Wednesday, October 26, 2011

Two Sraffian Propositions

A Wage-Rate Of Profits Fontier

One might infer the following from Sraffa's book, The Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory:

  • The distribution of income is not determined by the supply and demand for factors of production. Instead, it is determined by power, politics, and the evolution of social norms.
  • The returns to capital are not determined by consumers rationally choosing to trade-off consumption today for consumption sometime in the future.
Sraffa's models, I think, are consistent with these ideas, even if they cannot be formally derived from his propositions as a matter of mathematical proof. Various empirical findings published lately support these ideas1. I refer, specifically, to the arguments in Hacker & Pierson (2010)2 and to the research3 summarized in Chapter 10, "Why is saving for the future so arbitrary?" of Akerlof and Shiller (2009).


1One might even argue that certain empirical trends (and an emerging worldwide political movement) should be giving Sraffian research more salience.
2Over a decade ago, James Galbraith provided empirically-supported arguments about the importance of politics in determining income distribution.
3Over a decade and a half ago, Paul Davidson was citing a 1982 study by Danziger, Van der Haag, Smolensky, and Taussig on savings during retirement. Their empirical results were not consistent with a model of lifecycle saving built on a foundation of intertemporal utility-maximizing.


  • George A. Akerlof and Robert J. Shiller (2009). Animal Spirits: How Human Psychology Drives the Economy and Why It Matters for Global Capitalism, Princeton University Press.
  • Paul Davidson (1994). Post Keynesian Macroeconomic Theory: A Foundation for Successful Economic Policies for the Twenty-first Century, Edward Elgar.
  • James K. Galbraith (1998). Created Unequal: The Crisis in American Pay, Free Press.
  • Jacob S. Hacker & Paul Pierson (2010). Winner-Take-All Politics: How Washington Made the Rich Richer - And Turned Its Back on the Middle Class, Simon & Schuster.


Matias Vernengo said...

Ian Steedman has a very interesting paper on the second proposition ("Time Preference, Rate of Interest, and Abstinence from Accumulation," Australian Economic Papers, 1981) in which he argues, among other things, that this argument rests on the notion that consumption is the sole goal of economic activity.

Greg Hill said...

I'm wonder if Sraffa provided the critique, but the "positive" theory of income distribution is to be found in the Kaldor, Robinson, Passinetti models. But if you think Sraffa feeds into these, I'd be very interested in how this works.

Robert Vienneau said...

Matias, thaks for the reference. I quite like Steedman's works, but I haven't read that.

I think of Sraffa's work as providing a space for the Kahn-Kaldor-Pasinetti-Robinson theory of income distribution, as well as other theories. Isn't Sraffa's model consistent with taking the real wage as given, taking the rate of profits as given (perhaps as a result of policies of the monetary authority), or accepting the Cambridge equation? Doesn't Sraffa show the prices that obtain along most of Robinson's metallic ages?

Achim said...

Hi Robert,

I'm searching for the source of a quote that I remember but I'm not exactly sure about it and I cannot find it. I guess (but am not sure) that it was Kaldor who said something like that it was completely arbitrary whether you move along a production function or shift it in a neoclassical model. Do you perhaps know about the quote and where it comes from?

Thanks in advance,

Robert Vienneau said...

Achim, I don't know that quotation. It seems to me you may be talking about Kaldor's technical progress function, developed in his succession of growth models during the 1950s and 1960s. I believe that somebody published a paper showing that his particular formulation is observationally equivalent, despite Kaldor's intentions, to a Cobb-Douglas aggregate production function, in some sense.

Achim said...

Thank you Robert, I found it.

It goes:
"It follows that any sharp or clear-cut distinction between the movement
along a 'production function' with a given state of knowledge, and a shift
in the 'production function' caused by a change in the state of knowledge
is arbitrary and artificial."

Kaldor, "A Model of Economic Growth", The Economic Journal, 1957

Anonymous said...

I've read some of interesting papers on the neoclassical vs. sraffian debates in the net. now, long ago I wrote my diss. (German) on this stuff.
S. is still important but I now think there is something wrong with the proposition that there can be an equilibrium with rate of profit r greater than rate of growth g (eg. r>g=0). No. there can't. reswitching and all the paradoxes in neoclassical theory a n d in S's 1960 book (cif. joint production: rather crazy conclusions)and elsewhere stem from the non golden rule underpinnings.
If you make 575 wheat out of 280 wheat and 12 iron, and 20 iron out of 8 iron and 120 wheat the equilibrium is n o t pi=15, pw=1, r=25%. This is because the entire net income that goes to iron is really rent, a quasirent if you like more: in Marshalls sense. And the reason is: iron "sector" (no, think it over in walrasian factor terms: iron earns, not the sector!) certainly will not earn 25% on its "capital value" if the iron surplus rate amounts to zero. While wheat has a social rate of return of 43.75% and earns only and equally 25%( this is where irons rent comes from). Sorry, this is impossible. Suppose Henry George - like that there are two assets of which wheat grows at 43.75 and iron at 0%. The wheat value will have to decline relative to iron, right? no stationary price system could be a "supporting hyperplane" in N goods models as well. In a "real" economy (no money!!!)the supporting prices will generate "own rates of return" equal to supposed surplus rates. no divergence between these rates! So, Schumpeter (r=g (=0 in a stationary state)) is right and all our existing schools of economics are wrong.The outstanding brilliant von Neumann should be our guiding line. one can prove it via Tobin's q.