Sraffa's 'production of commodities by means of commodities' assumes that markets- and therefore 'market-makers' (arbitrageurs)- exist. However, people are not commodities. You can sell labour power. You can't sell yourself. The entrepreneur who combines factors of production is a free agent. He is not a slave.
Only things bought and sold on open markets are 'commodities'. If commodities are used in the production of other commodities, then they are classed as 'capital' or 'intermediate' goods. Their price is determined in the relevant market by the activities of arbitrageurs. They may be guided by Accountancy practices- e.g. 'historic cost less depreciation'- or the reverse might happen- i.e. Accountants 'mark to market'.
Wikipedia says-
'Sraffa reswitching is a concept in Sraffian economics where the most profitable production technique can change back to a more capital-intensive method
provided 'capital' intensity doesn't mean ratio of Capital to Labour. Sraffa thinks a machine isn't capital. It is actually labour, albeit supplied at an earlier period.
at higher interest rates,
At higher interest rates, people have an incentive to sell their capital stock and buy debentures. Sraffa assumes they won't act upon this motive. Either that, or he is not talking about a market economy. But, in that case, neither the interest rate nor the profit rate nor the price is determined 'endogenously'. Everything is set by the State- including who can buy at the set price and who can borrow and who can save and who can run an enterprise. Incentives don't matter. Punishments do.
after initially switching to a labor-intensive one at a moderate rate.'
Sraffa either assumes time travel or else there is no actual 'switching'. People merely say 'we should have switched. We couldn't because Time Travel hasn't been invented yet.'
Sraffa was working within a Marxist 'capital is dead labour' model. If he found inconsistencies or inefficiency in that model- that was of concern only to people living in command economies. It had no relevance for Societies where capital is allocated through financial markets.
In market economies, Capital is what people expect to produce a given stream of income. Its value is decided by 'market makers' or entrepreneurs undertaking that function. Thus if an engineer sinks a lot of his own money into a novel product we say he is making the market for it. If he succeeds, the money he spent is 'investment' and the plant and machinery he has created are 'capital goods'. But, if he fails, that money wasn't 'investment'. It was, at best, a write off or else an expensive hobby which involved pissing money against a wall. The plant and machinery he has are junk or scrap metal. It isn't a capital good.
On the other hand, if the State allocates funds to an investment project, then market forces don't operate. Prices and interest and profit rates are set by command. Subsequent appraisal may show that resources were misallocated. But that wasn't because of market forces. It was because the wrong commands were given.
Sraffa stipulated that 'current costs of production are the sum of present values of dated labour inputs whereby capital inputs correspond to dated labour costs'. This simply isn't true in a market economy. Sooner or later, accountants have to mark to market.
Current cost of production is just the actual money spent on combining factors of production. 'Historical costs' may be used to calculate profit but the Audit committee may object to this because it might lead to hostile takeover by an asset stripper or else unsustainable dividend cover (because depreciation allowances don't cover replacement cost) which itself may tank share price.
This phenomenon contradicts the neoclassical assumption that there is a consistent relationship between the rate of profit and the capital-intensity of a chosen technique.
It contradicts the assumption (unstated, perhaps unknown, to the neo-classicals) that arbitrage will ensure this outcome. In any case, by using arbitrary Accountancy protocols, you can always order the domain such that you get the desired graph of the function. But ex poste won't be ex ante because unanticipated things happen.
Sraffa argued that the possibility of reswitching complicates the idea of a simple, continuous measure of "capital intensity" as a determinant of production choice
It would if commodities weren't market phenomena in some sense. (You make a market for stuff you make even if you choose to give it away for free to someone you like. This is because there are people who want to buy it even if they can't do so.)
Accountants spend a lot of time valuing capital stock. Around the time the 'reswitching debate' began to rage, Accountants had to deal with the problem or inflation and technological obsolescence and rising land prices. The stage was being set for the 'asset stripper'. It was more profitable to buy an enterprise to shut it down and sell its assets. This was because 'historic cost' accounting produced a balance sheet which did not reflect 'break up' value.
Since Sraffa wasn't talking about a Capitalist economy, the debate wasn't really about capital. It was about stupid academics teaching nonsense.
What Ajit Sinha calls
Piero Sraffa’s profound contribution to economics.
had nothing to do with finding ways to economize on the use of scarce resources. It involved some stupid guys who got paid a little money to teach nonsense to careerist cretins.
Amartya Sen said
'It would be, I believe, a mistake to see (as has been sometimes suggested) in Sraffa’s analysis a causal system rival to the standard neoclassical model of the determination of prices, quantities, and the distribution of incomes.
In other words, it wasn't a contribution to economics.
Sraffa was changing the nature of the inquiry
away from anything which might be useful
—toward an important but neglected theme
neglected because it was useless
—rather than providing a different answer to a given question already in vogue in contemporary economics. —
Just as Sen doesn't help answer the question how India can be less poor. He changes the nature of the inquiry to focus on the capability to have the functioning to have the capability to have the capability to talk bollocks.
Ajit Sinha says-
When Piero Sraffa’s book Production of Commodities by Means of Commodities was published in 1960, it was received with perplexity by the larger economics community.
Commodities are produced by people. People can't be bought and sold like commodities- at least not since slavery was abolished. Thus commodities aren't produced by commodities.
The consensus which gained ground was that 'Piero Sraffa's main aim in writing 'Production of Commodities by Means of Commodities' was to provide a prelude to a critique of orthodox, neoclassical economic theory. His objective was to establish an alternative framework for the determination of prices and income distribution that was independent of the neoclassical concepts of supply and demand, marginal utility, and the marginal productivity of capital.'It was not clear what the work was all about.
Though leading economists of the day perceived that there was something profound in it, they were not able to put their finger on what that was. Sir Roy Harrod’s (1961) review of Sraffa’s book is the case in point. Though Harrod showed a profound lack of understanding of Sraffa’s treatise, he nevertheless acknowledged that “The publication of this book is a notable event. … A reviewer would be presumptuous if he supposed that he could give a final assessment of the value of its net product, or even single out what may prove to be its most lasting contributions. Before that result could be achieved, much prolonged consideration and reconsideration would be required” (p. 783).
Would the UK move towards or away from markets? Sir John Hicks believed that the rate of profit was already being set by the Government. Suppose Harold Wilson comes to power? Might the country embrace out-and-out Communism? There were people who believed Wilson was a KGB plant.
The book came to prominence in mid-1960 when the now famous capital theory debates between the “two Cambridges” reached their climax. Apparently, Paul Samuelson at the MIT, Cambridge, Massachusetts, had set his doctoral student David Levhari the task of disproving a proposition of Sraffa regarding “re-switching of techniques.” Levhari published his refutation of Sraffa’s proposition in the Quarterly Journal of Economics in 1965.
Geoffrey Harcourt once recounted to me that he was perhaps the first person in Cambridge, UK, to have come across this paper by Levhari at the Applied Economics Library. He went straight to Sraffa and told him that “there is a chap at MIT Cambridge who claims that your re-switching proposition is false.”
Sraffa responded: “No, he is wrong, and you show it to him!”
Harcourt responded: “Me? I can’t do matrix algebra.”
To which Sraffa responded: “Neither can I.”
So Luigi Pasinetti was asked to do the job, and the rest is history.
A good 1966 paper by Bruno, Burmeister and Sheshinski gives a clear account of how this unfolded.
Now suppose there are some goods that take more than one period to produce. One can either treat goods-in-process of different ages as different goods (with different activities)
which is what happens if you 'mark to market' for balance sheet purposes
or else calculate directly the implied price relationships.
In other words, rely on historic costs. This is fine if you have 'administered pricing' and all output can be sold at that price.
The Pasinetti-Sraffa numerical example uses precisely the latter type of capital model.
In which case, there is no profit maximizing. We aren't talking about a Capitalist economy. Also, the interest rate is set arbitrarily. Who gets to borrow or who is forced to save is decided by the State. In other words, the price system is not allocating resources.
There is one general common characteristic of all these models from which reswitching and other properties can be shown to follow.
It is that they can't exist in a market economy. If interest rates rise sufficiently, you don't get re-switching. You get a cessation of investment because everybody wants to be a lender, not a borrower. Of course, if the rate of return (marginal efficiency of capital) is some multiple of the interest rate, there would still be investment. But then the thing would be so profitable that choice of technique would not matter. Just do what is easiest for you to do. Maybe you only get to double rather than triple your money. What do you care? You are laughing all the way to the bank.
In 1966, Samuelson organized a symposium in the QJE, in which it was accepted by all parties, including Samuelson himself, that Levhari had made a mistake and that Sraffa’s proposition is, of course, robust.
Wikipedia summarizes the outcome very lucidly-
In a 1966 article, the neoclassical economist Paul A. Samuelson summarizes the reswitching debate:
- "The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves
not being able to sell up and put the money into debentures.
- more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more 'roundabout,' more 'mechanized' and 'more productive' — cannot be universally valid." ("A Summing Up," Quarterly Journal of Economics vol. 80, 1966, p. 568.)
this was obvious. These guys were old enough to remember the Great Depression.
Samuelson gives an example involving both the Sraffian concept of new products made with labor employing capital goods represented by dead or "dated labor" (rather than machines having an independent role) and Böhm-Bawerk's concept of "roundaboutness" — supposedly a physical measure of capital intensity.
There is no 'roundaboutness' if you have enough market makers with rational expectations. Why? Intermediate goods can be sold for something close to expected present value. This means, inter alia, that economies in its production can be gained and so others can enter the market for the finished good with much shorter elapsed time for break-even.
Instead of simply taking a neoclassical production function for granted, Samuelson follows the Sraffian tradition of constructing a production function from positing alternative methods to produce a product.
If we produce a thing we know we can produce it in a particular way. We can't be sure we will know how to produce it in a different way.
The posited methods exhibit different mixes of inputs. Samuelson shows how profit maximizing (cost minimizing) indicates the best way of producing the output, given an externally specified wage or profit rate.
He forgets that if the interest rate is higher than the profit rate, the project gets discontinued. Money is transferred to Debentures.
Samuelson ends up rejecting his previously held view that heterogeneous capital could be treated as a single capital good, homogeneous with the consumption good, through a "surrogate production function".
Anything can be treated as anything else for some purpose. Your accountant may say 'sell your business. Put your money into debentures. You will be better off.' He is treating assets as homogenous with respect to money returns.
Consider Samuelson's Böhm-Bawerkian approach. In his example, there are two techniques, A and B, that use labor at different times (–1, –2, and –3, representing years in the past) to produce output of 1 unit at the later time 0 (the present).
Two production techniques time period input or output technique A technique B –3 labor input 0 2 –2 7 0 –1 0 6 0 output 1 1
Then, using this example (and further discussion), Samuelson demonstrates that it is impossible to define the relative "roundaboutness" of the two techniques as in this example, contrary to Böhm-Bawerkian assertions.
B takes longer. Surely that makes it more 'roundabout'?
He shows that at a profit rate above 100 percent technique A will be used by a profit-maximizing business;
Not if B had already been chosen. You can't travel back in time. What will happen is the guy who would otherwise do A first tries to buy B. He would only go ahead with A if the profit rate was so high that he'd still be happy though reporting a higher rate of return.
between 50 and 100 percent, technique B will be used;
It can't be chosen in time period -2.
while at an interest rate below 50 percent, technique A will be used again.
Only A will be used unless it wasn't an option in time period-2 and can't buy out the guy doing B, you have no choice but to do A. So you have two different techniques without any switching between them. They have different rates of return. We might say, the 'marginal efficiency of Capital' is determined by the return on A which represents the addition, at the margin, to the Capital stock.
The interest-rate numbers are extreme, but this phenomenon of reswitching can be shown to occur in other examples using more moderate interest rates.
There is no 'reswitching'. If you committed to B, you either sell out or carry on. If you come into the game at time-3
The second table shows three possible interest rates and the resulting accumulated total labor costs for the two techniques. Since the benefits of each of the two processes is the same, we can simply compare costs. The costs in time 0 are calculated in the standard economic way, assuming that each unit of labor costs $w to hire:
where L–n is the amount of labor input in time n previous to time 0.
Reswitching interest rate technique A technique B 150% $43.75 $46.25 75% $21.44 $21.22 0% $7.00 $8.00 The results in bold-face indicate which technique is less expensive, showing reswitching.
If there is perfect arbitrage, B sells out or the guy doing A settles for a lower rate of return. Nobody can go back in time to switch technique.
There is no simple (monotonic) relationship between the interest rate and the "capital intensity" or roundaboutness of production, either at the macro- or the microeconomic level of aggregation.
There are plenty but they are arbitrary.
The proposition in question refutes the Clarkian-type neoclassical explanation of the rate of interest on capital on the basis of the “marginal productivity of capital,” which requires measurement of “intensity” of capital independently of the rate of interest.
Capital intensivity is determined by the money cost of physical capital relative to labour. This is independent of the rate of interest. It is computable based on the wage and the price of the capital goods in question.
Sraffa’s “re-switching” proposition showed that, in general, there is no logical way by which the “intensity of capital” can be measured independently of the rate of interest —
Because he doesn't have a market for capital goods. He is not talking about a market economy. Otherwise, whatever is produced in time-3 in B has a price. That means B is actually more capital intensive than A in period -2. But if the rate of profit is higher than the interest rate, A may be chosen alongside B.
and hence the widely held neoclassical explanation of distribution of income was logically untenable.
Anything at all can be made 'logically tenable'. The question is whether the thing is useful.
This victory was hailed as the crowning glory of Sraffa’s book, but it came at a high price.
People decided Capital & Growth theory was useless. Finance was a separate field. Good mathematicians could make money and do something useful in that field. Also, if you like Marxism so much, why don't you fuck off to the Soviet Union?
The orthodoxy interpreted Sraffa’s re-switching proposition as his main contribution to economic theory; they accepted its truthfulness and argued that the modern general-equilibrium orthodox economics need not aggregate capital independently of prices or the rate of interest, and hence the Sraffa critique of the orthodox theory was not fatal but rather minor.
So, either he made no contribution or made a minor contribution. That seems fair.
Samuelson’s (1959) non-substitution theorem had already shown that a General Equilibrium model with the assumption of constant returns to scale and no possibility of technical substitution can generate classical-type price solutions independently of demand functions. In 1982, Frank Hahn published an influential paper in the Cambridge Journal of Economics in which he claimed that Sraffa can be incorporated as a special case of the inter-temporal General Equilibrium Model (see Sinha 2010, 2016 for a rebuttal). All this led to a general perception among the orthodox that the book on Sraffa can finally be closed. In a strange way it appeared that Sraffians lost the war after winning the great battle.
Everybody lost the war. Samuelson as much as Sraffa. There was a time when people thought that maybe 'shadow prices' and networked computers could allocate resources efficiently. Sadly, this was not the case. Knightian uncertainty obtained with a vengeance- i.e. unexpected events occurred more and more frequently.
One reason for this, was that perhaps the war was fought on side issues. My last several years of archival research (largely funded by INET and CIGI, see Sinha 2016) has led me to conclude that the battles, both in the areas of pure theory and history of thought, were fought on the wrong terrain—the question of re-switching of techniques was not the central aspect of Sraffa’s pure theory. It is a book that was designed to challenge the orthodox economic theory in a more fundamental way—there lies a methodological and philosophical sub-terrain underneath the apparent economic theory of the book.
Indeed. Sraffa was trying to give a labour theory of value based account of Capital. He failed.
We should not forget that Ludwig Wittgenstein credited Sraffa for “the most consequential ideas” of the Philosophical Investigations (1953) and had put him high on his short list of geniuses.
Nor should we forget that Wittgenstein was wrong about everything.
Wittgenstein had regular discussions with Sraffa for more than a decade during 1930s and ’40s in Cambridge,
Sraffa tried his best to avoid talking to Witless.
England, and at many occasions he told his friends that those discussions “made him feel like a tree from which all branches had been cut” (Monk 1990, p. 261). Thus the philosophical sophistication and sharpness of Sraffa’s mind is beyond doubt. Unfortunately, Sraffa’s revolutionary contribution to economic theory was lost to the intellectual world because economists did not pay attention to the philosophical underpinnings of his economic theory.
He was trying to do stupid shit. If there was some merit to his approach, accountants and finance mavens would have already discovered and used it. Having a better theory of capital means you can become very rich. It must be said, Sraffa did make a bundle by buying Japanese scrip when it was undervalued. However, had the US not encouraged Japanese industry because of the Korean war, he would have lost money. In other words, something unanticipated made his investment profitable.
Actually, the book was designed to challenge the usual mode of theorizing in terms of essential and mechanical causation — prices are shown to be neither ultimately caused by labor or utility/scarcity, nor are they determined by the forces of demand and supply. It, instead, argues for a descriptive or geometrical theory based on simultaneous relations. Sraffa demonstrates that on the basis of observed input-output data of an interconnected system of production, one can show, by simply rearranging them, that the rate of profits of the system can be determined without the knowledge of prices, if the wage rate is given from outside the system.
In other words, if people are slaves or robots, wages have no effect in determining the allocation of labour or the incentive to work hard.
In this context, prices have only one role in the system and that is to consistently account for the given distribution of the net output in terms of wages and the rate of profits (introduction of rent of land does not make any difference to the result). Prices, in this context, do not carry any information that prompts “agents” to adjust their supplies and demands to bring about an equilibrium in the market. The questions of equilibrium as well as market structure are simply irrelevant to the problem.
Because Sraffa is assuming that workers are mindless drudges.
A consequence of this approach was a complete removal of “agent’s subjectivity” or demand, and “marginal method” or counterfactual reasoning from economic analysis — the two fundamental pillars of orthodox economic theory.
Counterfactual reasoning means 'what would happen if we chose not to do this.' If there is no counterfactual reasoning, nobody is making any choices. They are mindless drudges.
Sraffa wrote 'The marginal approach requires attention to be focused on change:- for without change either in the scale of an industry or in the 'proportions of the factors of production' there can be neither marginal product nor marginal cost.'
This is not the case. One can always ask what would happen if we cut output by one unit. How much would we save? That is the marginal cost.
In a system in. which, day after day, production continued unchanged in those respects, the marginal product of a factor ( or alternatively the marginal cost of a product) would not merely be hard to find-it just would not" be there to be found.
Your accountant can estimate if for you well enough.
What Sraffa’s alternative economic theory establishes is that income distribution in terms of wage rate and the rate of profits are linearly related to each other
if that is what you assume- sure.
and can be taken as given independently of prices. Now prices for any given input-output data must be such that those given distributional variables are consistently accounted for
Sraffa is assuming markets clear. But they may not do so. People form a queue. Those who arrived earlier can buy the good at the set price. The rest go home disappointed.
— a conclusion that stands in stark opposition to the orthodox economic theory, which maintains that both the size and distribution of income are determined simultaneously with prices. Sraffa’s discovery of the “Standard commodity” plays the central role in establishing this thesis; and his reinterpretation of classical economics is also rooted in the above proposition.
The 'standard commodity' is based on the notion that there is some fixed basket of goods necessary for labour to maintain itself. But this is very different during peace-time than it is during a war. Sraffa had lived through two big wars and one long 'cold' war. Man does not live by bread alone. He also needs submarines able to launch nuclear ICBMs.
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