The First Fundamental Theorem of Welfare Economics

by on August 13, 2007 at 7:24 am in Economics | Permalink

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.

1 Rue Des Quatre Vents August 13, 2007 at 8:00 am

Rodrik is on the run. Please keep up the chase!

2 paul August 13, 2007 at 8:39 am

Excellent critique!

3 Bruce G Charlton August 13, 2007 at 8:50 am

From the perspective of Niklas Luhmann’s complex systems theory,

http://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.

4 tadhgin August 13, 2007 at 9:22 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).

5 Alex Tabarrok August 13, 2007 at 9:55 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?

6 J. August 13, 2007 at 10:06 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.

7 Link August 13, 2007 at 10:29 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.

8 michael vassar August 13, 2007 at 10:38 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).

9 Dan Karreman August 13, 2007 at 10:55 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?

10 JasonL August 13, 2007 at 11:21 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.

11 eriks August 13, 2007 at 11:30 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.

12 Yancey Ward August 13, 2007 at 11:55 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.

13 Lee A. Arnold August 13, 2007 at 12:41 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?

14 Daniel Klein August 13, 2007 at 12:47 pm

I like Tyler’s tone–and Alex’s tone! We need bargainers and challengers. The “tone” criticism of Alex is perhaps partly a way of evading his substantive challenges.

15 Lee A. Arnold August 13, 2007 at 1:55 pm

Ronald Coase argued decisively (1937) that market outcomes are regularly improved by well-designed interventions. He called them “business firms.” And he showed later (1960) in “The Problem of Social Cost” that institutions in general are a widespread phenomena. Why? Because of costs. Some people maintain that Coase actually proved that by awarding property rights you can gain efficiency. Nonsense. That twists his argument, and he rejected it. Anyhow, around here, we’re throwing out efficiency.

16 Barkley Rosser August 13, 2007 at 2:10 pm

So, there are two arguments here and at least three schools of thought that are
banging into each other in the above commentary.

The arguments have to do with necessary versus sufficient conditions and then
with static versus dynamic efficiency. The three schools of thought are conventional
public finance a la Richard Musgrave (Rodrik’s view), Chicago school/public choice
free market view that accepts neoclassical analysis (Alex’s view, mostly), and the
Austrian view supported more by some of the commentators.

So, yes, the theorem is about sufficiency conditions, not necessary ones. Failure
of a condition to hold does not prove anything should (or can) be done by government.
OTOH, for all its abstraction one reason the Musgravian public finance school (and
Rodrik) point at it is that the conditions do seem to be linked with phenomena in
the real world that seem to be associated with misbehavior of sorts in the economy,
even if one does not like the Pareto criterion. Competition is a condition, and
monopoly power seems to be a problem sometimes (btw, the magic number from the
experiments seems to be four, that or above and usually pretty competitive).

Also, the completeness of markets condition has been seen to be tied to problems
associated with collective consumption goods and externalities with high transactions
costs or poorly defined property rights. And everybody also realizes that poor
information can be a problem, although it is probably least clear on this one that
government can do much about it.

So, the Chicago/public choice school accepts the theorem. However, it follows
the argument, stated by many here, that the government itself is inefficient,
bureaucratic, controlled by special interests, etc. etc. etc. and that therefore
even if there are these static inefficiency problems, efforts by the government to
fix them will just make them (or the economy more generally) worse. Of course some
efforts have involved the government trying to create markets, such as tradable
emissions permits for pollution.

The harder line Austrian position a la Mises/Hayek basically rejects the relevance
of the theorem at all. What matters is dynamic efficiency and not static efficiency.
Hence, one needs technological change and entrepreneurship and all that. I would say
that if one wants to pose this historically in terms of the competition of systems,
it was probably the technological stagnation of the Soviet system that hurt it more
than any static inefficiency in its competition with western market capitalism.

17 Yancey Ward August 13, 2007 at 2:18 pm

Barkley Rosser,

I am not sure I really understood that last point. Do you mean to say that the Soviet Union was efficient at getting food staples on the shelves, but failed to efficiently produce more technologically advanced goods?

18 Na Prática August 13, 2007 at 3:08 pm

If I got Rodrik right, the correct reading of his argument is:

1 – Economists support state intervention in some areas where there is no rock-solid empirical evidence for it, ONLY PLAUSIBLE THEORETICAL CONSIDERATIONS LOGICALLY DERIVED FROM USUALLY ACCEPTED PRINCIPLES, OF WHICH WE HAVE ONLY INDIRECT EMPIRICAL EVIDENCE (the whole market failures discussion).

2 – Some of these theoretical considerations should apply to industrial policy.

3 – We therefore should be open to discuss the convenience of industrial policy.

The theoretical considerations in question may be right or wrong, but there is at least some chance that they might be right (unless we accept that the whole market failures debate is nonsense, a step I am not willing to take). It is then a question of whether we want to act on that risk or not.

We accept to intervene, on uncertain grounds, in education but not in industrial policy because moral considerations imply that we must not, in any case, accept the risk of kids remaining uneducated due to a market failure (something that might happen, if there is some truth to the theoretical considerations). On the other hand, we find the risk of missing a couple of points in GDP growth (due to the lack of industrial policy) more acceptable, since we weight that against the risk of cronyism, state overstretch, etc.

The burden of proof, then, lies with Rodrik, who must argue that we attach too much importance to the arguments weighting against industrial policy, and that the risks we face by not implementing industrial policies are larger than we usually think. He proceeds to do that by presenting some case studies.

We may or may not find his evidence sufficient, but his argument is not trivially wrong.

19 Max August 13, 2007 at 3:38 pm

I would expect the real world application of idealized well designed interventions to work now as it always has. To see what I mean please review the results of the 20th century’s well designed interventions as implemented by fascism and communism. Those achieved historically lethal results.

20 Keith August 13, 2007 at 4:37 pm

On another note, I am very much enjoying the mutual cattiness between Dani and Alex.

21 Keith August 13, 2007 at 4:43 pm

I’m deeply sympethetic to libertarianism. I am also very deeply annoyed by the Feinmans and Huben and Arnold type of morons who just go into ad hominem ad infinitum and spew a lot of blather.

But I will throw these guys a bone, mainly because I think the bone has a point worth making:

My biggest problem with libertarianism comes down to this: The greatest benefit of civilization is running water, and it really looks like you need large-scale government intervention to deliver that. It just looks like our basic problems require the type of coordination that only smash-mouth government can provide. That tends to create a lot of very understandable attachment to government.

My main problem with government, though, is that it usually makes people a lot worse, and proves to be quite resistant to changes that improve it. Market participants, however, tend to be forced to improve.

22 Barkley Rosser August 13, 2007 at 5:06 pm

Yancey Ward,

Basically, yes. Sure, millions starved in the 1930s, and it was pretty grim foodwise right after WW II, although the latter was true in much of Europe as well as Japan also. By the fall of the USSR, indeed by well before then, nobody was starving or even close to it, with the food shortages being only those for certain specialized items, such as fresh fruit and vegetables.

The more obvious forms of static inefficiency were that the wrong amounts of goods were being relatively produced, too many tanks and not enough quality shoes (and, arguably, fresh fruit and vegetables). the other, harder to measure but very important, was quality. Lots got produced, but it was of poor quality. The Lenin Steel Works in Magnitogorsk was the biggest producing steel mill in the world, was a “Hero Plant” from its supplying steel for the tanks that won the battles of Stalingrad and Kursk, but when things finally opened up its output could only be sold internationally as scrap metal. Indeed, it is widely forgotten that Khrushchev’s specific forecast regarding “buying” the US came true. He used that phrase in regard to future amounts of steel, oil, and wheat production, for all three of which the USSR did eventually surpass the US, but so what?

There is also a literature (William Whitesell, 1990, Soviet Studies is an example) that argues quite seriously that Soviet manufacturing facilities were actually more efficient in using their existing technologies to produce quantities of specific output than comparable US facilities. Of course this does not deal with either the quality or “right goods” issues, but it does in fact relate to the static versus dynamic issue. The Soviet plants learned to use their existing tech so well because it changed so little, compared to US tech.

BTW, regarding the more specific question about industrial policy, I think Rodrik’s defense has been to cite the experience of some of the east Asian economies that used industrial policy and had strong growth experiences. There is a substantial lit that says that they grew in spite of those policies rather than because of them, but I think it is a bit unfair to tag Rodrik with having made some half-baked argument based on purely misinterpreted theoretical considerations.

23 Dave August 13, 2007 at 5:37 pm

The greatest benefit of civilization is running water, and it really looks like you need large-scale government intervention to deliver that.

You do realize that the trend in both the developed and developing worlds has been toward private provision of water for many years now. Admittedly government intervention seems to be necessary to get pipes laid, but after that there doesn’t seem to be any real payoff for government versus private provision of water. One has to be a very hard-core libertarian indeed to oppose public initial provision of distribution infrastructures.

24 Keith August 13, 2007 at 7:35 pm

Robert, you’ve got a point. You’ve been guilty of your share of cheap ad hominem attacks at other times, but you’ve actually been pretty good and on point on this thread, and I should’ve appreciated and encouraged that welcome development.

25 notsneaky August 13, 2007 at 9:14 pm

(btw, the magic number from the
experiments seems to be four, that or above and usually pretty competitive).

I’ve always thought that the whole thing about bounded rationality was actually a pretty good reason for the assumption of competition and price taking behavior. Usually bounded rationality is seen as a strike against these types of model but here I think it’s the opposite.

If you’ve got two players then the formal solution (optimization on the part of the agents) means basically a system of two equations. Suppose that these suckers are linear and that all the other things that could go wrong – knowing other person’s objective function, knowing the true rules of the game, etc. – don’t. Ok, I can invert a 2×2 matrix. More realistically if I’m, say, one of two shop owners in town, I can probably intuitively feel my way to the solution.

Three players, you got a system of three equations. And inverting a 3×3 is, of course, tougher than inverting a 2×2 but still doable. But the point here is about marginals.

The step from inverting a 2×2 to a 3×3 is still much less than the step from 3×3 to a 4×4 which is less than from 4×4 to 5×5 and then you gotta bust out your software package.
(in economic terms, this is because every time a new player gets added you not only have to consider the impact of that player’s actions on yours and vice versa, but also that player’s impact on other player’s actions and their impact on yours and backatcha, etc.)

At some point you’re gonna put your paper and pencil down and say, screw it, I’m just going to assume that whatever price prevails in the market now is the price I should be charging (or buying at).

That’s only one side of it though – as number of players increases the computations needed for “optimizing” increases at an increasing rate. The other side is that usually (“in a large class of models”) as the number of players in a game goes up the difference in payoffs you achieve between “optimizing” and just playing “price taking” goes down. So not only do the computations get harder, the incentive to do them gets smaller.

Of course this is completely informal and sketchy and there’s a lot of caveats and issues I’ve left out (like where to the prices originally come from and why they converge to the “price taking” level rather than an arbitrary one). I don’t really know how to formalize this intuition. I just know that when I go to a store I’m dimly aware (as an economist) that if I purchase an orange that’s one less orange on the supply side and the repercussions will work themselves through the system. But I’m not going to even try to set up that optimization problem with its millions of equations. I’m just gonna take the price of an orange as given. Even, I guess, if there were only four orange consumers in the world.

26 Lee A. Arnold August 13, 2007 at 10:41 pm

Keith, in a discussion of Alex Tabarrok’s argument about the conditions for efficiency in the First Theorem — wherein, by the way, almost everyone until you was following very closely, and understood that disproof of one thing does not prove its inverse to be true — you jumped to weigh-in on an entirely different argument, with a proof constructed of results misapprehended from experimental economics, plus 19th-century social Darwinism, plus your own opinions on government! And the best part about it is that you called OTHER people morons!

27 Justin August 13, 2007 at 11:48 pm

Alex, in logic and mathematics, it’s common for a major theorem (and it seems like anything called “the first fundamental theorem of…” counts as major) to be subjected to repeated attempts to weaken the assumptions necessary to prove the theorem. If those attempts fail, it becomes reasonable to guess that the assumptions are all necessary rather than just sufficient. You can’t rule out that a genius will come along and provide a proof using much weaker conditions, but it becomes reasonable to think that this won’t happen and no such proof is possible.

Has anything like this attempt happened with Arrow and Debreu?

28 Barry Payne August 13, 2007 at 11:58 pm

The characterization seems to frame the theorem as theoretically sufficient for an efficient market which is simultaneously insufficient to satisfy that necessary for an empirical outcome.

This seems to contradict a monotonic ranking between what is necessary or sufficient, at least by crossing the line from the theoretical to the empirical realm. If what is sufficient is not necessary, how can it be sufficent?

For example, it implies an efficient market could be achieved empirically on other subset conditions within the sufficient set that are broader than just government intervention, i.e. those posited by Vernon Smith, etc.

In any case, the confusion between economic and engineering efficiency is clear and unnecessary. They are not related.

For example, while electric power plants are designed for peak and baseload applications, many assert that the on-peak use should be shifted to off-peak use to improve the utilization factor of off-peak baseload units with lower running costs. However, this would increase the total cost of an optimal system, ceteris paribus.

Likewise, to claim that cars, lawnmowers, air conditioners etc. are “inefficient” based on engineering parameters is economically irrelevant. If they are used infrequently for short periods, the older vintage equipment with higher running cost and lower capital cost than new units will most likely achieve economic efficiency.

That none of it ever achieves 100% engineering efficiency is no more relevant than asserting that running is less energy-efficient than walking to avoid being run over by a bus.

29 Robert August 14, 2007 at 4:01 am

Barry Payne’s comment on utilities are misguided. Utilities shift power from peak to off-peak all the time (e.g., “demand-side management”) so as not to require so much peak capacity. They also shift power generated off-peak to on-peak by storing it, e.g., using off-peak power to pump water up-hill into a reservoir.

Anyways, I think it a puzzle why economists should care about the Arrow-Debreu model nowadays. It is not descriptive. Is the point of neoclassical economics to model an utopia set in cloud-cukoo land?

30 Barry Payne August 14, 2007 at 10:09 am

Per Robert, true, electric utilities engage in all sorts of activities to avoid current, avoidable running cost. But the reason they do it is because they cannot change the fixed, in-place, sunk capital costs that determine those running costs.

Otherwise, for example, the last peaking unit would not have been built, traded off for a larger baseload unit or various reductions in on-peak demand from other sources such as conservation or time-of-day pricing.

Per Tabarrok, “that the theorem’s conditions are not satisfied does not prove that market outcomes can be improved, even by ‘well-designed’ interventions”.

Much of the development of US electric generation, transmission and distribution systems in the twentieth century occurred under regulation designed to achieve efficiency gains not considered possible under competition.

Specifically, declining marginal costs remained below average cost to result in a natural monopoly (no longer true for most generation). The policy choices were to allow unregulated monopoly pricing above marginal and average cost or impose regulated prices at average cost. (Imposing prices at marginal cost would have resulted in bankruptcy for a natural monopoly.)

On occasions where competition was attempted among natural monopolies, it was obviously wasteful and inefficient. Examples were two or more sets of utility lines (electric, gas, telephone, water, etc) running down the same street. This was replaced with regulated, average cost-plus pricing by one provider.

Does this prove that a market outcome can be improved through intervention?

31 Timothy August 14, 2007 at 4:11 pm

Qingdao above makes an important point. The state certainly seems to have played an extensive, interventionist role in the development of South Korea, Taiwan, Japan, and the other Tigers. (The Japanese Ministry of International Trade and Industry used the phrase “planned markets.”) I expect that a history of Chinese development 1979-2010 would show similar patterns. Some quotations here.

32 Lee A. Arnold August 14, 2007 at 7:07 pm

Barkley, I’ll ask you instead: If the Austrian position is to reject the relevance of the theorem, how do they ensure that someone is not made worse-off by someone else’s dynamic efficiency? Because surely that is to impair the loser’s freedom. Is there some other concept or syllogism that they substitute?

33 sent August 15, 2007 at 2:15 am

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34 Barkley Rosser August 15, 2007 at 4:01 pm

Lee Arnold,

Well, Austrians tend to eschew Pareto criteria and their relatives. But I would say that the argument would be that the gains in growth from greater tech change are sufficient to compensate any losers. Of course the solution proposed by Austrians, more general economic freedom, presumably does not entail somebody having less freedom, although critics of the Austrians can point out that this is not necessarily the case.

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I’ve been wondering about this question about Pareto optimality for a while, specifically about “not making anyone else worse off”:

If our concept of “anyone” included future generations, is Pareto’s approach still possible?

Suppose, further, that our concept of “anyone” included other species, will the approach still work?

Thanks.

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