Comment by morningseagulls | Hacker News Reader

Comment by morningseagulls | Hacker News Reader

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morningseagulls

>The D in SMD was actually awarded the nobel prize in economics.

Debreu's work on general equilibrium, which was the basis of the award, had to skirt around the SMD theorem:

>Prize motivation: "for having incorporated new analytical methods into economic theory and for his rigorous reformulation of the theory of general equilibrium."[0]

In order for the Arrow-Debreu model[1] to give a unique equilibrium, which is usually desired, some strong (arguably, unrealistic) conditions must be assumed, otherwise there can be multiple equilibria, as guaranteed by the SMD theorem.[2]

In particular, the SMD theorem asserts that any polynomial function can be a market demand function, which fundamentally breaks the so-called "law" of demand in neoclassical economics. This is because most polynomial functions are not monotonically decreasing[3], as required by the "law" of demand, but give rise to demand curves that can curve up or down arbitrarily. As an example of such a function, just think of the curve generated by a generic cubic polynomial.[4]

This "anything goes" situation then leads to non-unique equilibria, since a supply curve can now intersect the market demand curve at more than one point. But since an equilibrium point is supposed to be where welfare is maximised in a society, the existence of non-unique equilibria means that there can be multiple economic arrangements under which social welfare is maximised. Then it's a matter of taste (i.e. "ideology") to decide which equilibrium point a society wants to be in.

[0] https://www.nobelprize.org/prizes/economic-sciences/1983/deb...

[1] https://en.wikipedia.org/wiki/Arrow%E2%80%93Debreu_model

[2] https://en.wikipedia.org/wiki/Sonnenschein%E2%80%93Mantel%E2...

[3] https://en.wikipedia.org/wiki/Monotonic_function

[4] A graph of such a curve is shown here: https://en.wikipedia.org/wiki/File:Monotonicity_example3.png

> Debreu's work on general equilibrium, which was the basis of the award, had to skirt around the SMD theorem:

Watch out for moving the goalposts. He was awarded the nobel prize after all. "Rigorous reformulation" does not sound like skirting at all.

> This "anything goes" situation then leads to non-unique equilibria, since a supply curve can now intersect the market demand curve at more than one point. But since an equilibrium point is supposed to be where welfare is maximised in a society, the existence of non-unique equilibria means that there can be multiple economic arrangements under which social welfare is maximised.

Economy (or climate or orbits) exhibit chatoic and complex behaviour and it is not surprising that they can have multiple stable points (look up bifurcation diagrams for a simple representation of chatoic solutions). If I am not mistaken, one can hear such things routinely in university economy classrooms today especially when giving caveats about models being wrong in general. Even when you include game theory and Nash equilibria with respect to economic solutions, there might not be efficient ways to reach the equilibrium points at all!

> Then it's a matter of taste (i.e. "ideology") to decide which equilibrium point a society wants to be in.

That is to assume that every equilibrium solution you get is tied to a specific policy or a set of them (or even more, an ideology!) or that points can be reached easily which are very strong assumptions. Maybe some ideologies don't exhibit any reachable equilibrium points or pertain only to unstable ones.

>Watch out for moving the goalposts.

Says the one who's been moving the goalposts in the first place. The point of this thread was about whether or not the Nobel prize in economics was anti-intellectual and ideologically biased. You chimed in with:

>>>The D in SMD was actually awarded the nobel prize in economics.

Which is why I responded, because this was a non-sequitur and an appeal to authority (of the people awarding the prize, and the question was whether or not these people were biased).

>He was awarded the nobel prize after all.

That means nothing in the context of this thread, and is another appeal to authority.

>"Rigorous reformulation" does not sound like skirting at all.

The SMD theorem was a big deal, yet Debreu wasn't awarded the prize for that, but for a rigorous reformulation of Walrasian equilibrium,[0] which has very strong assumptions.

In particular, that rigorous reformulation, known as the Arrow-Debreu model,[1] fails under weaker (i.e. more realistic) assumptions, because of the SMD theorem.

This is skirting the issue.

>Economy (or climate or orbits) exhibit chatoic and complex behaviour and it is not surprising that they can have multiple stable points (look up bifurcation diagrams for a simple representation of chatoic solutions). If I am not mistaken, one can hear such things routinely in university economy classrooms today especially when giving caveats about models being wrong in general. Even when you include game theory and Nash equilibria with respect to economic solutions, there might not be efficient ways to reach the equilibrium points at all!

A few points:

- It's nice and all that caveats are being given, but what tools are being taught to economics undergrads to handle chaotic and complex behaviour? Please supply links to some university course syllabus as evidence (I'm happy to read material in a language other than English).

- If economics students aren't being taught tools to handle chaotic and complex behaviour, then giving caveats is just paying lip service.

- Game theory and Nash equilibria are tools to deal with equilibria, which is what neoclassical economics is comfortable with. To be more realistic, you need to look at what happens in disequilibria, as you've pointed out yourself.

- Chaos theory also showed that equilibria may never be attained at all by a system, so the obsession with equilibria in economics is, at best, unproductive.

>That is to assume that every equilibrium solution you get is tied to a specific policy or a set of them (or even more, an ideology!) or that points can be reached easily which are very strong assumptions. Maybe some ideologies don't exhibit any reachable equilibrium points or pertain only to unstable ones.

Agreed. Unfortunately, neoclassical economics, thanks to its underlying ideology, assumes that equilibrium points can be reached by the "free market" and are desirable.

[0] https://en.wikipedia.org/wiki/Competitive_equilibrium

[1] https://en.wikipedia.org/wiki/Arrow%E2%80%93Debreu_model

"Then it's a matter of taste (i.e. "ideology") to decide which equilibrium point a society wants to be in."

I think this statement is quite representative of the world we live in, don't you? My personal experience is, strongest adherents to an ideology are the least productive people .

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