Thursday, August 23, 2012

Nick Rowe on Reswitching and the Capital Debates

Nick Rowe gives a shot to the capital debates, which is a nice development indeed. [Robert Vienneau has a lenghty reply here.] In spite of the importance of the topic, and the previous engaging of mainstream economists like Samuelson, Solow – to cite two prominent ones – the topic has all but vanished from modern mainstream economics, with a consequent loss of understanding.

Let me clarify a few things before we get to Nick’s post. As I argued in a previous post, classical authors (e.g. Smith, Ricardo and Marx) understood that they needed to determine the rate of profit independently from relative prices to avoid circular reasoning. The Labor Theory of Value (LTV) provided a solution. Prices were determined by labor incorporated (or commanded for Smith) and profits, and the surplus, were determined on that basis [Sraffa’s solution to the problems with the LTV build on Ricardo’s use of a commodity, corn, to measure the profit rate as a ratio of two physical quantities]. However, most neoclassical/marginalist authors today are completely oblivious to the fact that their theory too must deal with the independent determination of the rate of profit and relative prices, and that this is problematic if you also accept the notion of a uniform rate of profit (a natural rate of interest).

Also, and before I show why the problem is a general one, that any theory has to deal with it is essential to note that the rate of profit and the rate of interest must be in the proverbial long run (when everything is flexible and there is no ceteris paribus) in equilibrium. That is, either the rate of interest adjusts to the rate of profit (the position taken by Ricardo and Wicksell, which called the real variable the natural rate of interest), or vice versa (as Tooke and Sraffa believed; Marx and Keynes pose more problems to be clearly defined, but I would put them in this camp too).

In the case of neoclassical economics, if you want to determine the natural rate of interest by the interaction of the discounted profitability of investment and the intertemporal savings (i.e. consumption) decisions of agents, you must be able to bring the gains to present value (as in the examples provided by Nick). That means that the discount rate (to bring the investment schedule to present value) must be known, while the rate of interest you want to determine requires knowing the value of investment (the demand for capital goods). Thus, we encounter the circularity of the determination of the natural rate of interest in the Loanable Funds Theory, noted by Joan Robinson long ago.

Note also that the process implies that the rate of interest (which in equilibrium is equal to the rate of profit) is a variable that is determined by intertemporal decisions, which must equalize the rate of profit associated with the production of capital goods (i.e. produced means of production). What happens if, as Nick suggests, “There isn’t just one future period; there are many future periods.” Nothing much really happens, since for all those possible future periods, there must be a uniform rate of profit. For several different capital endowments, or several different sets of preferences (which seems to be what Nick has in mind), the interaction of investment and savings will solve for the rate of interest. But the inconsistency is still there.

But really what Nick is suggesting is that one might have a multitude of interest rates (which he refers to as the term structure, but think more of a term structure of interest rates associated with different capital goods, rather than financial ones, even if you do have monetary rates too). In fact, that is exactly what the mainstream did, when they changed the notion of equilibrium, as noted by Garegnani in his 1976 paper. It was only then, after the capital debates, that the Arrow-Debreu (AD; not Anno Domini) intertemporal general equilibrium notion became dominant. In that case you must give up the notion of a uniform rate of profit. Note that you cannot have both (in his replies to my comments Nick seems to believe that you can have it both ways; scroll down for the various comments which are worth reading I might add).

Nick says:
“I hadn't realised, until I read your comment just now, that *maybe*, when some people talk about “uniform rate of profit”, they mean something very different to what I thought they meant. I thought they meant: A uniform rate of profit across different industries (adjusting for or ignoring risk). But you seem to mean: A uniform rate of profit across different periods of time (i.e. a flat term structure). I would say that arbitrage is what creates a uniform rate of profit across different industries (or different assets). I would say that *nothing* creates a uniform rate of profit across different periods of time. The term structure is not (in general) flat. It could slope either up or down, or wiggle around. Even if we are talking about Wicksellian “natural” rates of interest. E.g., if everyone wants to go on a big consumption binge every 7 years, and fast for the remaining 6 years, (and if everyone knows about this), we are in general going to see a big spike in the term structure at 7 year terms.”

So let me clarify what I mean. Capital goods, the produced means of production, are an heterogeneous set of goods, but if one believes in competition (in the classical sense of free entry) then one must believe that a uniform rate of profit on the supply price of those goods will be established (not as a real world phenomena, but as a tendency; the long run is a theoretical construct). So what is established by free entry (and not arbitrage, which would be associated with the equalization of prices in an exchange economy) is a uniform rate of profit across sectors.

So what does that mean about the term structure? First, the term structure of monetary rates (i.e. the Fed Funds versus the ten year Treasury bonds) depends on the actions of the central bank, among other things (and I’ll let that for another post; mind you as you see I tend to think the monetary rates rule the roost, as Tooke and Sraffa). Nick is talking about the real or natural rate, having for reasons associated with the demand (the preferences about consumption in the future) different levels. That is, there would be more than one natural rate, associated with different preferences regarding consumption [echoes of the Sraffa-Hayek debate about the existence of several own rates of interest perhaps].

Yet, the point still is whether you have competition (free entry) or not. So if more people, as in Nick’s example, want to consume more in 7 years, wouldn’t the supply of capital adjust, to provide more in that year allowing for the consumption binge, and reduce the gains associated with providing more goods in that period? After all there is no reason for profitable opportunities, unless there are imperfections (e.g. lack of capital mobility or lack of information, which does not seem to be what Nick is arguing, since he says that "everybody knows"), to be left unfulfilled. The intertemporal nature of the decisions, meaning the decisions are being made now with all the information available about the future, does not affect the equalization of the rate of profit (interest). So competition should also lead to a uniform rate of profit not across different periods of time, but now for different states of preferences and the capital endowments (and technology of course).

Hence, the existence of a myriad of capital goods, or changing preferences (or technological change, which used to be the one that the capital debates concentrated more), do not per se justify abandoning the notion of a long term uniform rate of profit. That is what the AD model does. In the process it abandons the classical notion of competition (free entry) for one that has less meaning from the point of view of understanding capitalism (atomistic agents that are price takers; both links to the New Palgrave require subscription I'm afraid).

Note that the centrality of the results of the capital debates is that one cannot say that changes in relative prices govern decisions about the allocation of resources in any clear way. Not only capital will not be used more intensively with lower rates of interest (even if lower rates of interest may stimulate other forms of demand, not capital, and eventually lead to more demand for means of production), but also lower real wages (the relative price of labor force) might not lead to higher employment. Think of the policy implications of this result for Europe now.

But let me finish saying that beyond the differences we might have, real or of interpretation (and I think both things play a role), I think it is important to thank Nick for thinking about the relevance of these issues and taking them seriously, which can only lead to clarify differences and provide a better understanding, if not of the real world, about what economists think about the real world. And that is a step in the right direction.

22 comments:

  1. Matias: Thanks!

    "So let me clarify what I mean. Capital goods, the produced means of production, are an heterogeneous set of goods, but if one believes in competition (in the classical sense of free entry) then one must believe that a uniform rate of profit on the supply price of those goods will be established (not as a real world phenomena, but as a tendency; the long run is a theoretical construct)."

    Aha! And that does clarify it some more for me. (BTW, many neoclassical economists would not understand your terminology of "demand price" and "supply price", which harks back to Marshall(?), so you can see where lots of miscommunications arise.)

    Example: houses and golf courses are two capital goods.
    Arbitrage adjusts the relative demand prices of the two assets so that they yield "the" same rate of return. (Notice I just slid the whole term structure question under the rug by talking about "the" rate of return, as though it were a single number.)

    What ensures the demand prices equal the supply prices? Two main forces (there may be others I have missed):

    1. The supply price is the MC of producing an extra new house or new golf course. The relative supply price is the Marginal Rate of Transformation between new houses and new golf courses (the slope of the PPF with "new houses" on one axis and "new golf courses" on the other axis). Since some resources have a comparative advantage in producing houses, and others have a CA in golf courses (a continuum of differentiated labour, land, machines) that PPF will not be a straight line. It will be curved. Which is another way of saying that the two MC curves slope up. As relatively more houses and fewer golf courses are built, the MC of a new house rises relative to the MC of a new gold course.

    2. Preferences for housing services vs golf course services. The Indifference curve between those two services is not a straight line. Their demand curves slope down. If people see a bigger flow of new houses being built, and fewer new golf courses, that will change the time paths of future stock supplies, which will change the time paths of future rents on those two assets, which changes the NPV of those two streams of rents, which changes the two demand prices.

    As long as prices (of houses and golf courses) are not sticky we will see MC(new house)= P(new house) = ExpectedNPV of rents of new house at all times, not just in steady state. Same for golf courses. So the rates of return (ignoring term-structure) *at the margin* (Marginal Cost) will be equal across the two industries. Relative production of the two assets is what adjusts to equalise them (unless we hit a corner solution with zero production of one or the other).

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    1. Yes, but then we have a uniform rate of interest (profits). In that case you have the problem, admited by Samuelson (1966), that there is no reason to believe that relative scarcities actually regulate prices, and substitution may go the 'wrong' way.

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    2. Matias: You lost me here, I'm afraid.

      I've explained how I think rates of return get equalised across sectors. (And if they don't get equalised by those two things I mentioned, then we get a corner solution where investment drops to zero in one sector, of course).

      As far as i can see, we should still get the standard result that the Marginal Rate of Transformation between houses and golf courses equals the relative prices of houses to golf courses equals the Marginal Rate of Substitution between houses and golf courses. The only thing that's new is that a house is a bundle of dated places to sleep, and a golf course is a bundle of dated places to play a round of golf, so the MRS calculation has to do the sum of the Marginal Utilities of all the many many dated goods in each bundle.

      I really can't see why relative prices can't be said to reflect relative scarcities to any greater or lesser extent than they do in the simple example where there is only 1 time period. It's just demand and supply, except the demand is for a bundle of dated goods. But a sheep is also a bundle of wool and meat, and that's no reason we can't talk about the demand for sheep.

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    3. I don't understand the need to refer to arbitrage that much at all. We can put it in much simpler terms: if the profit rate is greater for housing than for golf courses across time and space, then more entrepreneurs will enter the housing market than are entering the golf course market in search of the higher profit rate. Thus, more resources/capital will be channeled into housing up until the point where the profit rate between the two industries is equalised.

      Pretty simple. As far as scarcities etc. go, this is a side issue. We're talking about the rate of profit, nothing more.

      Side note: Yes, I think Matias is using Marshallian terminology rather than Walrasian terminology. Post-Keynesians and Neo-Ricardians tend to come from this tradition which they see as more pragmatic.

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    4. Brief reply and clarifications. Again nothing you said in this reply changes the fact that with there is, with free entry, a tendency to a uniform rate of profit. If the profits in the housing sector are bigger than in the golf course sector (for whatever reason, higher preferences for houses, or lower costs of production of houses), more capital pours in and the profit is brought down in the housing sector. As pointed by the Illusionist. AD refers to Arrow-Debreu, a model that simply assumes away the idea of capital moving from one sector to the other. Assuming the problem away is not a solution.

      On the production function, you miss the point. You can always measure productivity of labor, and TFP should be abandoned, which is the only place that a production function is uses by empirical macroeconomists. See my post and papers on Okun's Law. Also, I don't see how one can justify to use an incorrect model, since it is the only alternative (which is not the case anyway).

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    5. The Illusionist: "I don't understand the need to refer to arbitrage that much at all."

      Suppose good land rents at $100 per acre and bad land rents at $50 per acre. What ensures that the price of an acre of good land is double the price of an acre of bad land? Suppose one house rents at $10,000 per year and a second house rents at $5,000 per year. What ensures that the price of the first house is double the price of the second? Suppose a golf course rents at $100,000 per year and a house rents at $10,000 per year. What ensures the price of the golf course will be 10 times the price of a house?

      "Arbitrage", in all three cases. Even if you can't build new land (you can't, of course). Even if it were impossible to build new houses or golf courses. Arbitrage also ensures *the* rate of returns from buying an old house or old golf course equals that of a new house or gold course. You can't build an old house or old golf course.

      Time preference, and arbitrage, determine the prices of all existing assets (land, real capital, financial, old and new) given expectations of the time-paths of future rents. Then the supply curves of production of a flow of new assets determine the flows of new investment in those assets at which the MC=Price condition will hold. (And people's expectations of future rents should also depend on their expectations of the time-paths of future production of new assets.)

      "Thus, more resources/capital will be channeled into housing up until the point where the profit rate between the two industries is equalised."

      But you need to talk about upward-sloping supply curves (marginal cost curves) of producing new houses and golf courses, and/or downward-sloping demand curves for the services of houses and golf courses in order to explain how those profit rates get equalised. Otherwise you get a corner solution. Sraffa doesn't do that. And it only gets equalised *at the margin*, so you need to talk about *marginal* cost. Ditto.



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    6. Matias: "Again nothing you said in this reply changes the fact that with there is, with free entry, a tendency to a uniform rate of profit."

      Of course. But across sectors, not across time, and at the margin, not on average (unless the MC curves are flat).

      "...more capital pours in and the profit is brought down in the housing sector."

      More labour pours in, more land pours in, and more machines pour in, to producing new houses, yes. (And they all pour out of producing new golf courses). But more "capital" pours in? Let's just say that there are customers who want to buy the newly-produced houses.

      "AD refers to Arrow-Debreu, a model that simply assumes away the idea of capital moving from one sector to the other."

      I'm really not following you there. That seems wrong to me. Take a very simple AD model. 2 time periods, and 2 goods, so it has 4 dimensions. There is a 4 dimensional Production Possibilities Frontier. In common language, there are two sectors, and investment in each of those two sectors. And (unless the PPF is a weird kinked shape) resources will be allocated across all of those 4 dimensions to the point on the PPF where the 4 dimensional price vector is tangent to the PPF (and the price vector is also tangent to the Indifference curves). It's exactly like the simple Irving Fisher diagram, only with 2 more dimensions because there are 2 different goods as well as 2 time periods.

      My verbal discussion above is just one way of talking about just such an AD model. I didn't invent my verbal discussion above. It's just one way of talking about standard neoclassical theory. But yes, the AD model is very abstract, and it really does invite the question: "What the **** is really going on inside that model?" And if you take the AD model, assume there's no land, and only 1 type of labour, and constant returns Leontief technology, so the PPF becomes a straight line in some dimensions and kinked in other dimensions....you get a Neo-Ricardian model. And if you forget to include preferences in that model (in particular, if you forget to include preferences with respect to the timing of consumption), you will find that the rate of interest is indeterminate. Just like Neo-Ricardian models.

      "You can always measure productivity of labor, and TFP should be abandoned,..."

      Hang on. There's land too.

      Plus, suppose 1 unit of labour used to be able to produce 1 unit of output in 2 years' time. Then a new invention means 1 unit of labour can produce 1 unit of output in 1 year's time. That's different from a new invention that means 1 unit of labour can produce 2 units of output in 2 years' time. And that difference matters, because people care about *when* they get to consume, not just how much they consume. If they didn't care about when they consumed stuff, all real interest rates would be 0%.

      Preferences matter for the theory of capital and interest. If everybody joined a doomsday cult, and stopped caring about the future, the prices of all assets (except those that can be consumed now) would drop to zero, and all interest rates would become infinite, and investment would go to minus infinity (or as far as it could go in that direction). Arrow Debreu includes preferences. Neo-Ricardians want to talk about capital and interest without talking about preferences. It can't be done, as this "doomsday cult" example shows.

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    7. "Suppose good land rents at $100 per acre and bad land rents at $50 per acre. What ensures that the price of an acre of good land is double the price of an acre of bad land?"

      Eh, supply and demand. Consumers and investors hold preferences regarding which land they wish to rent. If one plot of land is unproductive/ugly/whatever there will be less demand for it and the price will be driven down. You don't need arbitrage to explain this phenomenon. Arbitrage is a secondary phenomenon.

      Actually, I used to work in the housing market and I saw this process take place at close proximity. Arbitrage plays almost no role. Prices for land and houses are given on an almost weekly basis in the newspapers. Estate agents familiarise themselves with these prices. Sellers then approach estate agents. These agents are incentivised to get as high a price as possible (because they're operating on a percentage basis) without trying to price gouge (because this would mean that they were stuck with the house for a longer period and they would get less money in terms of work put in). Buyers then approach the estate agents and place bids on the house/land which are passed onto the sellers who decide, based on readily available information, whether they would like to accept the bid or hold out for a better one. If they reject the bid and are stuck with the house/land for a long time, they might approach the bidder and offer the house/land at the old bid price.

      No arbitrage needed. The economists just make that up. Arbitrage does take place in markets like those for used cars and a few other markets (some online sellers on eBay, as well as in financial markets) but, as I already said, its generally a secondary phenomenon. Supply and demand -- or cost-plus monopoly pricing -- are generally the rule of the jungle.

      "Time preference, and arbitrage, determine the prices of all existing assets (land, real capital, financial, old and new) given expectations of the time-paths of future rents."

      This simply is not true. Anyone remotely familiar with the markets you give as examples could confirm this. This is abstraction for the sake of abstraction.

      "But you need to talk about upward-sloping supply curves (marginal cost curves) of producing new houses and golf courses, and/or downward-sloping demand curves for the services of houses and golf courses in order to explain how those profit rates get equalised."

      You can put it that way if you want, but its all the same thing. If the supply-curve and the demand-curve meet at a point for housing that make it more profitable -- note that I say: more profitable; we're not talking nominal price here, but the spread between cost and revenue -- than golf courses, entrepreneurs will take advantage of this discrepancy by building more houses. This is about investment decisions, not about arbitrage.

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    8. "Matias: "Again nothing you said in this reply changes the fact that with there is, with free entry, a tendency to a uniform rate of profit."

      Of course. But across sectors, not across time..."

      According to the neoclassical theory the rate of profit should become uniform across both sectors (i.e. space) and time. This is because the neoclassical theory assumes that the profit rate is set by the interaction of the marginal product of capital and the marginal product of labour. If we assume that the rates of profit are the same across all industries and that one capitalist tries to raise their profit rate by giving the worker a lower amount of compensation, the worker is then assumed to remove their labour from that industry and move it to an industry that compensates the worker in according with the marginal product of labour -- or the worker will opt out of the market altogether as they will find that the lower wage offered means that they will find greater "utility" in leisure, thus the capitalists will be unable to find willing workers at the new wage rate being offered and they will be forced to offer a higher wage rate so that the original situation reestablishes itself.

      Competition is thus assumed to (a) ensure that one sector does not have a higher rate of profit than other sectors and (b) that a worker is able to always obtain their marginal contribution by removing their labour if compensation in line with the marginal product is not being offered.

      While I hate the neoclassical terminology, I believe you guys refer to this as the firm aligning marginal revenue with marginal cost. Given competition, in order for firms to drive up the rate of profit over time they would have to try to increase the spread between marginal revenue and marginal cost. But this would not be allowed to continue for any amount of time because the worker would not tolerate being paid less than their marginal product.

      From the Wiki page:

      "This vision produces a core proposition in textbook neoclassical economics, i.e., that the income earned by each "factor of production" (essentially, labor and "capital") is equal to its marginal product. Thus, with perfect product and input markets, the wage (divided by the price of the product) is alleged to equal the marginal physical product of labor. More importantly for the discussion here, the rate of profit (sometimes confused with the rate of interest, i.e., the cost of borrowing funds) is supposed to equal the marginal physical product of capital. (For simplicity, abbreviate "capital goods" as "capital.") A second core proposition is that a change in the price of a factor of production will lead to a change in the use of that factor – a fall in the rate of profit (associated with rising wages) will lead to more of that factor being used in production. The law of diminishing marginal returns implies that greater use of this input will imply a lower marginal product, all else equal: since a firm is getting less from adding a unit of capital goods than is received from the previous one, the rate of profit must fall to encourage the employment of that extra unit, assuming profit maximization."

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    9. TheIllusionist @9.15: You are confusing asset prices with asset rents.

      @9.43am: That Wiki page is just plain wrong, unless we are talking about a model with only one good. "More importantly for the discussion here, the rate of profit (sometimes confused with the rate of interest, i.e., the cost of borrowing funds) is supposed to equal the marginal physical product of capital."

      That statement doesn't even get the units right. Rates of interest have the units 1/time. The Marginal Physical Product of Capital has the units tons of wheat per year per tractor (or whatever).

      It is a gross caricature of neoclassical economics to say it assumes only one output good. (Only very simplified macro-models make that assumption). In my discussion above I have assumed 4 different goods: houses; golf courses; the services of houses; the services of golf courses.

      If you are getting your understanding of neoclassical theory of capital and interest from a Wiki page on the Cambridge Capital controversy discussing a one-good model, well, let's just say you won't understand it very well.

      Better let Matias respond.



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    10. (1) Nick, the rental market for housing and land is largely the same as the the market for housing and land as assets. Arbitrage doesn't play a huge role. I've seen this first hand. The reason I referred to asset prices is that this is how people purchase the properties in order to then rent them or whatever. This is how the "capital" is acquired.

      As far as the rental market itself goes, it's very similar and involves shopping around and haggling with landowners (i.e. supply and demand). You can also go through an estate agent -- especially in the case of land, which is the way this is typically done -- but you'll be charged a fee.

      There is, of course, investors who buy up land that is lying fallow in order to "flip" it, but as I said, this is a secondary phenomenon. Generally speaking, arbitrage is a secondary phenomenon within housing and land markets.

      If you want to talk about arbitrage without being woolly, you're going to have to give some concrete examples. I don't accept that because some model somewhere says that arbitrage is important in the rental market for land/housing that this is suddenly so. That's mysticism.

      (2) I'm sure Matias will respond too, but you're not dealing with the point I'm raising. I quoted the Wiki page to show why what I said was important -- but what I said is not on the Wiki page.

      My point was about how the neoclassical theory assumes that if capitalists try to increase their rate of profit by decreasing the amount they pay to labour, the theory states that the amount of labour supplied will fall. Since we've already agreed that the rate of profit will equalise across sectors, this ensures that it will equalise through time as well because "greedy" capitalists will be unable to find any labour below the going supply price, while "generous" capitalists will be out-competed by their peers who will pay only the minimal price asked.

      Eventually, if my understanding is correct, profits will fall to cost (zero) if technological innovation is not forthcoming. However, if we take account of the going rate of interest we must assume that firms will not continue to produce at a rate of profit below this rate of interest and so profits will never fall to zero. They will, however, "gravitate" toward the interest rate over time.

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  2. You know that "Neoclassical" model which assumes technology is given by C+I=F(L,K) (where I = dK/dt).

    The big problem with that model is that it assumes a perfectly elastic supply curve of newly-produced capital goods. (The PPF between I and C is a straight line, with a slope of -1. The MC curve is horizontal, with I on the horizontal axis and Pk/Pc on the vertical. Intertemporal preferences don't affect Pk/Pc given the stock K, and don't affect the rate of interest given the stock K. The IS curve is horizontal. Etc.)

    That model is not *the* neoclassical model. It is a very special case of the neoclassical model. It's what caused all (most?) of the trouble.

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    1. Of course not. However, the essential properties, related to substitution between factors of production are all there. And the AD, which actually says nothing about substitution, does not have a uniform rate of profit. Note also in this regard, that serious neoclassical authors like Franklin Fisher have been very critical of the aggregate neoclassical model. One of the results, which was developed by Fisher student (Jesús Felipe) is that TFP does not measure productivity, but incredibly it is still used by everybody. See this paper by Fisher and Felipe http://riscd2.eco.ub.es/~josepgon/documents/Felipe_Fisher.pdf. This is the sort of serious heterodox critique that the maintream should take into consideration.

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    2. Matias: "And the AD, which actually says nothing about substitution, does not have a uniform rate of profit."

      Yes it does, in the sense in which there is a "uniform rate of profit" (ie.e at the margin.)

      Because:

      1. The "no arbitrage" condition is built right into the model when it picks a particular numeraire, so all the "cross prices" have to be mutually consistent.

      2. Profit-maximisation plus competition yield the "Marginal rate of transformation = relative prices" condition, not only across 2 goods in one time period, but across different goods in different times periods.

      If you put 1 and 2 together, that is exactly the same as equalisation of profit rates across sectors *at the margin*.

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    3. Again arbitrage is about exchange economies (like in financial assets). What you need for a uniform rate of profit of produced means of production is free entry.

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  3. "And the AD,..."

    What's the AD? Aggregate Demand??

    I basically agree here. Production functions should reflect what the engineers know, not what the accountants know.

    Simple example: assume land produces wheat (no labour, no capital), the stock of land is fixed, and technology never changes. Suppose preferences changes, so that people became more patient, so interest rates fell. The price of land would rise relative to the price of wheat. If we measured land productivity as the tons of wheat divided by the *value* of land, productivity would (appear to) fall.

    Trouble is, you can tell econometricians this until you are blue in the face, but they won't pay any attention, unless you can show them a better way that's also practically feasible. (I don't know if there is a better way that's also *practical* so the data actually exist; not my area.)

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  4. In fact, it is Sraffa, and the Neo-Ricardians, who fail to provide an explanation of how profit rates get equalised across sectors. There is absolutely nothing in Sraffa and the Neo-Ricardians that rules out a corner solution in which only one sector exists, and all other sectors don't exist because they would be less profitable than the one sector that does exist. You need downward-sloping demand curves and/or upward-sloping supply curves to explain why (say) wheat isn't the only good produced and consumed.

    Take a very simple Neo-Ricardian model: one unit of labour produces one apple next year. One unit of labour produces two bananas next year. Assume apples and bananas are perfect substitutes (U = A+B). Assume all labour is identical (nobody has a comparative advantage in growing apples or growing bananas). Indifference "curves" are straight lines. The PPF and Isocost "curves" are straight lines. We get a corner solution in which only bananas are produced. The rate of profit in producing apples never equalises.

    You must talk about curved preferences and/or curved PPFs (with more than 1 type of labour or land) if you want to explain how profit rates get equalised across sectors. And those are precisely the things ignored by Neo-Ricardian models.

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    1. The neo-Ricardian critique abstracts away from preferences. This is the same as when you mentioned scarcity above (here you're assuming that bananas are, in a sense, more scarce -- i.e. they are harder to "get at" and require more labour inputs). This has nothing to do with the production theory that Sraffa et al were critiquing. Sraffa and the neoclassicals both assumed that preferences were fixed and so scarcer goods (bananas) that could be perfectly substituted for less scare goods (apples) were not produced.

      Frankly, I'm very surprised that you would think that the likes of Solow and Samuelson would have engaged with the argument in such a sustained manner if the critique had been as simple as the above.

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    2. Samuelson and Solow were defending their own theory from a Neo-Ricardian attack. I am now going on the offensive, and attacking the weak points in Neo-Ricardian theory. What they said or didn't say is irrelevant to my argument.

      "Sraffa and the neoclassicals both assumed that preferences were fixed..."

      Preferences can be assumed "fixed" in many very different ways. U=A+B is one way. U=min{A,B} is another way. U=A.B is a third way. And so on. And they all have very different implications. Neoclassical theory discusses the implications of different preferences for: prices; rates of interest; quantities; marginal products; etc.

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    3. I understand that. But I don't think this has much to do with the capital debates. And I think this is why this aspect was little focused on.

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    4. Gravitation towards equilibrium prices does not require demand functions. It requires something about excess demand points. Sraffa was very critical of the need to impose functional relations where non are necessary. There is an extensive literature on gravitation, and, in contrast with neoclassical models, they have no problem in showing existence, unicity, and stability.

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  5. "The Labor Theory of Value (LTV) provided a solution. Prices were determined by labor incorporated (or commanded for Smith) and profits, and the surplus, were determined on that basis"

    It was my understanding that the LTV defined "price" as being determined by the market. "Value" was defined as the technologically necessary cost of production (including normal profits), usually in terms of labour hours or energy/worker/hr, etc.. The difference between "value" & "price" was called Economic Rent, price with no corresponding cost of production, but instead due to some natural or legal privilege

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