Sunday, March 11, 2012

Sonnenschein–Mantel–Debreu theorem is Hogwash

The Sonnenschein–Mantel–Debreu theorem (named after Gérard Debreu, Rolf Ricardo Mantel, and Hugo Freund Sonnenschein) is a result in general equilibrium economics. It states that the excess demand function for an economy is not restricted by the usual rationality restrictions on individual demands in the economy. Thus microeconomic rationality assumptions have no equivalent macroeconomic implications. Its main implications are that with many interdependent markets the economic equilibrium may neither be unique nor stable. As Rizvi has stated it,[1] it is a "deeply negative result" for macroeconomic research. Wiki

OK, the counter example. When was the last time you bought a carton of eggs and found 13 eggs in the carton? When was the last time you bought a carton and found 11? When was the last time you bought a carton of aggs, one was broken and the grocer refused to replace it? What happens when eggs are expensive? The grocer cuts the carton in half and sell by the half dozen.

That is pretty damn stable, and on a macroeconomic basis I can compute the structure of flow in the egg business. My guess is the continuity assumption screwed their theory up, the economy is stable but not continues. I will look into this some more, but the stability come from the limited solution sets available. Optimum flow of goods only exists to the extent that we can separate them in the flow, hence the Gibbs separation and quantization and maximum entropy encoding.

8 comments:

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Daeros said...

your debunking concedes the primary point steve keen was trying to make. That consumers are not rational. By way of arguing that the supplier or the agent of demand behaved irrationally you concede the very point you're trying to argue against. Consumers are not rational, chaos rules and people don't shop the same damn way.

Daeros said...

you have debunked the theory by conceding it's accurate. Your response is self refuting.

Daeros said...

if consumers are NOT rational and do not behave rationally then they buy according to individual (not globalizable) preferences that are utterly unprogramable and unpredictable. The act of buying itself is an emergent an unpredictable deed and your theories have no bearing on macroeconomics because you cannot amalagaize two consumers together who buy based on preferences no one can even begin attempt to understand or "create" any attempts to amalgalize truly random purchases into a theory of macroeconomic consclusions would immediately fall on it's face because you are attempting to predict the behavior of the utterly unpredictable. Do they behave rationally or irrationally today? even rolling a dice isn't as unpredictable. only radioactive decay itself would be as "Random" as that.

Anonymous said...

your current debunking concedes the main point steve keen was scheming to make. That customers are certainly not reasonable. By way of arguing how the dealer or the adviser of demand socialized irrationally you acknowledge the very stage you might be attempting to argue towards. Individuals are not logical, mayhem rules and people never look exactly the same damn way.
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Anonymous said...

You are making a fundamental logical error. Mainstream economics reasons from individual behavior to macroeconomics. This is like saying A => B. Using the logic of the argument that derives this implication, the SMD conditions augment it to A => B iff C, where "C" is the condition of identical consumers and universally homothetic goods. Since C is not satisfied in the real world, critics like Keen argue that A cannot => B.

Your counter argument starts with B, namely that you observe markets to be stable. From this you seem to infer that A, the orthodox account of individual and market behavior, must be true. But many heterodox theories, such as institutionalism or regulation theory, offer alternative explanations that claim to explain patterns such as you describe and do not suffer the logical/empirical shortcomings implied by the SMD conditions.

Therefore, I do not see how your argument carries any weight.

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