The Sonnenschein-Mantel-Debreu Theorem states that the excess demand curve for a market economy of rational agents can take the shape of any function, subject only to three fairly general conditions: the function must be continuous, must be homogeneous of degree zero (https://en.wikipedia.org/wiki/Homogeneous_function), and must satisfy Walras's law (https://en.wikipedia.org/wiki/Walras%27s_law).
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.
Surely it's one thing to say that "curves can take any shape that meets those three conditions" and yet still hold that any observed or realistic actual curves will only take certain shapes - as long as the consumers and producers have the right information.
> as long as the consumers and producers have the right information
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.
It implies that you do not get absolutely 100% perfect allocation where everybody is maximally happy according to their constraints which is what "efficiently" means in that context. That is also a useless and impractical standard to hold any system to as any optimization problem is impossible if you have missing non-degenerate constraints/information.
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.
> 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?
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.
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.
By "right" I mean roughly correct. To your other points I suspect that close to correct is often enough and is more correct over time. But this is where research should be directed I suppose.
The problem is that a lot of people treat those assumptions as if they were sacred, fundamental laws of the universe.
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]
---
[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.
It has been proven that global utility optimization can be equivalent to solving a arbitrarily complex, arbitrarily non-linear, arbitrarily quickly changing, function. Great. There exists exactly zero techniques for solving all such systems even if the function was not unknown.
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.
As I wrote elsewhere on this thread (https://news.ycombinator.com/item?id=42783130), the problem is that a lot of busy people treat the "practical notion" that markets produce good, high-quality outcomes as if it were a fundamental law of the universe. It's not. There are no guarantees. Markets can converge to horrific equilibria. Let's be humble, open-minded, willing to rely on markets when they work, willing to try other things when they don't.
This fundamentally changes the debate on market interventions. It's now possible to argue that the current equilibrium is only meta-stable and that interventions that change the supply and demand curves can potentially kick us out of one meta-stable equilibrium and into another more efficient one.
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.
Free market economics is "singled out" because, at least in the Anglosphere, it is the only type of economy considred to reach an (eventual) optimum by itself.
For even longer time we have a REAL proof (not mathematical wordplay) that whenever, without exception, someone takes a swing at free markets it leads to people dying. IT has always been a disaster and people always have been exiting those societies where that happens towards more free societies. You yourself have plenty of options to go somewhere with less free market - Cuba, Venezuela, North Korea, Russia, even China. Have YOU emigrated to such a country?
> whenever, without exception, someone takes a swing at free markets it leads to people dying
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.
Can you give some examples on actual free market solutions are applied to public services?
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
You also have the option to go somewhere with even more of a free market, like Somalia. Have you emigrated to such a country? It turns out that societies can write laws for mutual benefit.
Oh, I'm a capitalist. I believe Churchill was right when he said that capitalism is the worst economic system ever invented, except for all the others that have been tried before.
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.
I think it's a pretty crude oversimplification to say it's a proof when the whole idea hinges on the whole rational actors axiom. Sure, it might be a proof with that axiom, but it doesn't say much anything about the real world.
I'm not sure I understand what you're saying. The whole edifice of "markets converge toward general equilibrium" rests on the assumption that people are rational, i.e., maximize utility -- which is economist jargon for "people are trying to do better for themselves." If you take away that, the whole theoretical edifice justifying markets collapses.
Sorry, I wrote the equation for homogeneity of degree one by mistake. I edited my post to the link to the Wikipedia page on homogeneity instead. Thanks.
I can't. There's basically no theory behind the "Laffer curve." IIRC, it relies on two assumptions. Assumption #1: If the income tax rate is 0%, the government will collect zero income taxes. This assumption is basically a tautology. No one can disagree with it. Assumption #2: If the income tax rate is the maximum possible, 100%, the Laffer curve assumes the government will collect zero income taxes, because taxpayers will find ways to avoid paying all income taxes. This second assumption is questionable, because taxpayers might successfully avoid paying only some taxes. Even if you agree with both assumptions, there's no agreement as to what tax rate would maximize government tax collections.
Another inconvenient truth for the theorem is that "a market economy of rational agents" is a mathematical fantasy and doesn't describe any real world market ever.
For other reasons I'm reading Adam Smith's Wealth of Nations and this seems like nothing that Smith would object to. He'd say there's a natural price that that the market price gravitates around - very much like that second graphic.
The point is there are multiple "natural prices" that the market price may gravitate around. If Adam Smith thinks there's only one "natural price", then he's wrong, and you probably want to read with that idea in mind.
So the nicely sloped supply and demand curves are economic equivalent of spherical cows and as much as we shouldn't design a milk industry around spherical cows, we shouldn't design an economy around a nicely sloped supply and demand curves.
For anyone here who doesn't get the reference to spherical cows, it's from an old joke:
> 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."
It would be really helpful to see an example of one of these naughty excess demand curves, along with the utility function for each agent. For an economy with a small enough number of commodities and agents that it might be comprehensible, say two or three.
It's an economic theory for characterizing market dynamics. The paper's conclusion: "Thus many of the problematic outcomes from SMD theory remain entrenched."
like every single social science therory dressed as economic research truth, the slight harder look at it crumbles all assumptions.
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.
The Sonnenschein-Mantel-Debreu Theorem states that the excess demand curve for a market economy of rational agents can take the shape of any function, subject only to three fairly general conditions: the function must be continuous, must be homogeneous of degree zero (https://en.wikipedia.org/wiki/Homogeneous_function), and must satisfy Walras's law (https://en.wikipedia.org/wiki/Walras%27s_law).
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.
Surely it's one thing to say that "curves can take any shape that meets those three conditions" and yet still hold that any observed or realistic actual curves will only take certain shapes - as long as the consumers and producers have the right information.
> as long as the consumers and producers have the right information
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?
I can make it worse.
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.
It implies that you do not get absolutely 100% perfect allocation where everybody is maximally happy according to their constraints which is what "efficiently" means in that context. That is also a useless and impractical standard to hold any system to as any optimization problem is impossible if you have missing non-degenerate constraints/information.
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.
> 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?
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.
"Right" is alas undefined and undefinable,
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.
By "right" I mean roughly correct. To your other points I suspect that close to correct is often enough and is more correct over time. But this is where research should be directed I suppose.
The problem is that a lot of people treat those assumptions as if they were sacred, fundamental laws of the universe.
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]
---
[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.
Source: https://www.amazon.com/gp/product/0262019124
Sure let's be humble. I think alleging that people holding the notion of free markets is a religious goal is not a humble opinion.
I did not allege that everyone holding that notion treats it like a religions goal.
"A lot of business people and government officials" ≠ "everyone."
Please don't attack a straw-man.
They're your words. I didn't say everyone. You didn't say everyone. Where's the straw-man?
It has been proven that global utility optimization can be equivalent to solving a arbitrarily complex, arbitrarily non-linear, arbitrarily quickly changing, function. Great. There exists exactly zero techniques for solving all such systems even if the function was not unknown.
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.
As I wrote elsewhere on this thread (https://news.ycombinator.com/item?id=42783130), the problem is that a lot of busy people treat the "practical notion" that markets produce good, high-quality outcomes as if it were a fundamental law of the universe. It's not. There are no guarantees. Markets can converge to horrific equilibria. Let's be humble, open-minded, willing to rely on markets when they work, willing to try other things when they don't.
This fundamentally changes the debate on market interventions. It's now possible to argue that the current equilibrium is only meta-stable and that interventions that change the supply and demand curves can potentially kick us out of one meta-stable equilibrium and into another more efficient one.
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.
Free market economics is "singled out" because, at least in the Anglosphere, it is the only type of economy considred to reach an (eventual) optimum by itself.
Not a disagreement with your take, which was helpful to me, but just your parenthetical aside.
Homogenous of degree 0, which is key to the conditions of the results in OP, means f(tx) = t^0 f(x) = f(x)
[https://en.wikipedia.org/wiki/Homogeneous_function]
Thank you. I inadvertently wrote the equation for degree one homogeneity, from memory. I replaced the equation with a link to the Wikipedia page.
For even longer time we have a REAL proof (not mathematical wordplay) that whenever, without exception, someone takes a swing at free markets it leads to people dying. IT has always been a disaster and people always have been exiting those societies where that happens towards more free societies. You yourself have plenty of options to go somewhere with less free market - Cuba, Venezuela, North Korea, Russia, even China. Have YOU emigrated to such a country?
> whenever, without exception, someone takes a swing at free markets it leads to people dying
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.
Can you give some examples on actual free market solutions are applied to public services?
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
You also have the option to go somewhere with even more of a free market, like Somalia. Have you emigrated to such a country? It turns out that societies can write laws for mutual benefit.
Oh, I'm a capitalist. I believe Churchill was right when he said that capitalism is the worst economic system ever invented, except for all the others that have been tried before.
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.
I think it's a pretty crude oversimplification to say it's a proof when the whole idea hinges on the whole rational actors axiom. Sure, it might be a proof with that axiom, but it doesn't say much anything about the real world.
I'm not sure I understand what you're saying. The whole edifice of "markets converge toward general equilibrium" rests on the assumption that people are rational, i.e., maximize utility -- which is economist jargon for "people are trying to do better for themselves." If you take away that, the whole theoretical edifice justifying markets collapses.
Don't you mean homogeneous of degree one?
Sorry, I wrote the equation for homogeneity of degree one by mistake. I edited my post to the link to the Wikipedia page on homogeneity instead. Thanks.
Ooh, now do the Laffer curve!
I can't. There's basically no theory behind the "Laffer curve." IIRC, it relies on two assumptions. Assumption #1: If the income tax rate is 0%, the government will collect zero income taxes. This assumption is basically a tautology. No one can disagree with it. Assumption #2: If the income tax rate is the maximum possible, 100%, the Laffer curve assumes the government will collect zero income taxes, because taxpayers will find ways to avoid paying all income taxes. This second assumption is questionable, because taxpayers might successfully avoid paying only some taxes. Even if you agree with both assumptions, there's no agreement as to what tax rate would maximize government tax collections.
In other words, nobody can draw the curve, but people assume it is a simple shape with a single maximum…which is why I made my silly request.
But if it were anything other than a talking point, I’d expect the possibility of complex Laffer curves with multiple local maxima.
Another inconvenient truth for the theorem is that "a market economy of rational agents" is a mathematical fantasy and doesn't describe any real world market ever.
I didn't know anything about this and found the article hard to understand at first, but thankfully the Wikipedia articles on the subject are pretty okay: https://en.wikipedia.org/wiki/Sonnenschein%E2%80%93Mantel%E2...
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.
For other reasons I'm reading Adam Smith's Wealth of Nations and this seems like nothing that Smith would object to. He'd say there's a natural price that that the market price gravitates around - very much like that second graphic.
The point is there are multiple "natural prices" that the market price may gravitate around. If Adam Smith thinks there's only one "natural price", then he's wrong, and you probably want to read with that idea in mind.
So the nicely sloped supply and demand curves are economic equivalent of spherical cows and as much as we shouldn't design a milk industry around spherical cows, we shouldn't design an economy around a nicely sloped supply and demand curves.
For anyone here who doesn't get the reference to spherical cows, it's from an old joke:
> 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."
Source: https://en.wikipedia.org/wiki/Spherical_cow
It would be really helpful to see an example of one of these naughty excess demand curves, along with the utility function for each agent. For an economy with a small enough number of commodities and agents that it might be comprehensible, say two or three.
It's an economic theory for characterizing market dynamics. The paper's conclusion: "Thus many of the problematic outcomes from SMD theory remain entrenched."
like every single social science therory dressed as economic research truth, the slight harder look at it crumbles all assumptions.
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.