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The First Fundamental Theorem of Welfare Economics
The first fundamental theorem of welfare economics is often misunderstood, especially by technical economists. Briefly, the theorem says that a market outcome is efficient (Pareto-optimal). The theorem, as proven with great mathematical beauty by Arrow and Debreu, requires a number of reasonably strong assumptions such as very large numbers of buyers and sellers who have perfect rationality and perfect information.
Since the conditions required for the theorem's proof are unlikely to hold in the real world it's common for people to reverse the theorem to suggest that markets cannot be efficient. Thus Rodrik says:
The First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions.
Now what is wrong with this is very simple. The First Theorem gives sufficient conditions for a market to be efficient it does not give necessary conditions.
Thus, as a matter of logic, the fact that the theorem's conditions are not satisfied does not prove that market outcomes can be improved, even by "well-designed" interventions.
As an empirical matter, the difference between the sufficient and necessary conditions turns out to be quite large. We know from Vernon Smith's work, for example, that markets can be competitive with only a handful of traders; nor do the traders have to be perfectly rational. In fact, markets can be very efficient with zero-intelligence traders.
Perhaps even more importantly technical economists seem to think that the First Theorem is the ultimate expression of "the invisible hand" or what makes markets good but in fact the First Theorem is but a pinched and limited expression of the virtues of markets. The First Theorem, for example, says nothing about innovation, experimentation, or the discovery process. Nor does the First Theorem say anything about markets and political philosophy. You will not learn from the First Theorem that markets are not simply a "mechanism," markets are peaceful exchange.
To be clear, I am correcting a misuse of the First Theorem. I am not asserting that markets are always perfectly efficient. But really what kind of standard is perfect efficiency anyway? The internal combustion engine isn't even close to being perfectly efficient but my car gets me to work every day, is fun to drive and gives me the freedom of the open road.
Posted by Alex Tabarrok on August 13, 2007 at 07:24 AM in Economics | Permalink
Comments
Rodrik is on the run. Please keep up the chase!
Posted by: Rue Des Quatre Vents at Aug 13, 2007 8:00:05 AM
You criticize Rodrik's logical ability, but then dispense with using mathematical logic to defend the unfettered market mechanism. Disingenuity! You have as much claim of the efficiency of markets as Rodrik has of interventions improving inefficiency. It's a matter of default assumptions, which require inductive reasoning, since deductive logic has yet to provide answers. However, if you take a look at the work done in General Equilibrium Theory, you will realize the numerous restrictions are needed as conditions to prevent the existence of multiple equilibria, and sunspot equilibria. Furthermore, the price=adjustment mechanism is a huge unknown, but in this regard Vernon Smith's work suggests that in a simple market convergence to a market price is rapid. This does not allow one, however, to infer this to be the case in a widely-dispersed, far-less-than-perfect market.
"But really what kind of standard is perfect efficiency anyway?" And what kind of hocus-pocus is this? One can estimate the efficiency of an internal combustion engine. True, it is not perfectly efficient, but one can make "interventions" to improve its efficiency. What is the measure of a market's efficiency? If a market is less than perfectly efficient, why is it not plausible to design interventions to improve its efficiency? Certainly this is not an illogical claim, nor one that can be ruled out without examination of details of the specific intervention. Your position (somewhat implicit) is that no such intervention could possibly exist. The word to describe your stance is dogmatic.
And furthermore, don't revise and weaken the definition of efficiency by uncritically applying a poor analogy to support your free-market dogmatism. Efficiency is too important a definition for this. Your last paragraph suggests internal combustion engines is the pinnacle of transportation mechanisms.
Posted by: samson at Aug 13, 2007 8:23:18 AM
Excellent critique!
Posted by: paul at Aug 13, 2007 8:39:10 AM
oops...
"Furthermore, the price-adjustment mechanism is a huge unknown, but in this regard Vernon Smith's work suggests that in a simple market convergence to a market price is rapid. This does not allow one, however, to infer this to be the case in a widely-dispersed, far-less-than-perfect-information market."
Posted by: samson at Aug 13, 2007 8:45:47 AM
From the perspective of Niklas Luhmann's complex systems theory,
www.hedweb.com/bgcharlton/modernization-imperative
there is no such thing as perfect efficiency since any system which is measuring efficiency has access to only a sample of information from an infinitely complex environment; and the system which is measuring efficiency is itself of finite complexity.
In practice, efficiency is measured on a finite sample processed for a finite length of time by an observing system of finite complexity. And the measurement of efficiency is a comparison between systems.
So, the answer to the question of whether a market can be made more efficient by more or fewer interventions can be modelled comparatively by an observing system (using a sample of data run for a finite time by a model of finite complexity) or else the comparison can be made by running the systems in competition, in real time, for a finite time - and then either making a comparison (based on a finite sample of observed data) or by seeing which one grows and which one shrinks/ goes extinct.
This latter approach has been done for a variety of command economies compared with more market orientated economies.
Although market orientated systems seem to outperform command economy systems in many contexts, this answer can never be *absolutely* compelling since all comparisons involve a selective sample of data over a finite period of time.
It can always be (logically) suggested that a different sample of information, different processing of this information, or a longer period of observation) might have yielded a different result.
Nonetheless, a meta system of policy strategy might include the result of such efficiency comparisons into its information processing, by favouring market orientated systems of organization as a first line policy.
Posted by: Bruce G Charlton at Aug 13, 2007 8:50:38 AM
Am I the only one deeply put off by Alex Tabarrok's tone?
I very often deeply miss Tyler Cowen when reading posts by Alex Tabarrok. Both on substance and on delivery.
Posted by: AM at Aug 13, 2007 9:13:02 AM
AM - the answer is no.
And I am not sure that, in this case, Alex's logic stands.
I read Rodik as saying that the long line of prerequisites for the first theorm, and their absence in the real world means that a well designed intervention can bring about a situation which satisfies the the prerequisites and is therefore results in pareto optimality.
The logic is sound.
Now, as Rodik is a "second best" economist he is interested in finding ways to make things better and is not trying to design the perfect intervention (which I suspect he thinks is impossible anyway).
Posted by: tadhgin at Aug 13, 2007 9:22:29 AM
The First Fundamental Theorem of Welfare Economics is proof that unfettered markets work best? No, not at all. The theorem merely provides a set of sufficient conditions for reaching an optimum. It is mostly used by critics of the market, who fallaciously argue that the failure of one of the sufficient conditions to hold is proof that the unfettered market is not best (as though we were talking about a necessary condition). The reasons for believing (not “proof,” because it’s not a mathematical proposition) that unfettered markets work best are not in Arrow-Debreu but in Mises, Hayek, and Kirzner.
Posted by: Lawrence H. White at Aug 13, 2007 9:35:12 AM
Larwrence White's paragraph (and post) is spot on. I regret not seeing it earlier and including a link.
AM - don't you think it's a bit rude to insult someone in their own house?
Posted by: Alex Tabarrok at Aug 13, 2007 9:55:45 AM
Not only Vernon Smith's work. The striking failure of experimental economics to observe oligopolistic behavior is a major reason that I've always thought that markets are more efficient than they look. See Friedman and Ostroy, http://ideas.repec.org/a/ecj/econjl/v105y1995i428p22-53.html
Posted by: Jonathan at Aug 13, 2007 10:05:06 AM
2 does not follow from 1:
1: If (long list of prerequisites for equilibrium obtains) then Pareto-efficient.
2. If not (long list of prerequisites does not obtain) then not Pareto-efficient.
Does Alex really need to write this out in symbolic logic form for you to be satisfied, Samson? It should be obvious that 2 doesn't follow from 1 to anyone who has had a week of intro to logic.
Posted by: J. at Aug 13, 2007 10:06:34 AM
AM,
Yah! If you want to insult someone, get your own blog and use THAT to complain about how they are offering the worst argument you've ever seen. I mean, let's be civilized here.
Posted by: Student at Aug 13, 2007 10:09:58 AM
Theorem: If one bakes a relatively flat piece of salty dough, covers with tomato sauce and molten cheese, one has a pizza.
If it is missing tomato sauce, is it a pizza?
Perhaps. A four cheese pizza, maybe.
Could one stage an intervention to make it more pizza like? Perhaps sun dried tomatoes, and it becomes a pizza margherita.
Posted by: Link at Aug 13, 2007 10:29:24 AM
Efficiency is a secondary effect and not a primary characteristic of markets. Policies that get boresighted on effficiency are putting the cart before the horse.
Posted by: Al Abbott at Aug 13, 2007 10:33:40 AM
Alex: A perfectly efficient internal combustion engine for the price of current internal combustion engines would blow away all existing forms of energy to about the degree that cold fusion would. Easily the most important technological development since the internet. Double digit impact on size global economy. Therefor, it's a fairly poor example of (we don't need perfect efficiency).
Posted by: michael vassar at Aug 13, 2007 10:38:48 AM
It sometimes seems to me that there is a metatheorem (waiting to be proved? or that I am too ignorant to know of?) about improving market efficiency: it is easy for the government to improve market efficiency if the government actors are smarter and/or have better information than the private market actors.
The converse, that it's not so easy if the market actors are as smart and knowledgeable as government actors, is probably going to be hard to prove as long as we are only making baby steps in precise reasoning about knowledge. ("Baby steps" is my impression from, among other things, composing a machine-checkable proof of part of the fundamental theorem of arithmetic. Reasoning about reasoning about the real world seems to be considerably harder than reasoning about reasoning about basic math, which seems to be quite hard.)
A similar "of course there is arbitrage for government" result applies if we enforce a taboo on private actors profiting from picking up on arbitrage opportunities that both they and government actors can see. E.g., if we take as fixed axioms that there will be rules where private actors can expect "windfall profits" to be taken away, or where various private coalitions are prohibited in the name of antitrust, or where it is forbidden to make long-term contracts in stable currencies because that would interfere with wise currency fiddling for macroeconomic manipulation, then there are likely to be opportunities for governments to improve on market outcomes in long term energy markets or infant industries --- if only just by partially mocking up the obvious market outcomes in the absence of such rules.
I would be more impressed by people arguing for industrial policy or macroeconomic stabilization or whatever if they more commonly took some time to state explicitly whether their justification involved the state actors being smarter or more knowledgeable or otherwise perfect than the private actors, and/or identifying and justifying assumptions that private actors won't pick up on arbitrage opportunities. I will be pleasantly surprised if someone can point to Rodrik doing much of this (or at least citing people doing it for him) for the policies he supports.
There is also a metrics issue: if the losses to the treasury from the 1980s S&L fiasco ca. trouble you less than the losses to depositors from 1930s bank failures Because They Were Firmly Under Central Control, or if deaths from FDA delays trouble you less than deaths from unregulated drugs because BTWFUCC, then it's pretty easy for central control to have a less bad outcome...
Posted by: William Newman at Aug 13, 2007 10:49:22 AM
OK, let me fix this for Alex:
The First Fundamental Theorem of Welfare Economics suggests, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions.
Feeling better now?
Posted by: Dan Karreman at Aug 13, 2007 10:55:05 AM
J, I do not understand you. I understand that your statement #2 does not follow from #1, but what does this have to do with what I said? I did not (and do not) disagree with Alex's explication of the First Welfare Theorem, that the conditions are not necessary, but sufficient. So what's your deal?
Posted by: samson at Aug 13, 2007 11:11:45 AM
"The First Fundamental Theorem of Welfare Economics suggests, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions."
This is a better statement, but it seems important to note that we know absolutely nothing about these interventions except that it is possible they exist. If you think about it, that is a fairly watered down conclusion. If there is a complaint, it might be that 'well designed' is a monumentally loaded descriptor.
As William Neuman suggests above, there is an element of hubris in the idea that the electoral process will come up with people who know enough to design these interventions, or even that such people would be available in Plato's Republic.
Posted by: JasonL at Aug 13, 2007 11:21:46 AM
Actually, both Rodrik and Tabarrok misuse the mathematics. The first fundamental theorem is just about particular mathematical relationships between abstract concepts. It isn’t, in itself, a “pinched and limited expression of the virtues of markets” as Alex put it, or a reason to intervene in social and economic interrelationships between real people (as Rodrik asserts).
If you take his statement literally, Rodrik's logical error is the more egregious. But a more sympathetic reading of Rodrik's post would allow that he was trying to characterize a broad group of economists in quick brush strokes. He wasn't doing the math, just using the 'first theorem' metaphorically to stand in for an attitude toward markets, and to dress up that attitude in the language of academic economics.
You might try to make the theorem into a statement about social relationships, certainly many economists do, but it requires a fairly fundamental (il)logical leap to assert that the problem is with the world when it doesn't fit some economists’ mathematical model.
The real problem here isn’t so much the constant fallacy of misplaced concreteness that underlies many applications of technical economics to policy issues, but the use of “science talk” to dress up the preexisting attitudes and policy preferences.
Posted by: Mike Giberson at Aug 13, 2007 11:28:24 AM
I think Rodrik intended to say something like, "given that many of these prerequisites often do not hold, a market outcome is not always as efficient as it can be, and can often be improved upon by government intervention." A conclusion like that follows from what he said in the beginning of the paragraph that Alex cites.
Those in the second group are inclined to see all kinds of complications, which make the textbook answers inappropriate. In their world, the economy is full of market imperfections (going well beyond environmental spillovers), distribution and efficiency cannot be neatly separated, people do not always behave rationally and they over-discount the future, some otherwise undesirable policy interventions can generate positive outcomes, and general-equilibrium complications render partial-equilibrium reasoning suspect.
Rodrik sloppily uses the word "proof", which Alex pounces on. J. is correct, Alex wins because Rodrik and the other second-best economists haven't proven anything. However, it's not difficult to see the point that Rodrik is trying to make when you put it in the context of the rest of the paragraph. Thus, I think that Alex's reading is pedantically correct, albeit slightly disingenuous.
And it's a little shocking to see Alex take umbrage at AM's comment, being that he seems to delight in using a combatative tone to incite those he disagrees with.
He wrote: You know exactly what the post means and it makes you mad as hell. Alex.
Posted by: eriks at Aug 13, 2007 11:30:32 AM
Samson, Mike's criticisms may be perfectly apt here. My complaint was that Alex was doing a pretty limited thing that didn't need mathematical logic. First, he wanted to point out that many economists come close to making a fallacy of inferring 2 from 1. Second, he wanted to provide some reasons to think that an inductive inference isn't safe either. He wasn't trying to prove in 400 words that unfettered markets are the most superior form of social organization.
Posted by: J. at Aug 13, 2007 11:32:07 AM
Are there government actions that could improve efficiency? I have no doubt that there are, but they are most certainly not the types of actions that people like Rodrik would advocate.
Given that a market is not perfect, it is certainly true there are actions that can move it towards the optimum (if one thinks that is a worthy goal), and those actions are determined by trial and error by the actors within the market, and in an iterative fashion. The problem that I see with governmental intervention is that evaluation of the outcomes is never based on the same set of better/worse observations that take place every second of every day in the market. Government failure is not penalized by market forces the way private actors are for being wrong. The errors of government grow year by year, only occassionaly offset by it's successes, and the successes are never open solely to governmental discovery. Given the present, I think an overpowering argument can be made that the best governmental actions are disengagement from the market.
Posted by: Yancey Ward at Aug 13, 2007 11:55:11 AM
Student (10:09:58 AM) made me laugh real hard. S/he seems to have a point, too.
Posted by: Michael Ward at Aug 13, 2007 12:23:50 PM
"But really what kind of standard is perfect efficiency anyway?" Are you discarding the only proof of the condition of "not making anyone worse off?" I.e., are you discarding part of "freedom?"
Similarly your internal combustion engine, by being inefficient, is a contributor to lung disease and climate change. Will this impair the lives of others? You will disprove this, how?
Posted by: Lee A. Arnold at Aug 13, 2007 12:41:44 PM
