Friday Economics 101 quiz time!

The appropriate response is “which answer would you like and how much are you willing to pay me to come up with it?”

No, no, no! The utility functions must be strictly increasing to make any allocation Pareto efficient. If one or both of the agents has a satiation point less than the total amount of the good, a whole lot of allocations are not Pareto efficient.

An Economics grad student. (A theorist, I admit.)

I got the same answer as puzzled. Iff the utility functions are strictly increasing (which is usual, but not universal) all allocations are pareto efficient.

That’s implicit in the characterisation of it as a “good” rather than a bad you bloody pedants.

Pedantic, absolutely. But is strictly increasing implicit in the definition of “good”? I don’t think that is right, actually.

(And the contrast with a “bad” doesn’t seem to me to have much to do with it – the issue isn’t whether the utility functions are increasing or decreasing but whether they ever flatten out.)

I gave almost the same answer as puzzled. But you don’t need monotonicity. You just need local non-satiation. If it’s monotonicity it means it’s a “global” “good” (so Daniel’s right).

And to be REALLY pedantic, after the jump you don’t give the answer to the question you pose before the jump (the one about information) but rather give the answer to the question “what is a Pareto optimal outcome here?”, so you shouldn’t be surprised that people answered your first, real, question rather than the one you answered.

Can we use calculators?

notsneaky, local non-satiation is not enough to make ANY allocation Pareto efficient. For example:

| G1 if G1 is rational
U1(G1) = {
| 0 if G1 is irrational

and U2(G2) = G2

Both preferences satisfy local nonsatiation but the allocation (2^(1/2), G – 2^(1/2)) is not Pareto efficient.

(Yes, there is an unpleasant task I must do and I am procrastinating madly.)

Um. I disagree.

Using the cake example, say guy 1 wants a quarter of a cake. Any more represents zero marginal utility. Guy two is increasingly happy with increasing cake. Giving each guy half is not pareto efficient, since taking a quarter away from guy 1 leaves him no worse off, according to his utility function, and makes guy 2 happier.

There are even fewer pareto efficient solutions if the agents’ utility functions are negative for some values of G1/G2. So I’d say the minimum information needed is to know the two utility functions. I’m fairly sure given any distribution of G into G1 and G2 I can construct utility functions that make that distribution non-pareto-efficient.

I have to agree with Daniel on the pedantry question. If you reach a satiation point, so that more of it would have negative utility, then at the point the good becomes a “bad”. Whether or not a good or bad depends on your current bundle of goods.

If you reach a satiation point, so that more of it would have negative utility, then at the point the good becomes a “bad”.

But reaching a satiation point needn’t imply this. Marginal utility could simply fall to zero at or past the satiation point.

Just guessing, one obvious point is that economists frequently use “Pareto optimal” in ways that draw on various expectations about optimality that aren’t satisfied, such as

Optimal outcomes are socially desirable
Well-behaved optimization problems have unique solutions

and so on. So, for example, it is easy to slide from “under certain conditions, competitive market outcomes are Pareto optimal” to “competitive markets are the unique best way of organizing society”.

Everything has a satiation point. Vanity of vanities, all is vanity.

Whatever my eyes desired I did not keep from them.
I did not withhold my heart from any pleasure,
For my heart rejoiced in all my labor;
And this was my reward from all my labor.
Then I looked on all the works that my hands had done
And on the labor in which I had toiled;
And indeed all was vanity and grasping for the wind.
There was no profit under the sun.

Nobel prize winning economist Amartya Sen has elaborated the mathematical basis for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge to Pareto efficient, but inequitable, distributions.[2] A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients is left worse off than before (when none had pie); there are many other such distributions (any where the entire pie is distributed). An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded, as welfare can be increased without reducing the welfare of any individual (e.g. just give the quarter pie to someone). The origin of the pie is conceived as immaterial in these examples, i.e. the pie was “free.” In such cases, in which a “windfall” that none of the potential distributees actually produced is to be allocated (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation.

Wow. Please forgive my poor construction of that last sentence.

I know Daniel’s point was that Pareto optimality doesn’t mean shit in terms of desirability of an outcome. But as an econ grad student all I could think is “as long as the utility functions are increasing”.

Just another piece of evidence that Economics is bad for the soul :)

Also, mq, there is no such thing as a satiation point for ice cream, regardless of what our host believes.

Also, doesn’t His Excellency need to know people’s preferences over others’ outcomes (aka social preferences)?

If either of them would be just as happy with less pie, and if the third would be more happy with more pie, then the solution isn’t pareto optimal.

I modified the example in the wikipedia article to indicate that each of the three people want “as much of the pie as possible”.

Crap, that won’t work either. So it looks like monotonicity is the minimal condition required.

notsneaky, what about the satiation point examples? Under some preferences, reducing one’s share can improve his lot without hurting the other guy.

I think His Excellency has to know a lot about preferences just to get efficiency. Assuming they’re monotone, assumes a lot. Assuming people don’t care about others’ preferences, assumes a lot. These things might break the welfare theorems, but they represent an argument against central planning, too.

More like, lack of knowledge about preferences is not an argument against central planning. It’s more of a whack at Hayek types specifically rather than economists in general.

Hmmm, I don’t want to turn this into a discussion about what Daniel meant. It’s not like he’s shy or anything.

Going on to what you say, I think you can see this argument roughly as a reply to the assertion “the market is great, it gives us a Pareto efficient outcome”. So, of course, a counterargument would say “Well, we don’t need to know anything in order to obtain a PE allocation – just give everything to dsquared”.

Now, to me this means that Pareto efficiency isn’t a valid criteria to compare both systems. By itself, it doesn’t really say anything about whether Hayekians are right or wrong.

Only if utility functions are A strictly increasing and B strictly decreasing. A does not necessarily entail B (often does not). Thus we need to know if B is true and if not we need to know if this is a case of simply distributing a good or of redistributing the good to arrive at Pareto efficiency.

Isn’t Daniel’s mistake the same as SamChevre’s who claims that utility functions are ‘usually’ strictly increasing? Of course they are usually not strictly increasing. The confusion comes in simply because economists make the strictly increasing assumption/simplification in order to make their models workable at all. This may not be too bad in large aggregation but once we are making small-N interpersonal comparisons the simplification becomes blatant.

“Going on to what you say, I think you can see this argument roughly as a reply to the assertion “the market is great, it gives us a Pareto efficient outcome”. So, of course, a counterargument would say “Well, we don’t need to know anything in order to obtain a PE allocation – just give everything to dsquared”.”

Except it doesn’t generalize to the case with more than one good.

Well, it ALMOST breaks down with more than one good. You can always give everything to one person and that will ensure a Pareto Efficient outcome.

With no although.

And of course it’s silly to compare the efficiency of planning vs. markets in a situation where there’s only one good. What the hey is this market gonna be IN? “I’ll trade you two units of chocolate ice cream for uhhhhhh….. two units of chocolate ice cream”?. Yeah sure, who needs a market then, centrally plan that sucker.

So:

With more than one good the only way that a social planner can be sure of implementing a Pareto Efficient allocation is either if a) she’s got lots and lots of information (more than just monotonicity) about preferences or b) she implements the extreme allocation of giving everything to one person.

So paradoxically, (barring a)) the only way that planning can be efficient is if it’s hella unequal. Pretty much more than a market would ever be.

the actual point of the joke was that in lots and lots of actually existing Coasian situations, a situation which begins with a ludicrously one-sided distribution, ends with a ludicrously one-sided negotiated outcome.

Thinking about it some more I think local-non satiation + continuity will get you there after all.

I think the point is that the ludicrously one-sided negotiated outcome can be Pareto optimal, and that anyone confusing “Pareto optimal” or “efficient” with “good” or “just” or “desirable” isn’t thinking clearly.

There’s a lot of people out there who will make public policy claims based on the possibility of Coase-type bargaining; whoever has an initial right is unimportant because if someone else wants it more they can make a deal. This is nonsense, of course, because it ignores resource constraints (you can want something as much as you like, but if you don’t have the money you’re not going to successfully bargain for it), but it’s not uncommon nonsense.

As a lawyer, I’d say it’s a very common type of error among lawyers; you teach something purporting to be economics to a roomful of people who pride themselves on being cold-bloodedly logical, and most of whom have difficulty with simple arithmetic, you get some very confused thinking.

As a lawyer, again, whenever I try to use economics jargon I fuck it up. While ‘resource constraints’ may have been the wrong words, I meant, in lay language, budgetary constraints — someone without money to spend can’t bargain for anything regardless of how highly they value it, making where you place the initial entitlement quite important from a distributional justice point of view. (And of course this isn’t a flaw in the Coase theorem itself, this is a problem for nitwits who think that the Coase theorem means you don’t need to worry about where property rights are placed.)

What does that have to do with Pareto optimality though?

it is by way of a demonstration that it isn’t a very good criterion by which to judge things.

Ok but then you could’ve just said “suppose total size of the pie is fixed and one person gets all of it. Then that’s Pareto Efficient” by the way of illustration. I can see why folks above were thinking that you were making some kind of statement about the comparative information needs of a centrally planned economy and a market one.

Also, no, by itself it’s not a very good criterion. It’s more of a necessary criteria than a sufficient one, since if you don’t have PO then you can always give more pie to someone, anyone.

There are two pretty important restrictions – ie pieces of information the central planner has – on the utility functions in the question: that my welfare depends only on own consumption of goods and that my utility depends only on my own welfare.

There is nothing in standard consumption theory that requires selfish or self-regarding preferences – they are a special case. For me, “all the cake to me and none to my daughter” is not a Pareto optimal allocation. I would be better off if she had a slice.