Showing posts with label Arrow–Debreu. Show all posts
Showing posts with label Arrow–Debreu. Show all posts

Monday, June 1, 2026

Two traditions in the history of ideas

The chart above is a summary of my history of thought class here at Bucknell. Over the last years I have used the Vaggi and Groenewegen textbook. The central divide in the history of economic thought is between the classical political economy tradition and the utilitarian-marginalist tradition. The classical tradition, running from Petty, Cantillon, and Quesnay through Smith, Ricardo, Marx, and later Sraffa, is organized around production, reproduction, surplus, accumulation, and distribution among social classes. Its object is the economy as a historically specific social system, marked by conflict over the surplus. By contrast, the Benthamite tradition, passing through John Stuart Mill, Jevons, Marshall, Pigou, and modern neoclassical economics, shifts the center of analysis toward utility, exchange, individual choice, scarcity, and the marginal calculus.

This divide in economics mirrors a broader division in social science, discussed by Randall Collins, between a conflict tradition, concerned with power, class, institutions, and historically evolving social structures, and a rationalist-utilitarian tradition, which begins from rational individuals and explains social order as the unintended or aggregate result of their choices (Collins has four traditions in sociology, and I'm simplifying here). In that sense, the Smith/Ricardo/Marx line belongs, despite its internal differences, to the conflict-centered political economy tradition, while the Bentham/Mill/Marshall line provides the economic counterpart to the rationalist/utilitarian strand of social theory.*

The same divide reappears in modern theories of value and distribution.** In the classical-Sraffian tradition, value is not derived from individual preferences or subjective scarcity, but from the technical conditions required for the reproduction of the system. In a Sraffa-Leontief framework, given the input-output relations of production and one distributive variable, such as the real wage or the profit rate, relative prices can be determined as prices of production. Distribution is therefore not solved by marginal productivity, but reflects a social and institutional determination of the division of the surplus.

By contrast, in the Arrow-Debreu intertemporal model, prices are equilibrium signals that reflect relative scarcities across commodities, dates, and states of nature, ultimately grounded in individual preferences, endowments, and technologies. In that framework, distribution is treated as the result of the initial allocation of resources and the competitive valuation of scarce factors, rather than as a historically specific conflict over the surplus.

Thus, the old contrast between classical political economy and marginalism survives in modern form as the contrast between reproduction, surplus, and distribution on the one hand, and scarcity, preference, and intertemporal exchange on the other.

* It is interesting that Friedman, in his classic Capitalism and Freedom, although he quotes Smith, mostly for rhetorical reasons, in my view, in his crucial chapter on the importance and antecedence of economic freedom over political rights, he only cites Jeremy Bentham as a precursor.

** On this, the kind of confusion in the profession is somewhat surprising. Some people (e.g. Cowen here) suggest that the classical tradition has no alternative to the simplistic labor theory of value (LTV), with prices proportional to the quantities of labor, and ignore the Sraffian model (see this). Alternative, some of the same people assume that the Marshallian, not even the general equilibrium version of say Knut Wicksell, has no problems, not considering the insurmountable issues with partial equilibrium shown by Sraffa's critique. The reasons for the change in the notion of equilibrium, noted by Garegnani go unnoticed by almost the whole profession.

PS: There are plenty of differences between authors in those two traditions. Clearly Friedman and Samuelson had many economic policy differences, and Samuelson and some left-Keynesians like Joan Robinson would agree on some of those.  But on an analytical level, Samuelson was closer to Friedman.

Wednesday, May 11, 2016

The great economic equations

A few days ago, Unlearning Economics twitted a link to an article on "The 17 equations that changed the world." Only one was an economic equation, The Black-Scholes one, and in all fairness it did not change the world, and is not even a central one in economics. First of all, Nassim Taleb has argued convincingly (for example, here) that Black, Scholes and Merton did not invent the formula, and what they really did was to provide a theoretical justification that was compatible with Arrow-Debreu general equilibrium (GE) views. Haug and Taleb say it clearly:
Indeed what Black, Scholes and Merton did was “marketing”, finding a way to make a well-known formula palatable to the economics establishment of the time, little else, and in fact distorting its essence.
So market participants already had formulas to price options, and the idea that their version of the formula "helped create the now multi-trillion dollar derivatives market," as suggested by Andy Kiersz, is clearly incorrect. Unregulated financial markets didn't need the Black-Scholes formula, economists did. And we know how well that ended. Deregulation and the nature of competition in financial markets would have led to the expansion of derivative markets anyway. But GE would not look like it could provide practical answers to real economic problems. Which turns out it couldn't. Besides, as discussed here before, the Arrow-Debreu general equilibrium model is not devoid of problems.

So what are, if any, the great economic equations, you ask. If I had to say one it would be either Keynes' multiplier formula, Y = I/(1 – c), or Sraffa's demonstration of the inverse relation between wages and profits, r = R(1  – w).* The first clearly shows that spending determines the level of activity and provides formal justification for counter-cyclical policies, which have indeed reduced the effects of recessions on the economy, even if, as Kalecki had noted it would happen, austerity is often imposed for political reasons. The second resolved an issue first clearly posed by Ricardo, is part of the clear understanding of what determines long-term prices, and shows the conflictive nature of the capitalist system. Both are central to understanding the way capitalist economies work.

* Where all variables have the standard meaning, Y is output, I investment, c the propensity to consume, r is the rate of profit, R is the maximum rate of profit, and w the wage share.

Saturday, November 30, 2013

Lars P. Syll On How to Get Away With Scientific Fraud With Economics Textbooks

By Lars P. Syll
As is well-known, Keynes used to criticize the more traditional economics for making the fallacy of composition, which basically consists of the false belief that the whole is nothing but the sum of its parts. Keynes argued that in the society and in the economy this was not the case, and that a fortiori an adequate analysis of society and economy couldn’t proceed by just adding up the acts and decisions of individuals. The whole is more than a sum of parts. This fact shows up already when orthodox – neoclassical – economics tries to argue for the existence of The Law of Demand – when the price of a commodity falls, the demand for it will increase – on the aggregate. Although it may be said that one succeeds in establishing The Law for single individuals it soon turned out – in the Sonnenschein-Mantel-Debreu theorem firmly established already in 1976 – that it wasn’t possible to extend The Law of Demand to apply on the market level, unless one made ridiculously unrealistic assumptions such as individuals all having homothetic preferences – which actually implies that all individuals have identical preferences.

This could only be conceivable if there was in essence only one actor – the (in)famous representative actor. So, yes, it was possible to generalize The Law of Demand – as long as we assumed that on the aggregate level there was only one commodity and one actor. What generalization! Does this sound reasonable? Of course not. This is pure nonsense!
Read rest here.