The Sonnenschein-Mantel-Debreu results after thirty years (2006) [pdf]
citeseerx.ist.psu.edu
citeseerx.ist.psu.edu
The very abbreviated TL;DR of this post is:
1. We are taught that markets look like this: https://upload.wikimedia.org/wikipedia/commons/8/8c/Supply-d...
2. By applying rigorous math ("general equilibrium theory"), it turns out that there is no reason that markets can't look like this instead: https://upload.wikimedia.org/wikipedia/commons/a/ab/SMD_Dema...
3. OP's article summarizes how economists have reacted to this problem.
Inconveniently for all economic theories, the implication of this mathematical proof is that excess demand and supply curves can take any shape that meets those three conditions. The nicely sloped supply and demand curves we've all been shown in Economics textbooks are basically figments of economists' imaginations.
Moreover, the textbook supply-demand curves we've always been shown are for only one good. The curves for all goods in a market economy are high-dimensional.
High-dimensional supply and demand curves can have multiple equilibrium points, and there is no guarantee that those points will be optimal or even good.
In other words, for a long time we've had proof -- proof! -- that "free markets" are not guaranteed to converge toward good outcomes.
Markets can get stuck in crappy equilibria.
But if it were anything other than a talking point, I’d expect the possibility of complex Laffer curves with multiple local maxima.
Homogenous of degree 0, which is key to the conditions of the results in OP, means f(tx) = t^0 f(x) = f(x)
Honest question: what is "the right information"? Unless you want someone choosing what is and is not the right information, which feels like market distortion, then "the right information" becomes "all possible information". And in practice, we as consumers don't even have a thousandth of "all the information", let alone a hundredth, let alone half. (For example, where can I look up the details of the entire supply chain of this phone in my hand, for every single material input it requires, to know what degree I'm culpable in supporting slave labor, which is something that would influence my purchasing decision?)
And then even if we gave someone all the information, or even some useful approximation of all the information, are humans even capable of using that to make decisions that are informed enough to allow markets to approach any sort of rationality? Given finite time, isn't it possible that the amount of time required to make a single informed decision is longer than a lifespan?
So then the question is, if useful amounts of information are neither practically available nor practically actionable, what might that imply about our absolute faith in market mechanisms that require the right information to operate efficiently?
We make decisions based on partial information, processed in a probabilistic manner. The logically right way to reason involves the update of a Bayesian network - each belief ties to each other belief. But updating a Bayesian network - even approximately, is an NP complete problem.
So we not only can't make a correct decision, we can't even try to approximate it in reasonable time. We can only apply crappy heuristics. Like, "Are you with me or against me?" Hence political alignment replaces our decision making. Even for apparently pure economic decisions.
not least as "consumers" idon't make economic decisions wrt to some a priori set of N weighted dimensions within which a gradient of desirability is defined, or in fact by any set of such dimensions.
They mostly make discretionary decisions wrt to a set of influences triggers habits and cues most of which are not about information or rational processes.
A hobby horse is that an increasing number of these are manipulated by those in a market with the resources to identify exploit them.
This is not uniquely the case for those making discretionary spending decisions... but it for those of us, that dissatisfaction—or dis-satiation—seems to perpetually "find its level." (I.e. the post-orgasmic clarify of the satisfaction of the craving, soon evaporates like the dew.)
The phenomenon of perpetual unsatisfiable desire for the Next Thing is so ubiquitous and accepted we don't even attend to it any longer; and so baked in that 2500 year old Greek myth gives us well-known parables (c.f. the myth of Tantalus).
Related: so, GLP-1 drugs like Ozempic have had discernible macroscopic impacts on "consumption" across many economic categories, enough so that the Economist magazine had a story IIRC on unease in industries most obviously based on addictive behavior.
I am curious whether there has been a partiuclarly-discernible impact in "expensive hobbies" defined by constant pursuit of the Next Better Thing e.g. audiophiles, collectors, constant-tinker hobbies like mechanical keyboards, modular synthesizers, etc..
The battle in the heavens of our psyches may be waged for the next period between GLP-1 agents on the one hand, and exploitation of ML on the other, uniquely powerful tool as it is for identifying and tuning efficacious triggers for addictive behavior.
See e.g. Akerlof, George A. (1970). "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism"
Akerlof shared the 2001 Nobel Prize in Economic Sciences with A. Michael Spence and Joseph E. Stiglitz for work on the impact of information asymmetry on markets.
In practice, the question becomes what systems result in the best outcomes given normal conditions and information. As a example, we see that total command economies are dramatically worse than markets at normal amounts of information. Alternatively, how can conditions be changed in normal fashions that can be consistently enforced to maximize system outcomes.
Things are further confused by the fact that we have a very poor understanding of even the implemented systems. What aspects are important, what are not? For instance, we can see that the modern Chinese economy is clearly more market-driven than previously, so the increased amount of market economics has been a dramatic improvement. Clearly, they were previously on the "too little market" side of that equation. In many ways, their markets are more "unrestricted" than the USA, but in others less, are they more market-driven than the USA or not? Are the ways in which they are important, are the ways in which they are not important? About the only thing we can really categorize are directional changes from a previous status quo and maybe we can categorize transformative impacts after the fact.
It is these sorts of questions and observations that matter. Quibbling about how a system is imperfect in a wholly impractical limit to argue against practical matters is just silly especially when those same problems are held by literally everything.
There are a lot of business people and government officials for whom the notion of "free, unfettered markets" is akin to a religious goal. Look around you.
There are NO guarantees that markets will work well. They CAN lead to horrific equilibria, like inequality so extreme that large groups of people cannot afford food and shelter without government assistance, or financial crises that seem to come "out of nowhere," with too many possible culprits that could be blamed (greedy speculators, greedy financiers, complacent banks, idiotic regulators, government-sponsored entities, etc.), depending on who you ask.
I say, let's be humble, open-minded, willing to try new things, and willing to change our views when the facts disagree with them.[a]
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[a] In the words of Lee Kuan Yew, who led the transformation of Singapore from one of the poorest to one of the wealthiest societies on earth:
> My life is not guided by philosophy or theories. I get things done and leave others to extract the principles from my successful solutions. I do not work on a theory. Instead, I ask: what will make this work? If, after a series of solutions, I find that a certain approach worked, then I try to find out what was the principle behind the solution. So Plato, Aristotle, Socrates, I am not guided by them…I am interested in what works…Presented with the difficulty or major problem or an assortment of conflicting facts, I review what alternatives I have if my proposed solution does not work. I choose a solution which offers a higher probability of success, but if it fails, I have some other way. Never a dead end.
> We were not ideologues. We did not believe in theories as such. A theory is an attractive proposition intellectually. What we faced was a real problem of human beings looking for work, to be paid, to buy their food, their clothes, their homes, and to bring their children up…I had read the theories and maybe half believed in them.
> But we were sufficiently practical and pragmatic enough not to be cluttered up and inhibited by theories. If a thing works, let us work it, and that eventually evolved into the kind of economy that we have today. Our test was: does it work? Does it bring benefits to the people?…The prevailing theory then was that multinationals were exploiters of cheap labor and cheap raw materials and would suck a country dry…Nobody else wanted to exploit the labor. So why not, if they want to exploit our labor? They are welcome to it…. We were learning how to do a job from them, which we would never have learnt… We were part of the process that disproved the theory of the development economics school, that this was exploitation. We were in no position to be fussy about high-minded principles.
"A lot of business people and government officials" ≠ "everyone."
Please don't attack a straw-man.
"A lot of business people and government officials" ≠ "people holding the notion" (your words).
PLEASE STOP attacking a straw-man.
If the notion of market fundamentalism is truly news to you, you may want to start here:
https://en.wikipedia.org/wiki/Market_fundamentalism
https://onlinelibrary.wiley.com/doi/10.1111/j.1467-8292.2009...
https://www.amazon.com/Crisis-Global-Capitalism-Society-Enda...
https://news.harvard.edu/gazette/story/2023/03/excerpt-from-...
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PS. I never said anyone calls it a religious goal. What I did say is that for a lot of business executives and government officials it's akin to a religious goal, i.e., they are unwilling to change their minds about "free markets" even when the facts contradict their beliefs. In fact, they are so unwilling to change their minds that even mathematical proofs -- proofs! -- won't do it.
That is proof that "free markets" are not guaranteed to converge toward good outcomes because it proves that every decision/optimization process that is believed to be even theoretically possible is not guaranteed to converge toward good outcomes. Singling out "free markets" as if they are even somewhat uniquely susceptible is just plain ridiculous. Everything is thoroughly screwed in the presence of arbitrarily complex functions.
As we have now seen and proven that everything is doomed in a arbitrarily malicious universe, it is only prudent to re-focus on problems under normal conditions and figure out the practical question of what systems produce good, high quality outcomes in a normal implementation over normal conditions.
I wish we had more empirical supply-demand curves so we could refine our priors on supply and demand curve shapes, but that's a topic for another day.
I never said we should do away with a market economy. All I said is that market economies are not guaranteed to converge to optimal or even good outcomes.
Markets CAN lead to horrifically bad equilibria (extreme inequality, financial crises, recessions, depressions, etc.). There are no guarantees that they won't.
So let's be humble, open-minded, willing to rely on markets when they work, willing to try other things when they don't.
Please don't attack a straw-man.
Do Scandinavian socialist democracies not count as an exception?
On the flip side, I think you will equally find that whenever free market solutions are applied to public services - healthcare, water, electricity, police, etc - people also die in large numbers. And although wealthy people generated by the free markets are philantropic, it's not in proportion to the harm inflicted on people. Only thing is, we ignore those disasters because they are inconvenient for the narrative.
It seems to be obvious that certain things (like public utilities) should just be controlled directly by the government, without any free markets involved, as long as your objective function is to optimize the average life quality of your citizens.
The closest I can think of are the metros of Tokyo free government takeover, but I am not sure how free those actually were of government regulation.
One of the struggles I have is that typically these public services may be carried out by private companies paid for by the government, but that is just begging for corruption
> Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer, "I have the solution, but it works only in the case of spherical cows in a vacuum."
so tiring.
best line on that paper: Much of the intuition that would seem to follow from the SMD results is still intact. Rationality, as Arrow said, does not have aggregate implica- tions, but now, we have to add, if only aggregate data are available.