Congratulations for your blog an for this lively debate. I´m not an economist yet reading Mr Rallo criticism of what he calls "neoricardian theory of value" I found this comment of him quite remarkable (sorry if my translation is somewhat poor, english is not my native language):
"It´s true any Price theory has to be able to explain the tendency of convergence of prices towards fragile market equilibriums, but the theory can not pass over the fact that those equilibriums, as the forces that are dragging prices towards them, are fragile because of the subjectivity of economics agents.
That will be tantamount to say Jack the Ripper did not kill his victims: it was the victims were ripped as a consequence of the relative spatial position of his necks and abdomens with the murdering knives.
It is the subjectivity of consumer preferences what determines the relative proportions of the goods to be provided, and it´s the subjectivity of the entrepreneurial expectations and calculus what set up productive plans directed to met the consumer preferences.
This does not mean, by the way, that objective circumstances do not play a role in individual subjectivity (human beings prefer to eat by physiological reasons; and the entrepreneurs can not implement physically impossible business plans) but that objective circumstances does not determine individual subjectivity in a way anybody can know."
So I am amazed. From a myriad of "individual degrees of utility" and time preferences for compsumption or absention thereof, there are relatively stable prices along significant periods of time.
And secondly, he seems to me to be claiming that if "objective circumstances" does not determine "individual subjectivity" in a way anybody can know (not even approximately) certalnly apart from entrepreneurs having magical qualities, I fail to see how can not you take into account that your workers have to eat, that a certain amount of nutritive substances is unfortunately indispensable and that you may know it. Or it is not the point, precisely that "objetive circumstances" have a decisive role in "subjectivity"?
No, I do not think it is the essence (perhaps it was a bit unfail to quote that concrete passage) nevertheless, I believe he considers the Sraffian critique a theoretical mean to "resurrect" objetive theories of value, as it can be inferred from this concrete passage. He thinks it can not be so.
"(...) Anyway and by way of conclusion, the key to Sraffa Theory of Valie is that demands has no role on the determination of the relative prices of commodities: nor the relative demand of present goods, nor the demand of present goods over future goods (temporal preference) What´s more, prices are not determined in the margin (between the consumer and the marginal producer) but are the result of relative prices between total output of production.
All objective theories of value are easily embodied in the Sraffian framework (including the marxist one, as Sraffa himself sought to reduce all cost to homogenuous quantities of labour) where are supply conditions what determines prices: commodities that produce commodities regardless of subjective marginal utility)
(...)
Criticism of the sraffian model.
My goal is to show that the two basic tenets of Sraffa are wrong:
-Demand of non basic goods does not play a role in price determination and
-The temporal preference, as it is assumed equal to 0% does not play a role in the determination of prices and productive techniques".
So, ¿do you think this is not an accurate representation of Sraffa position or intentions in POCBMOC?
I hold to subjective theories of value -- but not marginal theories -- and I think the Sraffa critique is correct. There is a quote from Sraffa which shows that he thought likewise -- I think Rob Vienneau had it on his blog at some point.
While you can use the Sraffa critique to resurrect objective theories of value, this is not necessary at all. Sraffa is critiquing marginalism, not subjective value theory as such. The problem is that marginalists and Austrians think that marginalism is the only subjective theory of value. It is not:
"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." -- Piero Sraffa (1964). Letter to Arun Bose, in (2)
It is not that Sraffa does not consider demand at all, but that he just assings it a secondary role in determinaning the equilibrium amounts of goods produced. But:
1) He distinguishes between basic and non basic goods, claiming that non basic goods do no determine relative prices (false). That would only be true under the false assumption of universal constant returns to scale. 2) He assumes zero cost of capital (false) in his theory of interest. 3) He does not considere the role of subjective calculations of entrepreneurs to determine production structures and, even inside his system, price relationships. Those subjective calculations, by the way, are moved by the marginal entrepreneur and the marginal consumer, and thus you cannot skip their crucial function inside the price system. 4) His theory is not useful to explain price changes (marginal changes). It is a theory of final rest, so that it is not useful to describe and understand desequilibria and price changes.
I can only respond to what I'm being given in English and so far your criticisms are both shallow and long familiar to anyone who has engaged even superficially with the debates.
I cannot speak to (1) and (2) because I haven't read the original piece and your comments here are are too short.
3) You can easily insert entrepreneur's into Sraffa's framework. It seems that your main criticism here is that Sraffa's framework is not COMPLETE. I think that everyone can agree on that. The framework can also, I should say, be completed or closed in many different ways.
4) Perhaps it his immediate framework is not useful to examine this. But this does not mean that it is incompatible. That is like saying that because marginalism often uses static analysis to explain price that they cannot deal with the transition of one price to another. Again, what you seem to be complaining about is the COMPLETENESS of his framework. I'm sure there are many Sraffian authors that deal with disequilibria and price changes.
At the end of the day I don't care much for Sraffian analysis. I find it too abstract and in many ways too like the thought-experiment nonsense that characterises Austrian and neoclassical theory. But his criticisms of marginalism stand pretty strong today so far as I can see. And they have pretty damning consequences for any theory that relies on a general equilibrium that relies on the interest rate -- which is what we're really discussing here.
3) You cannot insert the entrepreneur, because the entrepreneur is an element of change and desequilibrium (Schumpeterian creative destruction) while Sraffa's model is one of final rest and stable equilibrium. 4) I do not say that all his framework is incompatible with change. What I say is that his framework is just a very special case (whit lots of restrictive and unrealistic assumptions) of the much richer Austrian value and price analysis. Why do you need a theory that cannot explain change while you have another that can explain change and rest while encompassing the previous one? 5) His theory of interest assumes no time preference and no risk aversion (i.e. no cost of capital). Therefore, it could be a nice critique of marginal productivity theories of interest, but not of time preference ones. He goes as far as assuming that there is no advances of capital to factors of production, which is equivalent to say that capitalists play no role in the economy (once you assume that, it obviously follows that interest rates are arbitrary charges on aggregate income).
1) Yeah you can. Just knock the system out of equilibrium. Or posit equilibrium as a long-run gravitational condition that is never realised (as most Sraffians do). Again, I'm not a big fan of the Sraffian approach. But your criticisms are pretty bland.
2) Yes, I had that impression from the beginning. I didn't think your criticisms of Sraffa would be much more than "Austrian theory is better than Sraffa".
3) No, you're forgetting where this all started. I brought up Sraffa because his critiques of the marginalist theory of distribution and reswitching render any theory that allows a general equilibrium to be generated through interest rate price adjustment incoherent. You then pointed to your Spanish "critique" of Sraffa as proof that he was wrong or something. But now we know (point 2) that your critique had nothing to do with the point we were discussing at all.
I think you need to go and read up on the capital controversies in depth and reevaluate your business cycle theories in light of these. That's what I've been saying from the beginning. And I've (predictably) gotten nowhere.
1) The point is that the behaviour of entrepreneurs influences the final equilibrium position. It is not aimed to discover something which is given, but to create something that may not exist. Not to say that entrepreneurs' errors also influence the equilibrium position. How to explain decisions outside equilibrium assuming a passive tendency toward equilibrium? 2) You should read my criticism before judging it. What I say is that making unrealistic assumptions does not lead you to a clear description and understanding of price and value theory, and that you can understand Sraffian oversimplifications inside a more complete framework. 3) Sraffa's criticisms are based on a productivity theory of interest. It does not apply to marginal time preference theories. Reswitching leaves outside the picture that the function of interest rates is not to determine the shape of the structure of capital (for each level of interest, one degree of capital intensitivity), but to coordinate savers and inverstors and remunerate the formers for their provision of capital (of time and risk) to undertake the entrepreneurial activity. Once you understand that each level of interest is fully complatible (in equilibrium) with any profile and intensivity of capital structure (due to factors affecting supply and demand of capital), reswitching becomes unimportant: http://ead.univ-angers.fr/~granem08/IMG/pdf/DT-GRANEM-09-34.pdf It is just relevant for oversimplistic neoclassical capital and interest theories.
1) This is not a problem. You say that entrepreneurs disturb the equilibrium temporarily but then, as their insights are absorbed by other entrepreneurs and competition takes place, the original innovator's excess profits are eroded and the system tends back toward equilibrium (while never quite reaching it as more entrepreneurs innovate and disturb the equilibrium once more). This is the "gravitation" argument employed by most Sraffians.
2) This still looks to me like "my price/value theory is better than your price/value theory". I do not think that you have found any inconsistencies in Sraffa which is what you hinted at originally.
3) That means that Austrians cannot say that the capitalist economies distribute resources optimally. The neoclassical theory does this by saying that the rate of interest distributes resource usage between capital and labour to maximise both input's marginal productivity. From what you're saying the Austrian argument cannot do this. So markets would not necessarily distribute resources optimally. That raises an awful lot of questions indeed. In fact, it strikes me that the Austrian theory -- if it is as you present it here -- really has no basis to justify distribution of income without reference to past distribution of income.
Note: That last point might be worth looking into by people who are more familiar with Austrian capital theory than I am. It strikes me that JRR's theories may be idiosyncratic but if they are popular then it may mean that income distribution in such theories is arbitrary. That could be VERY damaging for the normative proclamations of such theories. Follow my thread and you might do a lot of damage to these theories. Frankly, I'm just not that interested.
I've been thinking about this. Will someone PLEASE look into this? LK? This is enormously important. If Austrian theory is not based on a marginal productivity argument then it cannot say anything about... well, anything.
It cannot, for example, say that wages are set at their optimal level by the market. Thus they cannot make a case against the minimum wage or unions.
If this is true I'll fall out of my chair. It would be hilarious if the Austrian shills were all attacking the minimum wage based on a theory that cannot argue that the market sets the wage at the optimal level!
All Austrian analysis I have seen assumes the marginal revenue productivity theory of wages, either as (1) a real world condition or (2) an state which the real world sometimes deviates from but is more or less still the essence of how wages are set.
Then LRR's theories are indeed idiosyncratic and he evades the reswitching critique by dropping his theory of distribution. Oh well. His theory is bunkum anyway.
1) That's is not what I am saying. Sraffa assumes solely one position of final equilibrium which does not depend on entrepreneurs decisions. But that is not true. Entrepreneurs change final gravitation equilibrium not only when they are correct (in which case, you may say that they are only anticipating that final gravitation point) but also when they fail (they change what the final gravitation point will be). 2) To say that prices depend on relative produced quantities once reached the equilibrium is only a truism without any scientific value. Once Sraffa tries to extract some theoretical implications from that truism, he needs to take for granted absolutely unrealistic assumptions, such as constant returns to scale or zero cost of capital. That is not a valid value and price theory. 3) You should look at Böhm-Bawerk, Fetter or Fisher interest theories. Those are not marginal productivity theories of interest. The process is quite different to the one you and all marginal productivity of capital school assume: capitalists' competition push up the present value of factors of production according to their expected future value; but present value is not increased up to its full future value, because present goods are more valuable than future goods. At the end, workers' income tend to coincide with their discounted marginal productivity (but not necessarily, since there may be very stable moats and competitive advantages), but this is not because capitalists take their share of total product according to their productivity, but because they are not willing to advance more capital in the present to anticipate the income that they will get back in the future. As Böhm-Bawerk said: "The completely just proposition that the worker is to receive the entire value of his product can be reasonably interpreted to mean either that he is to receive the full present value of his product now or that he is to get the entire future value in the future. But Rodbertus and the socialists interpret it to mean that the worker is to receive the entire future value of his product now". If time preference and risk aversion of capitalist were zero, workers would tend to earn their undiscounted marginal productivity (i.e their full future value), with capitalist having no share in total output. Obviously, that does not mean that the physical marginal productivity of workers has gone up, but that it has not been placed under any time-value discount. Certainly, you may say that all this could be understood as a theory of the marginal productivity of "time", but I do not find that a very useful description, since, as I said, you may reduce the discount on the value of future production without any change in the physical marginal productivity of time. It is just an issue of intertemporal valuation, which is not arbitrary at all: workers prefer to get now the discounted value of their future marginal product than wait up to the realization of that future value. By the way, Sraffa assumes that capitalists do not advance capital to workers (point 9 of his book), turning all his intertemporal analysis into a non-sense.
Congratulations for your blog an for this lively debate. I´m not an economist yet reading Mr Rallo criticism of what he calls "neoricardian theory of value" I found this comment of him quite remarkable (sorry if my translation is somewhat poor, english is not my native language):
ReplyDeletejuanramonrallo.com/2013/08/critica-a-la-teoria-neo-ricardiana-y-clasica-del-valor/
"It´s true any Price theory has to be able to explain the tendency of convergence of prices towards fragile market equilibriums, but the theory can not pass over the fact that those equilibriums, as the forces that are dragging prices towards them, are fragile because of the subjectivity of economics agents.
That will be tantamount to say Jack the Ripper did not kill his victims: it was the victims were ripped as a consequence of the relative spatial position of his necks and abdomens with the murdering knives.
It is the subjectivity of consumer preferences what determines the relative proportions of the goods to be provided, and it´s the subjectivity of the entrepreneurial expectations and calculus what set up productive plans directed to met the consumer preferences.
This does not mean, by the way, that objective circumstances do not play a role in individual subjectivity (human beings prefer to eat by physiological reasons; and the entrepreneurs can not implement physically impossible business plans) but that objective circumstances does not determine individual subjectivity in a way anybody can know."
So I am amazed. From a myriad of "individual degrees of utility" and time preferences for compsumption or absention thereof, there are relatively stable prices along significant periods of time.
And secondly, he seems to me to be claiming that if "objective circumstances" does not determine "individual subjectivity" in a way anybody can know (not even approximately) certalnly apart from entrepreneurs having magical qualities, I fail to see how can not you take into account that your workers have to eat, that a certain amount of nutritive substances is unfortunately indispensable and that you may know it. Or it is not the point, precisely that "objetive circumstances" have a decisive role in "subjectivity"?
Is this the essence of Rallo's criticism of Sraffa? Ha! Wow. That's pretty weak sauce.
DeleteAnd just to note: I believe in subjective, not objective, theories of value. But this is NOT a criticism of Sraffa.
No, I do not think it is the essence (perhaps it was a bit unfail to quote that concrete passage) nevertheless, I believe he considers the Sraffian critique a theoretical mean to "resurrect" objetive theories of value, as it can be inferred from this concrete passage. He thinks it can not be so.
ReplyDeleteHe is refering to POCBMOC. Begin quote
ReplyDelete"(...)
Anyway and by way of conclusion, the key to Sraffa Theory of Valie is that demands has no role on the determination of the relative prices of commodities: nor the relative demand of present goods, nor the demand of present goods over future goods (temporal preference) What´s more, prices are not determined in the margin (between the consumer and the marginal producer) but are the result of relative prices between total output of production.
All objective theories of value are easily embodied in the Sraffian framework (including the marxist one, as Sraffa himself sought to reduce all cost to homogenuous quantities of labour) where are supply conditions what determines prices: commodities that produce commodities regardless of subjective marginal utility)
(...)
Criticism of the sraffian model.
My goal is to show that the two basic tenets of Sraffa are wrong:
-Demand of non basic goods does not play a role in price determination and
-The temporal preference, as it is assumed equal to 0% does not play a role in the determination of prices and productive techniques".
So, ¿do you think this is not an accurate representation of Sraffa position or intentions in POCBMOC?
I hold to subjective theories of value -- but not marginal theories -- and I think the Sraffa critique is correct. There is a quote from Sraffa which shows that he thought likewise -- I think Rob Vienneau had it on his blog at some point.
DeleteWhile you can use the Sraffa critique to resurrect objective theories of value, this is not necessary at all. Sraffa is critiquing marginalism, not subjective value theory as such. The problem is that marginalists and Austrians think that marginalism is the only subjective theory of value. It is not:
http://fixingtheeconomists.wordpress.com/2013/08/13/marx-hegel-the-labour-theory-of-value-and-human-desire/
Here is the Sraffa quote in full showing that Rallo has completely misunderstand his intentions:
Deletehttp://robertvienneau.blogspot.co.uk/2007/08/sraffa-correspondence-on-demand.html
"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." -- Piero Sraffa (1964). Letter to Arun Bose, in (2)
It is not that Sraffa does not consider demand at all, but that he just assings it a secondary role in determinaning the equilibrium amounts of goods produced. But:
Delete1) He distinguishes between basic and non basic goods, claiming that non basic goods do no determine relative prices (false). That would only be true under the false assumption of universal constant returns to scale.
2) He assumes zero cost of capital (false) in his theory of interest.
3) He does not considere the role of subjective calculations of entrepreneurs to determine production structures and, even inside his system, price relationships. Those subjective calculations, by the way, are moved by the marginal entrepreneur and the marginal consumer, and thus you cannot skip their crucial function inside the price system.
4) His theory is not useful to explain price changes (marginal changes). It is a theory of final rest, so that it is not useful to describe and understand desequilibria and price changes.
JRR
I can only respond to what I'm being given in English and so far your criticisms are both shallow and long familiar to anyone who has engaged even superficially with the debates.
DeleteI cannot speak to (1) and (2) because I haven't read the original piece and your comments here are are too short.
3) You can easily insert entrepreneur's into Sraffa's framework. It seems that your main criticism here is that Sraffa's framework is not COMPLETE. I think that everyone can agree on that. The framework can also, I should say, be completed or closed in many different ways.
4) Perhaps it his immediate framework is not useful to examine this. But this does not mean that it is incompatible. That is like saying that because marginalism often uses static analysis to explain price that they cannot deal with the transition of one price to another. Again, what you seem to be complaining about is the COMPLETENESS of his framework. I'm sure there are many Sraffian authors that deal with disequilibria and price changes.
At the end of the day I don't care much for Sraffian analysis. I find it too abstract and in many ways too like the thought-experiment nonsense that characterises Austrian and neoclassical theory. But his criticisms of marginalism stand pretty strong today so far as I can see. And they have pretty damning consequences for any theory that relies on a general equilibrium that relies on the interest rate -- which is what we're really discussing here.
3) You cannot insert the entrepreneur, because the entrepreneur is an element of change and desequilibrium (Schumpeterian creative destruction) while Sraffa's model is one of final rest and stable equilibrium.
Delete4) I do not say that all his framework is incompatible with change. What I say is that his framework is just a very special case (whit lots of restrictive and unrealistic assumptions) of the much richer Austrian value and price analysis. Why do you need a theory that cannot explain change while you have another that can explain change and rest while encompassing the previous one?
5) His theory of interest assumes no time preference and no risk aversion (i.e. no cost of capital). Therefore, it could be a nice critique of marginal productivity theories of interest, but not of time preference ones. He goes as far as assuming that there is no advances of capital to factors of production, which is equivalent to say that capitalists play no role in the economy (once you assume that, it obviously follows that interest rates are arbitrary charges on aggregate income).
JRR
1) Yeah you can. Just knock the system out of equilibrium. Or posit equilibrium as a long-run gravitational condition that is never realised (as most Sraffians do). Again, I'm not a big fan of the Sraffian approach. But your criticisms are pretty bland.
Delete2) Yes, I had that impression from the beginning. I didn't think your criticisms of Sraffa would be much more than "Austrian theory is better than Sraffa".
3) No, you're forgetting where this all started. I brought up Sraffa because his critiques of the marginalist theory of distribution and reswitching render any theory that allows a general equilibrium to be generated through interest rate price adjustment incoherent. You then pointed to your Spanish "critique" of Sraffa as proof that he was wrong or something. But now we know (point 2) that your critique had nothing to do with the point we were discussing at all.
I think you need to go and read up on the capital controversies in depth and reevaluate your business cycle theories in light of these. That's what I've been saying from the beginning. And I've (predictably) gotten nowhere.
1) The point is that the behaviour of entrepreneurs influences the final equilibrium position. It is not aimed to discover something which is given, but to create something that may not exist. Not to say that entrepreneurs' errors also influence the equilibrium position. How to explain decisions outside equilibrium assuming a passive tendency toward equilibrium?
Delete2) You should read my criticism before judging it. What I say is that making unrealistic assumptions does not lead you to a clear description and understanding of price and value theory, and that you can understand Sraffian oversimplifications inside a more complete framework.
3) Sraffa's criticisms are based on a productivity theory of interest. It does not apply to marginal time preference theories. Reswitching leaves outside the picture that the function of interest rates is not to determine the shape of the structure of capital (for each level of interest, one degree of capital intensitivity), but to coordinate savers and inverstors and remunerate the formers for their provision of capital (of time and risk) to undertake the entrepreneurial activity. Once you understand that each level of interest is fully complatible (in equilibrium) with any profile and intensivity of capital structure (due to factors affecting supply and demand of capital), reswitching becomes unimportant: http://ead.univ-angers.fr/~granem08/IMG/pdf/DT-GRANEM-09-34.pdf It is just relevant for oversimplistic neoclassical capital and interest theories.
JRR
1) This is not a problem. You say that entrepreneurs disturb the equilibrium temporarily but then, as their insights are absorbed by other entrepreneurs and competition takes place, the original innovator's excess profits are eroded and the system tends back toward equilibrium (while never quite reaching it as more entrepreneurs innovate and disturb the equilibrium once more). This is the "gravitation" argument employed by most Sraffians.
Delete2) This still looks to me like "my price/value theory is better than your price/value theory". I do not think that you have found any inconsistencies in Sraffa which is what you hinted at originally.
3) That means that Austrians cannot say that the capitalist economies distribute resources optimally. The neoclassical theory does this by saying that the rate of interest distributes resource usage between capital and labour to maximise both input's marginal productivity. From what you're saying the Austrian argument cannot do this. So markets would not necessarily distribute resources optimally. That raises an awful lot of questions indeed. In fact, it strikes me that the Austrian theory -- if it is as you present it here -- really has no basis to justify distribution of income without reference to past distribution of income.
Note: That last point might be worth looking into by people who are more familiar with Austrian capital theory than I am. It strikes me that JRR's theories may be idiosyncratic but if they are popular then it may mean that income distribution in such theories is arbitrary. That could be VERY damaging for the normative proclamations of such theories. Follow my thread and you might do a lot of damage to these theories. Frankly, I'm just not that interested.
I've been thinking about this. Will someone PLEASE look into this? LK? This is enormously important. If Austrian theory is not based on a marginal productivity argument then it cannot say anything about... well, anything.
DeleteIt cannot, for example, say that wages are set at their optimal level by the market. Thus they cannot make a case against the minimum wage or unions.
If this is true I'll fall out of my chair. It would be hilarious if the Austrian shills were all attacking the minimum wage based on a theory that cannot argue that the market sets the wage at the optimal level!
All Austrian analysis I have seen assumes the marginal revenue productivity theory of wages, either as (1) a real world condition or (2) an state which the real world sometimes deviates from but is more or less still the essence of how wages are set.
DeleteThen LRR's theories are indeed idiosyncratic and he evades the reswitching critique by dropping his theory of distribution. Oh well. His theory is bunkum anyway.
Delete1) That's is not what I am saying. Sraffa assumes solely one position of final equilibrium which does not depend on entrepreneurs decisions. But that is not true. Entrepreneurs change final gravitation equilibrium not only when they are correct (in which case, you may say that they are only anticipating that final gravitation point) but also when they fail (they change what the final gravitation point will be).
ReplyDelete2) To say that prices depend on relative produced quantities once reached the equilibrium is only a truism without any scientific value. Once Sraffa tries to extract some theoretical implications from that truism, he needs to take for granted absolutely unrealistic assumptions, such as constant returns to scale or zero cost of capital. That is not a valid value and price theory.
3) You should look at Böhm-Bawerk, Fetter or Fisher interest theories. Those are not marginal productivity theories of interest. The process is quite different to the one you and all marginal productivity of capital school assume: capitalists' competition push up the present value of factors of production according to their expected future value; but present value is not increased up to its full future value, because present goods are more valuable than future goods. At the end, workers' income tend to coincide with their discounted marginal productivity (but not necessarily, since there may be very stable moats and competitive advantages), but this is not because capitalists take their share of total product according to their productivity, but because they are not willing to advance more capital in the present to anticipate the income that they will get back in the future. As Böhm-Bawerk said: "The completely just proposition that the worker is to receive the entire value of his product can be reasonably interpreted to mean either that he is to receive the full present value of his product now or that he is to get the entire future value in the future. But Rodbertus and the socialists interpret it to mean that the worker is to receive the entire future value of his product now". If time preference and risk aversion of capitalist were zero, workers would tend to earn their undiscounted marginal productivity (i.e their full future value), with capitalist having no share in total output. Obviously, that does not mean that the physical marginal productivity of workers has gone up, but that it has not been placed under any time-value discount. Certainly, you may say that all this could be understood as a theory of the marginal productivity of "time", but I do not find that a very useful description, since, as I said, you may reduce the discount on the value of future production without any change in the physical marginal productivity of time. It is just an issue of intertemporal valuation, which is not arbitrary at all: workers prefer to get now the discounted value of their future marginal product than wait up to the realization of that future value. By the way, Sraffa assumes that capitalists do not advance capital to workers (point 9 of his book), turning all his intertemporal analysis into a non-sense.
JRR