One inspiration for this post is stumbling across this abstract
2.0 MarxStart with labor coefficients and a Leontief input/output matrix, in physical terms. You can construct this from make and use tables for your country, given price indices by sectors.
For any existing capitalist economy, I expect that matrix to characterize a more than viable economy. After all the capital goods used up in producing the final demand in, say, a year are reproduced, some commodities will remain for consuming and investing.
As with any other matrix, a set of n Eigenvalues and corresponding Eigenvectors can be found for that matrix. And, if I recall correctly, the maximum Eigenvalue has an associated Eigenvector in which all elements are non-negative. The components for Sraffa's basic commodities are all strictly positive. And they are in the proportions of Sraffa's standard commodity. If wages are zero (the worker's live on air) and the final demand is all invested, the final demand will be in proprortions of Sraffa's standard economy and the economy will expand at a rate of growth related to this eigenvalue. One can read von Neumann (1945) as describing this model of uniform growth.
So given the technique in use in a capitalist economy, a composite commodity of average capital composition is picked out. Georg von Charasoff called this composite commodity 'Urkapital' which, I guess, is translated as "original capital". In some sense, this urkapital is a commodity of average organic composition of capital. This numeraire is picked out by the technique in use. In the production of this numeraire:
- The rate of profits, as calculated in the system of embodied labor values, is identically equal to the rate of profits, as calculated in the system of prices of production.
- Gross output, as evaluated at embodied labor values, is equal to gross outputs, as evaluated at prices of production.
- Net output, as evaluated at embodied labor values, is equal to net output, as evaluated at prices of production.
- The division of net output between workers and capitalist makes no difference to the above invariants.
So Volumes 1 and 3 of Marx's Capital are consistent.
3.0 Marginalist EconomicsIf one is ill-informed and malicious these days, one could insist that Sraffa's model is a special case of a neoclassical model of intertemporal equilibrium. Consumers maximize utility, and managers of firms maximize profits. Initial endowments just happen to be so that the economy expands along a steady state growth path.
4.0 ConclusionsBut, of course, utility-maximization is nonsense, especially inter-temporally. Furthermore, the von Neumann ray has saddle-point instability. As Joan Robinson showed with her models of metallic ages, one need not assume that the workforce is fully employed in the long-run.
The model that has no need of restrictive assumptions is the more general.
I suppose you know https://link.springer.com/article/10.1007/BF02480895
ReplyDeleteNo. I stumbled across it. I use to be able to download academic articles at a local Liberal Arts College. I cannot do this these days.
ReplyDeleteI am not complaining. My parents lived through the Great Depression. My grandfather died in a mill then, and my grandmother could not keep the family together. His brother was a tail gunner in WW II. In my home town, there were race riots when I was about 4. I'm not sanguine about our prospects, but I realize how awful history was.
«If one is ill-informed and malicious these days, one could insist that Sraffa's model is a special case of a neoclassical model of intertemporal equilibrium. Consumers maximize utility, and managers of firms maximize profits. Initial endowments just happen to be so that the economy expands along a steady state growth path.»
ReplyDeleteThat's me! :-) Actually I "insist" that Sraffa's model is the core of a neoclassical *static* model (not even intertemporal equilibrium, but then intertemporal equilibrium is just a sillu device to create a static model across time), and as usual I add that was precisely the point made by P Sraffa, as in "*Prelude to a critique* of economic theory". At the very beginning I remind you that he says:
“Let us consider an extremely simple society which produces just enough to maintain itself. Commodities are produced by separate industries and are exchanged for one another at a market held after the harvest [...] set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated; such values spring directly from the methods of production”
«Furthermore, the von Neumann ray has saddle-point instability.»
The difference with neoclassical models is simple: neoclassical Economics has several ridiculous or inconsistent assumptions (documented mostly by Steve Keen in "Debunking Economics") whose purpose is essentially to ensure that such terrible things do not happen. The initial formulation was even designed to ensure that the optimization landscape was purely convex, that is a dome with a single and obvious maximum.
Because if there are many local maxima then JB Clark's "fable" that income, absent government intervention, is uniquely and solely determined by marginal productivity, cannot hold, because it also depends on the happenstance of which local maximum one ends up trapped by.
I see Arrow-Debreu-Lucas style models of Economics as variational models inspired of course by laplacian determinism (the "economy as orrery" models, with the Walrasian auctioneer driving "tatonnement" outside of time in the role of Laplace's daemon. Such models also try to escape the dire issue of the Sonnenschein–Mantel–Debreu theorem, or simply ignore it.
But with the optimization landscape carefully if inconsistently constrained so that "simulated annealing" in its generality is not needed because here is an obvious and single maximum point so that that JB Clark's "fable" just "happens" to be realized, and there is therefore no need for government intervention is needed to "raise the temperature" to escape from particularly low local maxima. But of course I am making no sense at all.
BTW I am not sure that mr. Viennau is "au fait" with some aspects of the history of economic thought and why Walras did that model, and how it is related to Laplacian philosophy, and why Marshall went another way, etc. etc.; but these are "deep secrets" of the history of political economy that are rarely discussed in public any more :-).
BTW I have just looked at the relevant Wikipedia entry and it has some good comments:
ReplyDeletehttps://en.wikipedia.org/wiki/Walrasian_auction#Walrasian_auctioneer
«Walras suggested that equilibrium would always be achieved through a process of tâtonnement (French for "trial and error"), a form of hill climbing. More recently, however, the Sonnenschein–Mantel–Debreu theorem proved that such a process would not necessarily reach a unique and stable equilibrium, even if the market is populated with perfectly rational agents.»
«The device is an attempt to avoid one of deepest conceptual problems of perfect competition, which may, essentially, be defined by the stipulation that no agent can affect prices. But if no one can affect prices no one can change them, so prices cannot change. However, involving as it does an artificial solution, the device is less than entirely satisfactory.”
and a startling revelation:
«Walker and van Daal argue that the idea of the Walrasian auction and Walrasian auctioneer resulted from Jaffé's mistranslation of the French word crieurs (criers) into auctioneers. Walker and van Daal call this "a momentous error that has misled generations of readers into thinking that the markets in Walras's model are auction markets and that he assigned the function of changing prices in his model to an auctioneer."»
In that case I guess Walras' model was more like that of a "bourse". But there are criers also at auctions, for example in some wholesale commodity markets, that are arranged as auctions.
I guess I must get a copy of that new translation, particularly easy for me currently. Reading (or re-reading) the original works usually is highly rewarding.
I am not a german speaker, but the "ur" prefix is used in various ways:
ReplyDeleteGeorg von Charasoff called this composite commodity 'Urkapital' which, I guess, is translated as "original capital".
and "original" might be replaced by "super"/"ultra", "platonic", "meta", "base", "standardized", "intrinsic".