to reason, since IRS leads to monopoly) because the PPF may become convex to the origin.

      But if there's no technological possibility to transform current consumption into future consumption by adopting a different technique (so the investment demand curve is vertical), all that means is that the intertemporal PPF is reverse-L-shaped (the feasible set looks like a rectangle), which means that the rate of interest is determined by the slope of the intertemporal indifference curve at the point on the PPF.

      If you don't use preferences to help determine the rate of interest, then the rate of interest is (usually) indeterminate in that model. The exception is where the PPF is a straight line, in which case the rate of interest is determined by the Marginal Rate of intertemporal transformation (i.e. by technology alone). Just like in Robert's model which I discuss above.

      It is straightforward to apply this sort of model to get a unified rate of profit across different industries (at the margin). Let there be two capital goods: houses and golf courses. Let the PPF between new houses and new golf courses be concave to the origin (because some people and land have a comparative advantage in producing one or the other). If the rate of profit on houses, at the margin, exceeded that on golf courses, there would be greater investment in new houses and less investment in new golf courses. Which moves the economy along the PPF and increases the Marginal cost of building a new house and reduces the Marginal Cost of building a new golf course, until the profit rates are equalised at the margin. (A second equilibrating force is that house rents would be expected to fall over time and golf rents would rise over time as you invested more in houses and less in golf courses.)

  12. I'm going to come back in a few days, to let Matias have a chance to catch up. (And also let him fix that bit in the post where he accidentally misreads my "US" as "UK" and thinks I'm even more confused than I am!)

  13. The tangent of the profit-wage curve (given the technique) is the capital intensity. For neoclassical perspective, a technique should have a straight profit-wage curve, so as to have equal capital intensity per technique. Also technology (the set of techniques)must be concave (ie, a set of straight lines, each one with different tangent, creating a convex envelope) so as to create a soft transition between technique and technique, and this transition must be from a less capital intensive to a more capital intensive when you have a lower interest rate. That means that the demand for capital intensity is downward sloped in relation to interest rate. This means that each technique=a certain capital intensity, and you switch to more capital techniques with a lower interest rate. This is the base and soul of the FPP and NOT the other way round. You need this to be true in order to have capital/labour substitution and then all supply (of capital and labour) creates its own demand by means of substitution. Now, the fact that families save relatively more to have more income in the future MUST have a counterpart in capital intensity: you save more, you are in dissequilibrium in the loanable funds market, the interest rate goes down and this changes the capital intensity towards a more capital intensive technique, and this creates the way to the new equilibrium.

    Now, what happens if the profit-wage curve is concave? the capital intensity of the technique is upward sloped respect to the interest rate. So, there is no 'single capital intensity' within the technique! So, in this case, if there is no other technique you won't have a "so the investment demand curve is vertical)" but an upward sloped investment curve! Are you sure you get equilibrium that way? And if you do, is it a convergent equilibrium or is it just useless?

    And notice that you're wrong: intertemporal PPF and all this capital controversy stuff ALREADY takes as given that all profit rates are equal, and this is not wrong. The problem is that, in order to have natural rate and equilibrium wages, you need substitution between labour and capital (which one good/equal capital intensity between branches of production cobb douglas function does systematically). Now, the results in Cambridge controversy is that you don't get subsitution between labour and 'capital' as a whole in an economy, and therefore, there may be upward sloped curves of demand of capital and labour with jumps. This means that those markets cannot 'clean' their own supply, and there are abortive savings and abortive unemployment.If that's true, how can you even talk about PPF as if you were on the frontier!

  14. Genaro: I'm glad you are on here, because: I think you actually understand what you are talking about; you are willing to try to explain it; so I think I might actually learn something.

    A couple of preliminaries:

    "This is the base and soul of the FPP and NOT the other way round."

    What is "FPP"? Factor Price ??

    "The tangent of the profit-wage curve (given the technique) is the capital intensity."

    When you say "the profit-wage curve" do you have total profit income on one axis and total wage income on the other?

    When you say "the tangent" do you mean "the slope of the tangent"?

    I may not return to this immediately. I've got other stuff on.

    Just to lay my cards on the table: I'm a money/macro guy, not a general equilibrium theorist; I can't do math; I've read almost nothing on capital theory in the last 30 years.

  15. Genaro,
    Feel free to point to Figure 2 in this post:
    I graph the wage-rate of profits curve for each of three techniques. And in Figure 1, I show the investment curve that follows in each case. Like you, I do not explicitly reference Samuelson's (1962) surrogate production function article.

  16. Nick
    I'm glad that you're taking this problem into account.
    I made a mistake: FPP=PPF, in spanish everything is upside down (IMF=FMI). But also goes for factor price. And I tend to think that every theorist in the marginalist tradition is a GE theorist,even if they don't know they're. And that's the main problem, because we should know what we're talking about. I mean, if we deduce b from a, if a is false, so is b, even if the theorist that thought b did not know that b came from a.

    The whole point of capital controversy is the long perid equilibrium in marginalist economics, where marginal costs= average costs=unitary costs= prices, and then
    P*Y=C or P=C/Y or, if we're thinking in terms of factors
    P=K(1+r) +wL. if capital has a set of techniques that makes it a substitute of labour, you could find a proportion r/w so as to fit the actual scarcity of savings given time preferences and supply of labour given leisure/consumption preferences. Now, how do you aggregate 'capital' K? In value. What does that mean? That you need relative prices to get K. But you need K to get the relative prices. Is this a problem. Yes, but a problem that, as we'll see, has other very serious issues with income distribution.

    Let's say we gave two goods: corn and steel, and you only feed workers with corn, and both corn and steel are inputs of the production function. Then, if we want to dissagregate K, we have:

    Pc*C=[Pc*Cc+PsSc](1+r) +wLcPc
    Ps*S=[PcCs+PsSs](1+r) +wLsPc
    Cs and Sc are corn and steel used to produce corn, Lc is labour used to produce corn, Cs and Ss are corn and steel needed to produce corn and Ls is labour needed to produce corn. Now, dividing by C and S in each case,
    the non-capital letters are technique data here. Notice that here, the problem is that, in fact, capital good are the only goods that are produced by consuming other goods (which is circular). If you think wages or part of wages as necessary commodities to feed and reproduce workers (as, perhaps, Marx or Bortkiewicz could have done), they would go into the sets of 'capital' goods, and the resolution will be similar but more complex. Now, using Pc as a numeraire:
    1= [cc+ (Ps/Pc)*sc](1+r)+w*lc
    Ps/Pc=[cs+ (Ps/Pc)*ss](1+r)+w*ls
    If you solve the system, and being Ec=surplus in corn and Es=surplus in steel, you get

    r= [Es*Ps/Pc+Ec]/[(Sc+Ss)*Ps/Pc+(Cc+Cs)]
    Ps/Pc=(1-w*lc)/(sc(1+r)) -cc/sc

    From this we get that we cannot determine the rate of profit independent of relative prices and neither can we determine the relative prices without determining the rate of profit. So, if there's any change in the rate of profit, the relative prices will thange and so will the 'quantity of capital'...then what does this 'quantity' mean?

  17. But there's more from where this came from. Imagine a system with a capital good and a consumption good:

    1 =Pk*kc*(1+r)+lc*w
    The solution to this by cramer is
    w=[1-kk(1+r)]/[lc+ (lk*kc-lc*kk)(1+r)]

    Then the wage rate is a function of the profit rate. So, when r=0, all the surplus per worker (the production not consumed by the production method itself) of the economy goes to wages and there is an r=R that makes wages 0. Here comes the profit/wage curve. Notice that if lk*kc=lc*kk, then the function w(r) is linear, as in figure 2 of Robert. Now, let's see what this implies, rearranging the terms:
    kc/lc=kk/lk=> the capital intensity of techniques is equal between branches of production, which is a weird assumption from the start (I cannot believe that corn production is equal in capital intensity than steel production).
    if kk/lk>kc/lc, the form of the curve will be different: it will be concave as kc*lk-kk*lc<0.
    And the other way round if kk/lk (y-w)/r=k. This, if you look at Robert's figure 2, is the quotient between two sides of a rectangular triangle (given r): y-w is the segment between the point the workers get all the surplus and the actual wage, and r is the actual rate of profit. This is equal to the tangent of the angle between the the start of the wage curve, the point of the wage curve given the rate of profit and the vertical axis and the parallel line of the horizontal axis in the point where the actual wage goes.
    Now, in marginalist theory, r=dy/dk
    dy/dk=dw/dk +dr/dk*k+r*dk/dk
    dy/dk=dw/dk+dr/dk*k+r as r=dy/dk
    -k=dw/dr, which is the tangent of the wage curve.
    You may notice that those two tangents are different, one is the real and one is the theoretical in marginalist theory. For those two to be equal the wage/profit frontier needs to be linear as the tangent of the rect between the start to the wage curve and the wage curve where the actual profit rate is set must be the same as the wage curve and the same as the tangent of the wage curve itself! but this is an extreme case. And notice that we're talking only about two goods, imagine a few thousands as in a real economy! The wage curve is a roller coaster!

  18. And there is more: marginalist theory needs in order to have substitution between factors (ie, at a given preference for leisure/work and consumption/saving, and therefore scarcity of savings and labour, there must be a w/r that clears both markets) to have a)an only capital intensity per technique b)switching from lower capital intense techniques to higher capital intesive techniques with a lower interest rate, so as to replace capital with labour until you find an equilibrium between savings and investment.
    The problem with a) is that when the profit/wage frontier (wage curve) is not straight (y-w)/r changes when r changes, and then, the demand of capital is not "vertical" for each technique, as in Robert's figure 1. In particular, if the capital production is more capital intensive than the consumption good production, (concave curve) the demand for investment is upward sloping, as in Robert's blue line, and this is a bad behaved curve. Imagine a upward sloping investment curve and an also upward sloped savings curve. First, they may not touch anywhere. But if they do, they should be divergent. But let's say they aren't. Imagine a change in intertemporal preferences for more saving. this will move the savings curve to the right, the interest rate will be lower....and the new equilibrium savings=investment will be lower!!! and This happens even if you have the best financial system ever!! Abortive savings here looks much more keynesian (and normal) than in the whole "financial intermediation problem". And this happens even if you don't switch techniques.
    to b), imagine a more labour intensive technique that is straight line and a more capital intensive technique that is concave. Here, you start at a less capital intensive technique (straight line), when r is lower you choose a higher capital intensive technique (concave curve), which is what the theory would expect, and the with a lower r you switch back to the lower intensive technique! Then, there may not be substitution between capital and labour when you change techniques! Higher wages may imply higher demand of workers and higher interest rates may imply higher capital intensities.
    Now imagine a whole set of roller coaster wage curves, all making up and downs in the demand for investment within the same technique and making jumps between a technique and the other, sometimes in the "right" direction, and sometimes in the "wrong" direction. How can someone say, in this set that there will be equilibrium in the marginalist sense (prices, quantities and distribution), that wage flexibility will give you full employment and anything about how the loanable funds market set the interest rate?
    Here for reswitching (figure 2)(the figure is upside down, though)
    I'll be very very busy. I'll catch up on saturday, at best.
    And Robert and Matías are good guys, and their will is good. It's just that sraffians tend to think that all economists know what they're talking about...perhaps because economists should know. And they both know much more than me about the capital controversy... Robert's blog is a must read.

  19. In the second comment there is a missing part when it says "And the other way round if kk/lk (y-w)/r=k"
    it's "and the other way round if kk/lk<kc/lc"
    and then "if

  20. I confess I am getting a tiny bit peeved.

    Matias said this about me: "Regarding point 4, there is an incredible confusion in the comment by Nick. Sraffa’s system never assumes any aggregate production or a one good economy."

    Here is my point 4:
    "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."

    Matias has almost certainly simply misread my "Cambridge US" as "Cambridge UK". No big deal. But I have pointed this out to him twice, and he still hasn't seemed to notice.

    Or is there some other explanation for this confusion? Do any of you guys see my point?

    Genaro: Thanks for the clarifications. Sorry for the delay.

    1. Yep, sorry about the confusion. I thought in that passage you were talking about UK not US side of the debate. THanks for clarifications.

  21. Genaro: OK. I have now read your comments.

    I agree it would be a very special assumption to assume that all capital goods were produced using exactly the same capital labour ratios as consumption goods. And only under that assumption would it be possible to think in terms of an aggregate production function like C+I=Y=F(K,L)

    I do not make that assumption. I do not need to make that assumption. I do not need to aggregate capital goods. I reject the statement that r=dY/dK. I measure capital goods in physical units. Let R be the rental rate on a physical capital good. Then R=dy/dK. But R is not the rate of interest.

    And yes, you need to know the prices of capital goods Pk, as well as their rentals R, to find the rate of interest r. And to solve for both r and Pk, you need to know preferences. Especially, time-preferences.

    Can I ask you to read my (short) post where I explain how I think r and Pk are determined? It is a very simple model of capital theory. But much better than the one-good Cambridge US model.

    I am still thinking about price-Wicksell effects and the savings and investment curves, and how best to explain my views on that. I will return to that later.

    1. You need to use units. Capital goods don't produce themselves (with the exception of seeds and livestock!) so you end up with units like "bars of pig iron per factory per day".

      But the trouble is that you need to know the prices of capital goods before they are manufactured. What are those prices? Well, in practice they're cost-of-production-plus-chosen-rate-of-profit, since the markets for manufacturing capital goods are thin and non-competitive. So there *is* a way to get such a model...

      ...but in practice the chosen rate of profit is determined by whether the manufacturer of capital goods can get more nominal profit by investing in T-bills, and we're back to the rate of interest coming first!

      Now, you can do something with a multiple-time-periods model (rate of interest in time period 1 determines price of capital goods in time period 2 determines theoretical rate of interest in time period 3).... and then you can actually get a model of bubbles and busts under Free Banking systems. This is irrelevant to a system with a Central-Bank-determined interest rate, though.

    2. I'd like to point out something which has been said by a gazillion people, but apparently most notably by Irving Fisher: "solving for equilibrium" is completely useless in practically every economic problem. Equilibrium conditions *never* exist, no matter how you define equilibrium -- and worse, conditions only even approximately close to "equilibrium" within certain commodity-like markets.

      (There are some long-run game-theoretic equilibria which appear to have happened evolutionarily, but that's a different sort of equilibrium.)

      Why am I bringing this up here, when equilibrium hasn't been mentioned? Because *it matters what order things happen in*, it matters which is cause, which is effect, and which is neither -- and equilibrium thinking causes economists to have *mental confusion* about this. I'm seeing this repeatedly and in subtle ways from Nick Rowe -- *disregard* for the critical importance of getting cause and effect right; I also see it in the dismissal of MMT by "conventional" economists -- it's again *disregard* for the importance of "which comes first", and the equilibrium thinking has *trained* them into this disregard.

      Every model must be *explicitly* time based if you are to think clearly at all.

      And there generally aren't any useful "equilibrium patterns" over time; the bust and bubble cycle is one, I guess, but not one which is susceptible to a math-heavy model. (A non-math-heavy model, yes.)

  22. Some firms produce consumption goods, and other firms produce capital goods. Consumption goods and capital goods (almost certainly) are produced with a different mix of inputs. That means that the higher the prices of capital goods relative to consumption goods, the greater the quantities of capital goods supplied relative to consumption goods.

    Each capital good earns rents, equal to the value of the marginal product of that capital good. The price of each capital good will equal the Present Value of the (expected) stream of rents it earns. The lower the current rate of interest, the higher that Present Value, and the higher the price of those capital goods, and the greater the quantities of those goods firms will wish to produce, and the fewer resources left over to produce consumption goods. So there is a positive relation between the current rate of interest and the current quantity of consumption goods that firms are willing to produce given currently available resources. The higher the current rate of interest, the more consumption goods (and the less capital goods) firms will want to produce.

    Now we bring in preferences. Given their incomes from the current production of capital goods and consumption goods, and their expected future incomes, if the current rate of interest falls, people will want to buy a greater amount of current consumption goods (and a smaller amount of future consumption goods). So there is a negative relation between the current rate of interest and the quantity of current consumption goods people want to buy.

    Put the positive relation and the negative relation together, and solve for the current rate of interest at which the quantity of current consumption goods firms want to produce and sell equals the quantity people want to buy.

    This system may or may not converge to some long-period equilibrium in which interest rates stay constant over time. So what if it doesn't converge?

    What do you think is wrong with that model? (That is not a rhetorical question.)

    1. What is wrong with that model depends on what you want to use it for.

    2. There is no such thing as "the value of the marginal product of that capital good". The value of it is an *endogenous variable* dependent on the *entire macroeconomic state*, but especially on the division of income between wages and profits.

      That's what's wrong with that model, and Sraffa's most famous body of work was devoted to demonstrating this fundamental problem.

      Second problem:

      Sure, capitalists make a prediction, an expected stream of rents, which you might think would allow you to evade Sraffa's first criticism. However, these predictions are notoriously inaccurate. Most of the pricing is determined by *differing opinions* on the future stream of rents, which anyone who's ever been in a bidding war would understand. You've just left that out, when it's the entire determiner of the state of the economy. Consistently wrong opinions on the future stream of rents are the primary driver of bubbles in the economy, of course.

      So "what do you think is wrong with that model"? EVERYTHING is wrong with that model! I didn't even get to paragraph three!

      Sigh. Perhaps Keynes did well at economic theory because he actually speculated in the stock market and was good at it; he knew "animal spirits".

      I've found the most useful economic theories are rooted firmly in actual behavior, and you have to study the actual behavior of an actual section of the economy in order to understand it. (For instance, most "labor markets": bosses tell workers what wage they're going to take, then treat 'em like servants, and the workers do it because they need to eat. You can make a model of that, but it looks pretty Marxist.

      Early classical economics was all about coal, iron, and mass-produced grain -- bulk commodities where different producers' versions are practically indistinguishable -- and it describes commodity markets pretty well, but doesn't describe any other markets. It's been high insanity to attempt to shoehorn the theory of commodities to apply to other things, and most of the history of economics has shown that doing this doesn't work.

      Having a good theory of money requires understanding how banks actually behave. Hence, MMT.

      Et cetera et cetera et cetera. Each part of the economy is DIFFERENT, driven by different predominant psychology. Economics *should* be developing separate theories for separate areas, the way physics had separate theories of optics, waves, mechanics, etc -- economics is nowhere near ready to develop unified theories as physics did in the late 19th century.)

  23. "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."

    The above is incredibly confused. A one-good model does not allow a full long-run neoclassical model to be constructed without talking about time preferences. See here for me quoting Stephen Marglin on this point:

    Furthermore, Solow explicitly discussed Irving Fisher's model in his exchange during the CCC with Pasinetti over the "rate of return" and a certain unobtrusive postulate. And Dorfman, Samuelson, and Solow, if I recall correctly, explicitly discuss trading consumption off today for consumption tomorrow in their 1958 book Linear Programming and Economic Analysis.

    1. Robert: stop obfuscating. You know very well that Matias said I was talking about Sraffa's system. And that I was not talking about very long run equilibrium, which may or may not exist, depending on the model. And it is unsurprising to me that an economist like Solow would be aware of models like Fisher's.

  24. Let me add fuel to the fire. At its most basic, the "exogenous rate of interest" theory says that some large operator, such as a central bank, *sets* the rate of interest, and everyone else pegs to that rate (perhaps with a "creditworthiness adjustment").

    This is, in fact, how the economy actually operates, and how it has for centuries. You can ask the Fed Board of Governors, Open Market Committee, every bank which pegs its rates to the Fed rates....

    The competing (and discredited) "endogenous rate of interest" theory suggests that the rate of interest naturally arises through a large group of interacting people -- many individual actors causing it to arise as a result.

    When has this *ever* happened? Even before central banks, most lending was dominated by a very small number of very rich and very powerful bankers -- whoever had the hoard of gold. (Those people could determine the interest rates, unless the gold mining supply disrupted the rates.)

    Perhaps during the Free Banking period in the 19th century?... but even there, the bankers set out and advertised rates of interest, and then waited to see whether people would borrow at those rates.

    So the basic "how things actually work" evidence says that the rate of interest is exogenous now, and even in Free Banking periods, exogenous on short timescales. Only on long timescales in a Free Banking period could is possibly be anything but exogenous, and the long-run determination of interest rates during such a period has not been empirically studied.

  25. neroden: the rate of interest is certainly not exogenous. The Bank of Canada adjusts the rate of interest to try to set it where (it thinks) desired saving equals desired investment, to try to keep inflation at the 2% target. That means the rate of interest is endogenous, and responds according to what is happening in the economy. The Bank of Canada knows that if it tried to set an exogenous rate of interest, that is unaffected by what is happening in the economy, the result would be an unstable equilibrium.

    This is how things actually work.

    1. That's not exactly true. The rate is still exogenously set by the Bank of Canada. The choice of a 2% inflation target is arbitrary. If they went for 4% or for a full employment target that would require a different interest rate in most circumstances. Hence, the rate of interest is exogenous. What you are dicussing is what is the target that binds the reaction function for the central bank.

  26. Nick,
    a) in Marginalist neoclassical theory, in absence of "risk", the long run interest rate is the cost of opportunity of production, and then returns on capital and the real interest rate must be equal. Notice that the long run real interest rate is the "natural rate", which comes from the loanable funds market equilibrium. (ie, long run profit rate=>natural rate=>endogenous rate). The short run nominal rate is exogenous, but a divergence from the natural rate will create (demand=I>S) inflation until that gap has been closed and the real rate (1+i)/(1+pi)=1+r

    b) and no, you're not rejecting r=dY/dK nor y=F(K,L). When you assume "flexible competitive markets" you're assuming Say's law,ie, if relative prices, even factor relative prices are flexible, all supply creates it's own demand, and then, if prices are flexible, there will be a w/r=w/i of equilibrium of distribution that guarantees that all supply of labour and savings creates its own demand. Now, this is assumed true in marginalist economics, as they seem to believe it has been proved -but they haven't, it depends on equal capital intensity of branches of production. If they're not, there may not be a w/r that creates the fact that all planned savings will become all planned investment and all planned labour supply will become all planned labour demand (where marginal productivity of capital=r=i and marginal productivity of labour=w). And then, with unequal capital intensity between branches of production, even with prices as flexible as you want (even with miserable 2 dollars per month as wages)you will NOT get equilibrium, there may be no equilibrium and no natural rate (ie, the short run rate of interest is exogenous even in the long run, and you do not need to adjust to the natural rate), and even if there is an equilibrium, it may be divergent. Plus, you may change capital intensity within the same technique.

  27. c)On capital goods: Sraffians, and all the "classics" (from Quesnay to Wicksell) talk of capital as capital in circulation (inputs) and capital intensity is between inputs and labour. This is made in an explicit idea that is that capital goods are both inputs and outputs, in the sense that you produce commodities by means of commodities. Sraffa clearly distinguishes three types of capital: inputs, fixed capital, that only comes into the cost of production in the quote that this capital good has been depreciated (ie, if a capital good is useful for ten periods, only the "first year of use" goes into the cost of production in t=1, and old capital, that cannot be produced anymore, and therefore is treated like land and rent.
    Now, what you say is wrong, particularly on prices of consumption/capital. First, price of reproducible fixed capital goods may be taken as the present value, but that present value in the long run (equilibrium) must be equal to the cost of production of the fixed capital good, and this depends on the rate of profits and income distribution and capital intensity, so a change in the rate of profit still changes everything. And moreover, a higher rate of profit (return on capital and "price" of saving or adding new capital to production) may actually make capital prices lower, because of the "mixed inputs" you're talking about. And then,if it's so much cheaper, you will replace labour for capital, At higher r!!!, which makes no sense: factors of production should be substitutes for neoclassicals, ie you demand more capital with LOWER interest/profit rate.
    And btw, Sraffa has "something" like your grandfather's theory of land. Each land perceives rent because of scarcity between two methods of production. If the price of corn goes up, so does the rent on land, until it's more profitable for the capitalist producing corn to use a different technique. Then here capital comes to solve the land's scarcity problem.

    d)The whole long period equilibrium vs short period equilibrium should be revisited. It's not a "short period" that in the long run may or may not converge into a "long period" equilibrium. Short period equilibrium was developed because of the failure of long period marginalist analysis, and it just assumes the things that the long period analysis couldn't prove (ie, substitution of factors in perfect competition). That's why short period analysis is so exigent in terms of theoretical conditions of equilibrium: you postulate (don't prove) an equilibrium and force agents to be well-behaved, because if they aren't, there may be no equilibrium, or equilibrium may change.
    To sum up: long period analysis in marginalist sense could prove factor substitution but was flawed because of it's logical deficiency of not taking into account the heterogeneity of capital goods and capital intensity. Then short period arises, but short period equilibria do not prove either equilibrium: they just "make it happen". But agents, even if they're "superrational" may not tend to
    it. That's why everything must be determined before the maket is open: the auctioneer has solved the problem before the agents could even start thinking about it. They cannot be mistaken

  28. The choice of a 2% inflation target is arbitrary.

    Not only the target is arbitrary, but the fact that one sole instrument (the interest rate, or expectations thereof) has been designated to reach it ignores the fact that any meaningful target is necessarily the product of many independent variables. These can be as wide ranging as the legal and cultural frameworks, psychological phenomena, other trends, institutional arrangements, world markets, migration, fiscal policy, inequality, supply bottlenecks etc. etc.. And while some of these factors may fall outside of what can reasonably be called the 'economic sphere', many do not. And even if so, they all have an influence on it and so cannot be brushed aside by being modeled as ceteris paribus.

    The attempt to draw a direct connection between an interest rate and the notion of economic equilibrium seems about as feeble as assuming the Queen's descendancy from God is the main cause for relative political stability in the UK.


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