Friday Economics 101 quiz time!

by Daniel on April 25, 2008

One for the junior-birdman Hayekians, Coasians and such like:

Consider a finite quantity of a consumption good G, which is to be divided into two allocations G1 and G2 for two different agents with utility functions over G described as U1(G1) and U2(G2).

What would be the minimum information that a central planner would need to have about U1 and U2 in order to be able to calculate a Pareto efficient allocation G1/G2?

Answer after the jump – I just asked three economists this question and they all got it wrong.

Any division of a cake into two parts is Pareto efficient[1]. In this case, the Pareto condition just means that, once you’ve made the allocation, you can’t change it without taking a bit of cake of one guy to give to the other.

[1] Actually the planner wouldn’t even need to divide it – “all for you, none for you” is a Pareto efficient allocation, and one that shows up surprisingly often in real world cases of Coasian negotiation.

{ 70 comments }

1

robertdfeinman 04.25.08 at 5:40 pm

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

2

Dave 04.25.08 at 5:43 pm

And for the reat of us who don’t speak Econibberish, the point is?

3

puzzled 04.25.08 at 5:44 pm

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.)

4

bob 04.25.08 at 5:46 pm

puzzled is right in comment 3.

5

SamChevre 04.25.08 at 5:50 pm

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.

6

dsquared 04.25.08 at 5:54 pm

Oh come on, pedant posse, that’s implicit in my description of G as a “good” rather than a “bad”.

7

dsquared 04.25.08 at 5:56 pm

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

8

dsquared 04.25.08 at 6:00 pm

Ah mobile devices, the lazy man’s way to double posting and spurious http errors.

9

bob 04.25.08 at 6:04 pm

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.)

10

Kevin Donoghue 04.25.08 at 6:16 pm

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

Having drunk too much last night, I’m inclined to think it’s very wrong indeed.

11

notsneaky 04.25.08 at 6:25 pm

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).

12

Aaron Swartz 04.25.08 at 6:27 pm

Ah, it’s like they always say: premature pareto-optimization is the root of all evil.

13

notsneaky 04.25.08 at 6:31 pm

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.

14

mq 04.25.08 at 6:32 pm

Yeah, I was thinking what puzzled said. Plenty of goods have a satiation point. Like ice cream. If D-squared arguing ice cream is not good! Say it isn’t so!

15

ejh 04.25.08 at 6:44 pm

Can we use calculators?

16

John Emerson 04.25.08 at 6:52 pm

You can always feed leftover cake to hogs or chickens, or push Tom Friedman’s face in it, or give it to the homeless. It is not possible for there to be too much cake.

17

puzzled 04.25.08 at 7:01 pm

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.)

18

puzzled 04.25.08 at 7:03 pm

The formating on my post is really off.

I meant U1(G1) = G1 if G1 rational, 0 otherwise;
U2(G2) = G2

Then if agent 1 gets square root of 2 and agent 2 gets G – square root of 2 is not a Pareto efficient allocation.

19

Matthew Kuzma 04.25.08 at 7:15 pm

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.

20

Matthew Kuzma 04.25.08 at 7:17 pm

In fact! I’m fairly sure I can prove my above statement. It’s been a long time since I constructed a proof, but it seems pretty easy to demonstrate that given G1 and G2, it’s possible to construct a U1(G1) and U2(G2) such that some transfer of goods from G1 to G2 doesn’t decrease U1 and does increase U2.

21

Walt 04.25.08 at 7:49 pm

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.

22

lemuel pitkin 04.25.08 at 8:00 pm

Puzzled and Matthew Kuzma are right, and dsquared is wrong.

Does it matter? Well, it depends why dsquared asked the question.

If he asked it to show that economists often get basic questions of economics wrong, then the correction can’t be ruled out on grounds of pedantry, since pedantry was the whole point. So it does matter.

If he asked it for some other reason, he should probably tell us what that is.

23

bob 04.25.08 at 8:03 pm

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.

24

P O'Neill 04.25.08 at 8:07 pm

I’m not sure I see the Coasian angle. There is no mention of property rights to the cake.

25

John Quiggin 04.25.08 at 8:12 pm

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”.

26

pushmedia1 04.25.08 at 8:15 pm

Yeah, so what’s the answer? His Excellency the Benevolent Dictator needs to know preferences are something less than monotone and something more than locally non-satiable?

27

abb1 04.25.08 at 8:17 pm

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.

28

David Weman 04.25.08 at 8:20 pm

“If D-squared arguing ice cream is not good! Say it isn’t so!”

Dsquared is actually the only one I know who has dissed ice cream. Shocking but true.

Is it a British thing? I read somewhere they’re pretty impovershed when it comes to ice crea, or at least used to.

29

lemmy caution 04.25.08 at 8:24 pm

30

Matthew Kuzma 04.25.08 at 8:37 pm

Lemmy caution: Wait, I thought a pareto optimal solution was one in which no further pareto improvements could be made. So then two people with half a pie and one with no pie is only pareto optimal if the people with pie lose utility for any marginal decrease in pie. 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. Basically, my understanding of it (gained admittedly from the definition on Wikipedia) is that something can’t be pareto efficient simply by being better than before, but by not being able to be improved within certain constraints.

31

Matthew Kuzma 04.25.08 at 8:39 pm

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

32

lemuel pitkin 04.25.08 at 8:47 pm

25-

I was thinking the point was probably something along those lines. In which case, ok, the “bloody pedants” response is fair…

33

Maria 04.25.08 at 9:20 pm

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.

34

notsneaky 04.25.08 at 9:21 pm

Damn you puzzled and your pedantry. Local non-satiation and continuity?

35

pushmedia1 04.25.08 at 9:26 pm

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

36

lemuel pitkin 04.25.08 at 9:28 pm

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

No, the question did explicitly rule that out by presenting U1 as a function of G1 and U2 of G2.

37

lemmy caution 04.25.08 at 9:29 pm

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”.

38

lemuel pitkin 04.25.08 at 9:30 pm

Daniel’s point was that Pareto optimality doesn’t mean shit in terms of desirability of an outcome.

Actually, I think he meant something different. 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.

39

notsneaky 04.25.08 at 9:30 pm

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

40

pushmedia1 04.25.08 at 9:36 pm

Mr Pitkin, G1 = 1 – G2 (under some normalization), no?

41

pushmedia1 04.25.08 at 9:42 pm

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.

42

notsneaky 04.25.08 at 9:43 pm

pm1, that’s the budget constraint, not preferences.

43

Maria 04.25.08 at 9:45 pm

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.

44

pushmedia1 04.25.08 at 9:54 pm

In the planner’s problem the constraint binds… I just interpreted D^2 as saying U(G1) are preferences the planner sees.

In any case, you can imagine preferences over the “rest of the pie” (e.g. 1 – G1).

45

aaron_m 04.25.08 at 10:09 pm

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.

46

notsneaky 04.25.08 at 10:11 pm

“It’s more of a whack at Hayek types specifically rather than economists in general.”

I’m not so sure that Hayekians put that much emphasis on lack of information about preferences. The whole “Use of Knowledge In Society” thing is about tacit knowledge about production.

47

notsneaky 04.25.08 at 10:14 pm

“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.

48

notsneaky 04.25.08 at 10:17 pm

pm1, I meant that the fact that G1=1-G2 doesn’t imply that folks care about each other’s preferences. As long as u1 is just a function of G1 and not of G2 then Lemuel’s right.

“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.”

Yeah but even with monotone and non-interdependent preferences the example won’t work if you got more than one good. So end of story right there.

49

notsneaky 04.25.08 at 10:20 pm

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.

50

Maria 04.25.08 at 10:40 pm

notsneaky, I was going to say that. So I guess I’ll just say you’re right, although giving everything to one person is always Pareto efficient.

51

Maria 04.25.08 at 10:40 pm

With no although.

52

Miracle Max 04.25.08 at 11:05 pm

I want to know how the three errant economists answered.

53

notsneaky 04.25.08 at 11:22 pm

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.

54

Punditus Maximus 04.25.08 at 11:28 pm

Wait, we’re supposed to assume that G is the only good in the entire world?

If not, then we need to know something about the marginal rates of substitution between G and dollars.

Or else all we really need is to give some G to each person and tell them to trade until they’re happy.

55

dsquared 04.25.08 at 11:41 pm

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.

56

ben saunders 04.25.08 at 11:53 pm

My original answer was that utility is strictly increasing with cake. (Monotone or whatever that is in technical language).

Reading some replies, I think it may be a bit like the distinction between welfare and resource egalitarians. Did you want a Pareto optimal distribution of cake (i.e. no one can have more cake, without someone getting less)? If so, Daniel is right, no knowledge of utility functions is necessary.

If the aim is Pareto efficiency in the domain of utility, you would need to be sure both are gaining utility from all their cake to be sure that a transfer of cake wouldn’t lead to a loss-less utility gain.

57

notsneaky 04.26.08 at 12:20 am

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

58

notsneaky 04.26.08 at 12:21 am

“a situation which begins with a ludicrously one-sided distribution, ends with a ludicrously one-sided negotiated outcome”

What does that have to do with Pareto optimality though?

59

LizardBreath 04.26.08 at 1:49 pm

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.

60

puzzled 04.26.08 at 5:35 pm

And exactly who would make such a claim? The first thing any teacher says after introducing the concept is that Pareto efficient is not necessarily desirable.

61

LizardBreath 04.26.08 at 5:55 pm

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.

62

notsneaky 04.26.08 at 10:23 pm

Well, there’s all kinds of problems with the Coase “Theorem” (it was actually a subject of some recent Econ blog discussion, see for example Michael G’s blog: http://yetanothersheep.blogspot.com/2008/04/coase-theorem-still-dead.html)
but it doesn’t “ignore resource constraints”.

The resource constraints are taken care of in the definition of a non-Pareto-efficient allocation; a situation where it is POSSIBLE to make someone better of without making anyone else worse off.

63

LizardBreath 04.26.08 at 10:45 pm

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.)

64

notsneaky 04.27.08 at 12:20 am

That’s sort of the point of the Coase Theorem. If you got property rights you don’t need to worry about efficiency, just equity. But yeah, some people misuse it.

65

dsquared 04.27.08 at 4:23 pm

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.

66

newshutz 04.27.08 at 5:10 pm

Isn’t the key bit of information the central planner needs is how much of G can he take for himself?

“All animals are equal, but some animals are more equal than others”

67

notsneaky 04.27.08 at 6:53 pm

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.

68

concerned_economist 04.28.08 at 3:04 am

This entire exchange (question, “answer” and comments) is ridiculous. As a casual reader of CT I am sometimes struck by how often the posts and comments have strident anti-economics perspectives. To start a thread by posing a question (a “pop quiz”) which supposedly three economists answered incorrectly only to then post the incorrect answer yourself is an embarrassment. To get publicly hung by your own noose at the hands of an econ grad student is just deserts.

69

Mark Picton 04.28.08 at 1:08 pm

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.

70

notsneaky 04.28.08 at 6:46 pm

But that’s really just the case with 2 goods.

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