Friday, May 16, 2014

Robert Murphy, the Austrian theory of the rate of interest and Piketty's 'Capital'

In the comments to another post it was suggested that I checked Robert Murphy's discussion of the relevance of the capital debates for Austrian economics.* The basis for my comments is Murphy's recent post on the topic here. It seems that the capital debates are somehow connected to a critique of Piketty's views on inequality from an Austrian point of view, but the post here, which was also linked in the comments, is less than clear about that.

The question is why would the capital debates, which basically criticize the main tenets of marginalism, be relevant for a marginalist school of thought like the Austrians. Shouldn't the logical flaws of marginalism affect Austrians too? [The answer is yes, by the way, but we'll get to that].

First of all, Murphy gets the main point of the capital debates wrong. He seems to think that the lack of a natural rate of interest results from the difference between aggregate capital, which must be measured in monetary terms (which he refers to as financial capital), and physical capital (which he, interestingly, refers to in the Sraffian terminology of Marx and the classical political economy authors as produced means of production). Note that it does NOT matter whether capital is in aggregative (monetary) form or if you have an array of physical capital goods, as I explained before, it is still necessary to equate aggregate investment to savings.

In Keynesian economics the equalization of investment to savings is done by the multiplier process and by variations of the level of income leaving space for a monetary story for the rate of interest. In all neoclassical (marginalist) models, including the Austrian, it is the rate of interest that equilibrates investment to full employment savings. That rate of interest is the natural rate of interest.

Murphy seems to think rather confusedly, that the idea of disaggregated capital implies that Austrian (really it would be the case for any model without aggregative measures of capital, like the Arrow-Debreu General Equilibrium too, which is hardly an Austrian model) models do not have a natural rate.** Let me repeat it then, any model with disaggregated means of production (capital goods) still requires for the equilibration of aggregate investment to full employment savings, it requires a measure of the quantity of capital that corresponds to aggregate investment, and that means, by necessity, a rate of interest that equilibrates investment and savings. The point of the capital debates is that there is no direct relationship between the intensity of the use of capital and its remuneration, that is, no guarantee that at lower rates of interest more capital would be used, and full utilization of resources would be produced by the free interplay of market forces (something that Murphy, as an Austrian, believes in).

Worst, Murphy seems to think that the capital debates applies only to the capital market. He says: "the relationship between the productivity of capital and the interest rate is not directly analogous to the relationship between the productivity of labor and the wage rate." As it turns, the point of the capital debates is that if you reduce the wage rate, there is also no guarantee that more labor would be utilized, and there is no necessary relationship between marginal productivity of labor and real wages (and the evidence in favor of that is also flimsy, to say the least). In other words, the capital debates apply to the marginalist labor market too. No 'factor of production' is remunerated according to marginal productivities (Samuelson got that right, all the neoclassical parables are problematic, and it is a bit surprising to find this amount of confusion so long after the capital debates have been resolved).

So its seems that it is not just Piketty that "has no clue about Capital." The fascinating thing about Murphy's critique of Piketty's lack of knowledge about capital, is that for him this suggests that Piketty's  wealth tax would be a bad idea (note that critiques from the left, like Galbraith or Palley are not against a wealth tax, but suggest that inequality must be combated in other ways too, with stronger unions, more regulated capital, full employment policies, etc.). Here Murphy seems to think, like Tyler Cowen, that taxes would punish entrepreneurs and reduce the dynamism of capitalism. Because, you know (wink wink nudge nudge, say no more), without taxes, and other impediments, capital would be more efficiently utilized. So here is an economist that criticizes higher taxes as the solution for inequality, by suggesting that the notion of capital used to defend a wealth tax is flawed, and uses that very same flawed notion of capital (without even getting it) to defend a laissez-faire solution.

* By the way, not the first time I'm asked to comment on Austrians (see here and here). Austrians stand for economics like Libertarians for politics, and they are a militant group, which would be my guess of why there are so many people concerned with Austrian theory. Love for Hayek and Ayn Rand are highly correlated among teenage students, in my experience. And that's not very good company for Hayek.

** The fact that Murphy does think the capital debates are about aggregation is clear when he asks: "Does anyone know, does Piketty’s book elsewhere deal with the problem of aggregating capital?"

27 comments:

  1. Perfect Python reference. Reminds me of that famous Solow quote about Friedman: "Everything reminds Milton of the money supply. Well, everything reminds me of sex, but I keep it out of the paper"

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    1. That's one of Solow's best quotes. I like the one in which he compares Lucas to Napoleon. "Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the Battle of Austerlitz."

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  2. You are ignoring, as Keynes did, that a fall in wage rates leads to a fall in the costs of production, including the costs of capital goods. Any stipulation of a fall in output prices by virtue of a fall in nominal demand, should be accompanied by recognition of a fall in unit costs, thus rendering the deflationary death spiral doctrine a flawed one.

    With respect to the Keynesian multiplier doctrine, it should be understood that Keynes' multiplier doctrine contradicts Keynes's marginal efficiency of capital doctrine. The multiplier doctrine suggests that any autonomous productive expenditure will lead to a sequence of subsequent series of (declining) expenditures. Now surely this would increase profitability. And yet the marginal efficiency of capital doctrine on the other hand suggests the opposite takes place, that an incremental increase in productive expenditures will lead to a reduced profitability.

    It should also be noted that contrary to what his followers believe, Keynes did not actually address the argument from the classicals that a fall in wage rates and prices cures depressions. In The General Theory, Keynes not only did not critique whether a fall in prices can cure unemployment, but he astonishingly dropped that context altogether assumed that prices are increasing! If this sounds too incredible to be true, just read page 136 of the GT.

    Now with regards to this particular debate on capital, you make a number of errors. No, it is not true that a natural rate of interest can be wedged into a context of real, heterogenous goods. For if 10 present t-shirts are traded against 12 future t-shirts, and 20 present apples are traded against 25 future apples, and we assume these are the only goods produced and sold, then what is "the" natural interest rate?

    Of course, the Austrian theory of natural interest is NOT predicated on heterogeneous real goods, but on the difference in valuation between present and future goods as such. This is a very general conception that requires careful usage and consideration. In a monetary economy, the natural rate of interest is best understood as the average rate of nominal profits that would prevail in a free market, and this average rate of profit is the regulating mechanism that constrains interest rates. In a central bank hampered economy, interest rates are no longer constrained by free market forces, but become affected by non-market money manipulation. This sets off malinvestment.

    Your post is in general replete with the usual unnecessary partisan attacks and confusions typical from Keynesians. No is not true that economists need to "measure" disaggregated heterogeneous capital. Only states and those who try to control oir lives would find any use for such a measure. A healthy economy needs nobody to measure total capital. Self-interested profit seeking and loss avoidance, subject to private property rights, is necessary and sufficient for allowing maximum economic coordination. Nobody has to measure aggregate capital, and nobody has to measure the rate of interest that would equilibriate investment and saving, in order to the economy to grow and for full employment to be constantly tended towards.

    Your claim that Murphy "seems to think" this, and "seems to think" that, are hallmarks of straw men tactics. Murphy did not, contrary to your claim, utilize Piketty's flaws on capital to make a case for laissez faire. Murphy was laissez faire and has been making laissez faire arguments for years, since before Piketty wrote this book.

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    1. Major Freedom, your claims are replete with the usual unnecessary confusions typical of Austrian School economists. Starting with your opening statement, please take a look at Chapter 21, entitled "The Theory of Prices". See p. 294 of the GT, where Keynes claims "The general price level depends partly on the rates of renumeration of the factors of production which enter into marginal costs and partly on the scale of output as a whole." What basis do you then have for concluding that Keynes ignored the effect of costs on prices? This is total fabrication on your part, which is sad to see, because you actually appear to have read Keynes in the original...but then again, that has not stopped prior Austrian School influenced economists/commentators like Hunter Lewis or Henry Hazlitt from fabricating similar patently false claims.

      Regarding a fall in capital goods costs from a fall in wages and its effect on aggregate income and output, please take another look at Chapter 19, Changes in Money Wages, particularly pp. 262-5, where Keynes explicitly discusses the special conditions required for a fall in wages to lead to higher aggregate consumption and investment spending/output. The case of markets self-adjusting back to full employment on the back of wage and/or price changes requires very special conditions which generally are not available in the world we actually inhabit. The discussion is so thorough (including a reference to Fisher' debt deflation process in point 7 on p. 264) that Keynes concludes (on p. 267), "There is, therefore, NO grounds for the belief that a flexible wage policy is capable of maintaining a state of continuous full employment...". Well, in fact, there are a few grounds he does list, but they are unlikely conditions to obtain in the economies we inhabit, which makes mainstream macroeconomic theory, which has become little more than aggregated microeconomics (thereby ignoring all of the associated fallacies of composition which Keynes tried to point out a lifetime ago) a special theory, not a general theory of economics.

      There is much more you have unnecessarily confused, including the multiplier story (think about the increase in the capital stock from investment spending, which is a supply legacy for future production periods, and so creates less scarcity of capital goods, hence less of a return to owners of the capital stock in the future) But take heart, you are in good company. Even Paul Krugman, who wrote the forward to the most recent edition of the General Theory, has been unable to actually read the words that Keynes wrote. While Krugman goes on and on about how the solution is to increase inflationary expectations via monetary policy in order to escape the liquidity trap he imagines to be the sole impediment to growth in the developed world economies, he apparently neglected to read the second part of the quote above, where Keynes also concludes monetary policy, unaided by public or public/private investment, is equally unable to produce a state of continuous full employment. It appears both New Keynesians, and Austrian School economists and commentators, would do well to pay a visit to their eye doctors before making any more false claims on Keynes.

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    2. Rob Parenteau,

      All absolutely right. "Major_Freedom" has no idea what he's talking about.

      He has also just invented his own definition of the natural rate:
      "the natural rate of interest is best understood as the average rate of nominal profits that would prevail in a free market"
      --------------
      Ultimately, this bozo has no interest in what any Keynesian or Austrian economists actually say or said.

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    3. Well Major Freedom, it seems you don't really get the point of why lower real wages do have a negative impact on the level of activity. The debate on Real Balance effects (Keynes' and Pigou effects) is relatively old, and Kalecki gave the coup de grace in that respect back in 1943. Don Patinkin has wrote extensively including in the old edition of the New Palgrave for a summary. Lower wages might very well reduce the cost of capital and lower the rate of interest, and that is known as the Keynes effect (so much for Keynes not knowing about it! Read chapter 19 of the GT before you say something like that dude). And also lower real wages and prices would lead to positive wealth effects (the Pigou effect; response by Kalecki is devastating). So Keynes suggests that while these are possible outcomes, the counter-effect of lower wages, and prices on indebted agents (which face a higher burden) and on income distribution (lower real wages redistributing income against groups with higher propensities to consume) would more than outweigh the positive effects.

      For the silliness of the rate of interest being based on intertemporal differences as being a different theory of interest read my replies linked in the post to the Spanish Austrian economist. Austrians should learn basic algebra.

      Also, there no straw men tactics in pointing out what seems to be the case given what Murphy says, after all many people write things they do NOT understand and hence do not necessarily believe. THey must be shown the proper logic of things. Many decide not to learn

      Best of luck to you!

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    4. THanks for pointing to chapter 19, and the other well thought arguments Rob!

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    5. Rob Parenteau:

      With that introduction, this reply of yours is guaranteed to be full of straw men and confusions.

      I never claimed Keynes ignored the effects of costs on prices. I said he contradicted the context of a fall in prices (on page 136) in his critique of the classical claim of the ability of a fall in prices to cure depressions.

      He wrote that capital goods prices rise with a rise in net investment, despite the fact that the rise in question is predicated on a fall in prices. The law of demand applied to capital goods.

      How in the world can any alleged thoroughness be predicated on a conclusive statement from Keynes that he can't see any reasons for why a fall in prices and wages can cure depressions?

      You don't seem to understand the technical reasons for why Keynes believed that falling wages cannot cure depressions. The main reason he gives has to do with the utterly fallacious MEC doctrine, which is tied to his contradictory assumption of rising capital goods prices. In short, Keynes believed that a fall in wage rates would only reduce demand and prices of output. He did not think to consider falling wages as falling costs of producing capital goods, and thus an opportunity for capital goods prices to fall and thus NO necessary reduction in profitability due to a fall in demand and prices of output.

      He claimed "all else equal" when discussing falling demand and prices of output, despite the fact that all else is certainly not equal.

      You seem to confused on a number of points. First, Keynes' argument of the multiplier has to do with spending, not real growth. He believed that an autonomous increase in net investment *spending* would be followed by a series of successively declining *expenditures*. Now surely that would have the effect of increasing profitability. And yet that contradicts his MEC doctrine, where he holds that an increase in net investment would decrease profitability. Second, a larger supply of capital goods does not reduce profitability, real or nominal, and it does not reduce returns, real or nominal. A higher supply of capital goods (brought about by actual savings information, not misleading information from central banks) has the effect of increasing real profitability and real returns. In terms of nominal profitability and return, this depends on nominal differences in spending. The same spending on capital and the same (higher) spending on total output will lead to a stable positive profitability, and this can fully accommodate stable growth in capital and total output on the basis of gradually falling money costs per unit and output price per unit.

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    6. Matias:

      1/2

      "Well Major Freedom, it seems you don't really get the point of why lower real wages do have a negative impact on the level of activity."

      I said lower wage rates. I did not say lower real wages.

      Lower wage rates that enables a fall in capital goods costs and output prices does not reduce real wages. And, if the context is a depression, where there are a number of unemployed persons, and a substantial quantity of postponed investment, then a fall in wage rates would likely be accompanied by a rise in total wage payments, the same reason why total spending on cars went up after they drastically declined in price during the 1920s, and closer to the present, why total spending on iPhones went up after they declined in price to reach the affordability of the great bulk of the population.

      Falling wage rates is NOT ipso facto a fall in real wages.

      "Lower wages might very well reduce the cost of capital and lower the rate of interest, and that is known as the Keynes effect (so much for Keynes not knowing about it! Read chapter 19 of the GT before you say something like that dude)."

      Incorrect. Keynes assumed a RISE in capital goods prices when he critiqued the efficacy of a fall in wage rates to cure depressions. He claimed that the reason a fall in wage rates cannot cure depressions *is due to a declining MEC.* On page 261-262, he considers the "crude conclusion" that a fall in wage rates can cure depressions, but if you look at his reasons for how it might seem to happen, if you read the whole of GT, you'll see that for the hypothetical possibilities he gives, he has rejected them all. He writes it might work if the MEC shifts to the right (which it can't do under his assumption of declining MEC), or if the rate of interest falls (which it can't do under his assumption of a minimum 2%).

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    7. Matias:

      2/2


      Keynes' whole theory can be summarized by this claim of his:

      "For if entrepreneurs offer employment on a scale which, if they could sell their output at the expected price, would provide the public with incomes
      out of which they would save more than the amount of current investment, entrepreneurs are bound to make a loss equal to the difference; and this will be the case absolutely irrespective of the level of money wages."

      Keynes writes of two critical ideas that underlie the IS curve. Savings, which he constantly conflates with cash preference, and net investment. It is his claim that as net investment increases, the rate of return on capital must fall, that is the problem with his critique of the classical theory on falling wage rates. He wrote:

      "If there is an increased investment in any given type of capital during any period of time, the marginal efficiency of that type of capital will diminish as the investment in it is increased, partly because the prospective yield will fall
      as the supply of that type of capital is increased, and partly because, as a rule, pressure on the facilities for producing that type of capital will cause its supply price to increase . . . .Thus for each type of capital we can build up a schedule, showing by how much investment in it will have to increase within the period, in order that its marginal efficiency should fall to any given figure. We can then aggregate these schedules for all the different types of capital, so as to provide a schedule relating the rate of aggregate investment to the corresponding marginal efficiency of capital in general which that rate of investment will establish. We shall call this the investment demand-schedule; or, alternatively, the schedule of the marginal efficiency of capital."

      Keynes contradicted the context of a fall in wage rates and prices!

      "Also, there no straw men tactics in pointing out what seems to be the case given what Murphy says, after all many people write things they do NOT understand and hence do not necessarily believe. THey must be shown the proper logic of things. Many decide not to learn"

      What he "seems" to say is not what he said in this case. You're straw manning him.

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  3. Murphy, in his articles on Piketty , focuses on Pikettys apparent support for the view that the marginal product of capital equals its rate of return.

    Murphy correctly explains that this is untenable in the light of the Cambridge Capital Controversies.

    He then explains that this is not an issue in an Austrian model where interest rates , rather than being derived from the marginal products, are derived from he time preference of those participating in the market.

    This rather confusing post does not seem to address any of the main point in either of the linked to articles.

    - "Murphy seems to think rather confusedly, that the idea of disaggregated capital implies that Austrian (really it would be the case for any model without aggregative measures of capital, like the Arrow-Debreu General Equilibrium too, which is hardly an Austrian model) models do not have a natural rate." . Are you suggesting that Austrian models don't have a natural rate , ?

    - ""the relationship between the productivity of capital and the interest rate is not directly analogous to the relationship between the productivity of labor and the wage rate." Do you see this an untrue statement in the light of the CCC ?






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    1. I find a confusion/ambiguity along these lines in Austrian School economics. Some, like Murphy, claim interest rate is merely a function of time preference of consumption. It is a rate of exchange, if you will, between jam today and jam tomorrow (alternatively, a relative price, but across time). Yet surely this offers us only one side of the puzzle, namely the demand for future consumable products. We also need to know the supply side, or the ability to transform current materials into future products. That is where the marginal productivity of capital comes into play. Otherwise, it would appear the theory of interest rate determination in Austrian School economics is, oddly enough, an example of demand side only economics - which ironically, is usually how Keynesian economics is assessed

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    2. Nah, this isn't a matter of looking at demand versus supply. It's a matter of being clear about what "the real rate of interest" means. It's actually what you do in a Fisher diagram or an Arrow-Debreu model too. Here's Nick Rowe walking through it all.

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    3. Hi Rob and Robert, you raise an important point. I'm sorry to say that time preference argument, which is typical of the disaggregated intertemporal models from the 1930s onwards leading to Arrow-Debreu, are still as I noted in the post and in several other in the blog very much the same and as problematic from the Capital Debates point of view. Exactly for that Robert you're basically using the very same notion as Piketty. I suggest the following previous posts on Nick:
      http://nakedkeynesianism.blogspot.com/2012/09/nick-rowes-misconceptions-about.html

      http://nakedkeynesianism.blogspot.com/2012/09/nick-rowes-misconceptions-about_20.html

      http://nakedkeynesianism.blogspot.com/2012/08/nick-rowe-on-reswitching-and-capital.html

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    4. Thanks for your reply.

      If the rate of interest (I use the term to mean the same as rate of profit) is derived from the marginal product of capital then we clearly have circular reasoning (the value of capital is a function of the rate of interest. but the rate of interest is determined by the value of capital being used.).

      If however (as many Austrians believe) the rate of interest is determined purely by time preference then it has no dependency on the amount of capital. It is no more subject to circular reason than the Straffrian model that appears to see the rate of interest as an exogenous (or perhaps socially) determined variable.

      You could criticize the Pure Time Preference theory on other ground but (as far as I can see) not that one.

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    5. Hi Rob. Not sure how the Sraffian system is circular. It is mathematically a fact that you can solve for long term prices and a uniform rate of profit for given technological coefficients and one exogenous distributive variable (either the rare of profit or the real wage). Sraffa was the ultimate logician. He did not commit circularity mistakes. Ask Samuelson. Lets say that interest are determined by preferences. You still need to adjust the time preferences to the ability to obtain more consumption in the future. THat would be the marginal productivity of capital. So you cannot scape the need for a measure of capital. THERE IS NO WAY OUT. Seriously people, read Samuelson 1966. Samuelson had many defects, but at least he knew when to concede when he was wrong.

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    6. I was not saying that Straffa was using circular arguments - i was saying that as he is not, then neither are Austrians who believe that interest rates are based entirely on time preference and not at all on the value or productivity of capital.


      You say "Lets say that interest are determined by preferences. You still need to adjust the time preferences to the ability to obtain more consumption in the future. That would be the marginal productivity of capital."

      If the "ability to obtain more consumption in the future" changes then this may cause relative prices to change but will not have any direct bearing on interest rates.

      For example: A new technique is discovered that doubles the output of widgets using the same inputs and production time as before. The same amount of "waiting time" on the employed capital now generates twice as much output. Initially profits in the widget business will be above average for the economy. New entrants will cause adjustment in the price of inputs (upwards) and output (downwards) until the rate of profit adjusts to the rest of the economy. This rate of profit (excluding risk) will still be equal to the rate of interest based on time preference alone.

      So: The rate of interest is determined totally independently of the amount or productivity of capital. The relative prices of capital and the goods produced by that capital are rather determined by this rate of interest.


      Now: It is possible that "the ability to obtain more consumption in the future" makes people fell richer and this may change their time preferences. But I do not see how that be made into a circular argument.





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  4. If anybody cares, in this article from several years ago I walk through some of Sraffa's numerical examples to explain how he viewed interest as flowing from institutional forces, not marginal products. I am aware of these controversies. To say that the Cambridge Capital Controversy involved a debate about "aggregating capital" is pretty standard; e.g. Joan Robinson herself identified the notion of "K" in a production function in her witty diagnosis of the problem, and these JEP authors identify measuring the capital stock as the first of 3 central disputes in the debate.

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    1. Might be standard but is simply wrong to say it is about aggregation. Intertemporal models with disaggregate capital are still open to the capital critique, and the idea of time preference is still very much a marginal productivity argument. Not difficult to get actually.

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    2. Hang on a second. Consider this:

      ====
      In “The Production Function and the Theory of Capital,” Joan Robinson
      (1953–1954, p. 81) wrote:

      ". . . the production function has been a powerful instrument of miseducation.

      The student of economic theory is taught to write Q 5 f (L, K ) where L is
      a quantity of labor, K a quantity of capital and Q a rate of output of
      commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labor; he is told something about the index-number problem in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units K is measured. Before he ever does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next."
      =======

      Prof. Vernengo, what is your claim?

      (A) Joan Robinson in the above isn't pointing out that there is a serious problem in aggregating all of the capital goods in the economy into a single number "K."

      or

      (B) Joan Robinson (like me and plenty of other of historians of economic thought) was also misinformed about what the CCC was about?

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    3. Prof. Vernengo,

      OK I can see you are a formidable opponent on this stuff... I don't have the time to read your links but I will put this on my calendar so I don't lose track of them.

      In the meantime, it may interest you to know that I have tried to get the Austrians to realize that Hayek never gave a great reply to Sraffa (on natural rates of interest), and that Ludwig Lachmann totally fumbled. It's in Section II of this paper.

      Needless to say, most Austrians were not convinced by my case.

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    4. On B, yes Joan Robinson was mistaken about the K debates. But mind you, not in the same way you are. She noted, as many Post Keynesians, and a few hybrids (like Shackle) that uncertainty made all the questions of investment decisions murky and the question of re-switching irrelevant. This was part of her 1970s turn into History vs Equilibrium.

      On A, yes there is a problem in aggregation, but that's NOT what is relevant about the K debates. THe problem is that there is no inverse relation between remuneration of K, the rate of interest, and the intensity of its use. Hence, with price flexibility (and lower interests) there is no guarantee that K will be fully utilized. And that's valid for the labor market too, by the way, where nobody would complain about the aggregation of labor figures.

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  5. THEY are the militant group? lol

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  6. Matias,

    "the idea of time preference is still very much a marginal productivity argument"

    Could you explain why?

    Thanks.

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    1. Yes, as I said I will post something later this week. Too many things to do. In short, just note that the marginal rate of substitution (MRS) between consumption today and in the future, must be equal in equilibrium to the marginal productivity of capital (MPK). THere is nothing new here. What Rowe (and Murphy) use is essentially a version of the very traditional marginalist model. The rate that equilibrates MRS and MPK is the natural one.

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    2. Matias: but MRS and MPK don't even have the same units (unless the consumption good(s) and the capital good(s) are the same).

      My post says that the equilibrium condition is:

      MRScc=(1+r)=1+(MPK/MRTci)+(dMRTci/dt)/MRTci

      (where MRTci is the marginal rate of transformation between production of the consumption good and the capital good).

      http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/05/mrscc1r1mpkmrtcidmrtcidt.html

      But yes, my post is definitely a marginalist model.

      I look forward to your post. Maybe we will come to some sort of agreement. Or at least understand better where we differ.

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  7. Dr. Murphy, I'm not an economist so I wanted to ask you question regarding Piketty's "r > g" claim.

    From my perspective, I don't see any meaningful distinction between human capital and non-human capital. Human capital has a rental rate (the wage) and it has a price in the form of the cost of education or any other attempts by people to increase the productivity of their labour, and the interest rate plays just as much a role in the price of human capital as it does in non-human capital.

    It makes just as much sense to say that r is rate at which the capitalist's assets appreciate as to say that r is the rate at which a person's human capital appreciates. Given this, I don't see how the value of the interest rate can affect how aggregate income is distributed between capital and labour.

    Am I missing something? Given that I've seen nobody make this point I'm thinking there may be some mistake in my argument.

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