Cardinal Utilities?

Economics Economics Questions
1

Why can’t utilities be measured? Because there can be no such thing as a unit of happiness. In the case of distances we can make ostensive definitions of a unit of distance: a meter, we can say, is this long. A pound is this heavy. But we can’t say: a util is this happy.

But perhaps one can be allowed to say that he prefers C to A 3 times as much, while he prefers B to A only twice as much. Here we merely state a relationship between the choices. In other words, let A be one util; then B will be 2 utils, and C, 3. Here we seem to have a unit: A. One util is whatever happiness A provides. One can object by saying that it’s unclear how to multiply happiness by constants. How does twice as much happiness “feel”? How can any person determine how many utils he is experiencing, even given a unit? How can we know, for example, by exactly how much to discount marginal utilities? So, even this is problematic.

But don’t we sometimes say that we would prefer B to A by “a little,” while we would prefer C to A by “a lot”? It is an accident of our psychological makeup that we can’t divide utilities by each other to find out by what factor we are better off. But if we can vaguely judge “a lot” vs. “a little,” then isn’t it in principle possible? I believe a standard strategy is to calculate utilities in terms of money. Again, this is problematic, because of differing utilities of money. But it seems that imprecise calculations are both possible and actual.

2

Rothbard would retort: three times in terms of what? Utility is purely subjective. Even how much one’s “three times more” differs from another’s.

-Jon

3

To which they say utility functions are equivalent up to monotonic transformation and the equations have the same solutions regardless of which is used.

4

To which we retort: you can’t have an equation regarding something that is purely subjective and resides only in the mind.

5

And their proof of this would be, what?

-Jon

6

Let me rephrase the problem a little bit. If according to subjectivism we can say that C ranks higher than B ranks higher than A, and therefore, to give this a cardinal slant, C/A - B/A > 0, it is ever legitimate to say: C/B - B/A > 0, that is, that C is “much better” than B, while B is only “a little” better than A?

7

Which means that you’d first choose C, then B and then A - “ranks higher” is just a figure of speech ?

You can’t write that. A, B, C are supposed to represent numbers measuring…what ? Your own objection still applies :

8

I mean, “ranks higher on one’s value scale.” It’s not a figure of speech but a standard expression. It means that at some particular time t A, B, and C are not “co-attainable” (that is, you have to choose one of these desires to satisfy), and that you prefer C to B, and B, to A. From this it could be deduced that you would pick C at t, or, if, for example, you became aware that C was impossible to achieve or satisfy, then you would pick B at t.

I may be equivocating with respect to the sign “>”. If we represent “C ranks higher than B” as C > B, then it may not be reasonable to rewrite this as C - B > 0. But the puzzle remains. Can we say that the distance in happiness between C and B is greater than the distance in happiness between B and A?

9

But there are no actual heights involved - nothing you can measure using a rule.

Yes, that’s what I said. I guess my punctuation/wording wasn’t that clear.

How do you measure the distance in happiness ?

10

You “rank” alternative ends as “first,” “second,” “third,” etc. The end ranked first is said to be “higher” on the value scale than the end ranked second.

You would measure the distance by feeling it, by sort of introspecting and asking what you want and how much you want it. As I said above, obviously there is no way to assign precise numbers to utilities, but one might be able to do a rough-and-ready gauging of distances. Or how about this: I would be much happier if someone gave me $1,000,000 as opposed to $2, but only a little bit happier, as in my life wouldn’t really change, if someone gave me $2 as opposed to $1. On the other hand, it’s much more difficult to measure someone else’s distances. I suppose a father can decide which of his children will enjoy a present more. But great insight into a soul, whether your own or another’s, is required.

Actually, Rothbard writes that “there is no way whatever of measuring the distance between the rankings; indeed, any concept of such distance is a fallacious one.” But he adds in a footnote: “We might, in some situations, make such comparisons as historians, using imprecise judgment. We cannot, however, do so as praxeologists or economists.” In other words, economists do not spend their time studying people’s souls. I suppose that’s as good an answer as we will be able to get here… don’t you find it annoying that you post a puzzle only to realize in the end that its solution is found in some canonical work?

11

Dimitri, you might be interested in this: http://libertarian-left.blogspot.com/2008/03/interpersonal-comparisons-of-utility.html

12

Here’s Mises version :

" A man owns five units of commodity a and three units of commodity b. He attaches to the units of a the rank­-orders 1, 2, 4, 7, and 8, to the units of b the rank­-orders 3, 5, and 6. This means: If he must choose between two units of a and two units of b, he will prefer to lose two units of a rather than two units of b. But if he must choose between three units of a and two units of b, he will prefer to lose two units of b rather than three units of a. What counts always and alone in valuing a compound of several units is the utility of this compound as a whole­–i.e., the increment in well­-being dependent upon it or, what is the same, the impairment of well­-being which its loss must bring about. There are no arithmetical processes involved, neither adding nor multiplying; there is a valuation of the utility dependent upon the having of the portion, compound, or supply in question."

13

There is a way to assign a dollar value to the degree one prefers one good to another. Let’s say you win a door prize and you get a choice between item A and item B. If you prefer item A to item B, the question is by how much? Well, the doorprize administrator can determine in dollars how much you prefer A to B by offering you B+$x. At the point at which you are indifferent between A and B, you prefer A to B by $x.

Now, money is itself just another good, so this really does not solve the problem of measuring units of subjective preference.

One of the easiest ways to see that it doesn’t make sense to measure utility in an objective unit is the impossibility of defining exactly what it is that we are preferring. “How many units of happiness does a bottle of water confer?” Well, it depends. If you had been stranded in the desert for the last two days and you came across a heartless merchant who would not give you water for free, you’d probably give anything he asked in exchange for a bottle of water. The happiness you’d derive from that bottle of water would be very, very great.

But most bottles of water you drink give only a very small amount of happiness relative to other things you might consume, such as a vacation in Hawaii, It is not enough to track even the individual preferences of every human in an economy for every kind of good in that economy - you would have to at least track the individual preferences of every human in an economy for every specific good in that economy, in every specific situation in which each individual happens to be, or even plans to be.

Assuming we could assign a unit to happiness, the calculation problem is still insurmountable. The Wikipedia article on the economic calculation problem argues that since anything which can be calculated by one universal Turing machine (of which the brain’s calculational capacity is an instance) can, in principle, be calculated by any other universal Turing machine, there is no in-principle calculation advantage to 6 billion individuals over one. However, this skirts several serious problems. First, some problems are more amenable to parallelization than others, so that parallelization results in genuine speedup (see Amdahl’s and Gustafson’s laws). There is good reason to believe that economic calculation is one of these problems. Second, calculation is only half (maybe less than half) the problem - communication is as much or more of a problem. How would a central planner foresee that I could get stranded in the desert and end up in dire need of a cold bottle of water? And failing foresight, how would I communicate this information to the central planner? Any circumstance which cannot be predicted no matter how much computing power is applied (I would argue that most economic particulars cannot be) must be communicated. The economic calculation problem is a genuine problem and the socialists must surmount this problem among many others.

Clayton -

14

Wrong. How do we know you are indifferent?

15

Mises’ version of the calculation argument has to do with ownership first and foremost, does it not, and only derivatively with utitilities?

-Jon

16

To be precise, Clayton, if you accept the door prize of B+$x over A, it shows that you preferred to accept B+$x over accepting A. It does not show that you preferred B by $x over A. There’s no reason to believe that you would have taken A if the money had not been offerred, at least in your example, nor is there reason to believe that you would not have taken B plus the money if fewer than $x had been offerred. Further, we can’t account for the possibility that you are being motivated to accept the bundle of B+$x for reasons besides the general value that you place on B and the $x. For example, maybe the person offerring the door prizes is a cute girl, and you think B is the more macho thing to accept, and you do so even though to be perfectly honest, you like A better than B. Or you might think that if I’m trying to pay you to take B, it must mean I’m running out of A’s, so you’ll take the B so the people who really want A’s can have one, even though maybe you would normally have taken the A over the B+$x. Or maybe you made a bet during dinner that could be settled for less than $x, and you don’t have any other money on you, but you really don’t want to get hassled by the person you made the bet with until the next time you see them. So at that particular moment, the $x could be really valuable to you, even though in the scheme of things, A would probably have given you more long-term happiness (so in other words, we could be dealing with time preference and situational accidents here). The point is, you can’t eliminate all of these things from an observation of a real world event. And if you could, the experimental conditions would need to be so precise that they wouldn’t extend to normal observations, and so would only be useful as trivial facts about a particular experiment.

I mean, the problems go on and on, and we could literally go on for hours about everything that makes it so you can’t possibly determine anything about a person’s tendencies from a particular observation. And then we could go on for longer about all the reasons that you can’t infer anything about a person’s wellbeing from understanding their tendencies. And then we could go on for longer about all the reasons that knowing about a person’s wellbeing wouldn’t necessary tell us what to do as social planners. And we could drive it all home by pointing out that if we wouldn’t be able to be “correct” or “perfect” social planners even with all this knowledge, we especially can’t be “correct” or “perfect” social planners without any of that knowledge.

17

Sorry for bumping this ancient thread, but I’m still not quite satisfied with many Austrians’ very strong rejections of cardinal utility as a concept.

I think everyone would agree that there is no way to make interpersonal comparisons of utility, and that there is no way for an outside observer, or even for the actor himself, to put actual numbers on his utility.

Still, doesn’t every decision need some sort of internal (mental) “unit of account” in order to compare the expected psychic benefit of two outcomes and decide which end to aim for? “Ah, but all you need to know is which of the two outcomes you prefer. That is ordinal utility.” you might then respond. But let’s view this from the perspective of the actor. If the actor is selling a bike and one buyer is willing to buy it for 8 carrots and 3 stuffed goats and another is willing to buy it for 5 stuffed goats and 4 carrots. In order to decide which person to sell the bike to, does he not need some way of comparing the utility of consuming carrots to the utility of whatever you can do with stuffed goats? Is it not required to somehow estimate (in your own head) to intensity of “utility” you will experience when eating one carrot, when eating two, three or ten carrots and compare it to the intensity of utility experienced when utilizing a stuffed goat, two stuffed goats, or five?

We need to be able to “lump together” the expected utility of different types of experiences in order to make choices for situations where the different possible outcomes each involve several independed ends, each yielding independent psychic benefits and/or psychic costs. And that includes virtually all decisions we ever make.

We may call this unit of account “intensity of good feelings” or whatever. It is true that no one can put a number on it, no one can measure it and no one can make interpersonal comparisons using it. But the acting individual nevertheless has to use a single scale to compare all different sources of utility, even if he does not understand how he comes to the conclusion that he prefers four stuffed goats and four carrots to a bike, but not three stuffed goats and five carrots.

It is this “unit of account” I think many neoclassical economists tries to symbolize with the letter U in their utility functions. You cannot use it to calculate anything. It is pointless to, as is commonly done in microeconomics and portfolio choice theory, estimate utility functions using numbers and figuring out the optimal amount of inputs to maximize utility. That is pure nonsense. And I agree with Mises that the use of mathematical functions is inappropriate to describe economic/praxeological relationships. Still, that does not necessarily mean that the concept as such is flawed. We could never find out how an individual evaluates the expected utilities of certain ends, but we do know that he does evaluate it and that he must have some sort of unit of account to compare the utilities of different ends.

With that in mind, is it really so unrealistic to use some mathematical equations, which Austrians often raise objections to, such as MU1/P1 = MU2/P2 which simply states (in an economy with only two goods) that an individual will purchase good 1 up until the point where the utility of the last unit of good 1 divided by its price equals to (or is less than, if you object to the psychological state of indifference) the utility of the last good purchased divided by its price?

This does not involve interpersonal comparisons of utility, but it does involve comparisons between the utilities of different ends using a single unit of account (U), namely a comparison between the utility of the consumption of good 1 and the consumption of good 2. If an individual had no single unit of account for utility, wouldn’t his mind then be subject to Mises’ economic calculation problem when making decisions?

These are just some thoughts I had. It is almost 2 am now so what I wrote may not make all that much sense, but I would still really appreciate it if someone could explain where my reasoning went wrong.

18

When deciding between choices, your value scale represents always represents them as a “consumption package”. Your scenario can be explained just like any other “single” action, and it all boils down to whether or not the additional end of carrots ranks higher than the forgone end of stuffed goats. There is no “unit of account” utility needed to explain this. Take another example, you go to a resturant and order the rotisserie chicken. Then the waiter asks, “BBQ sauce or Honey Mustard?” Now the chicken is “the same”, but now you need to consider BBQ and honey mustard. Well, just like considering between whether 4 additional carrots ranks higher than 2 stuffed goats, your ranking of BBQ sauce and honey mustard determines which “consumption package” (the two chickens) you buy.

If you would sell the bike for both options, and if the 4 additional carrots ranks higher than the 2 forgone stuffed goats, then you would choose Basket A. You only ever need ordinal rankings to make decisions, never utility “units of account”.

19

Thanks for the reply.

Yes, I realize now that I used a bad example, as ultimately it boils down to a higher or lower preference for four carrots compared to two stuffed goats. Let’s view another example instead. You are selling a bike and buyer A offers one stuffed goat and one carrot and buyer B offers one calculator and one vacuum cleaner. Suppose that your ordinal ranking is as follows:

1: stuffed goat, 2: vacuum cleaner, 3: calculator, 4: carrot (where 1 is the highest on your value scale)*

The choices you have are two bundles: Your highest preference plus your lowest preference (bundle I), or your second highest preference plus your second lowest preference (bundle II).

How do you know whether to trade for bundle I or bundle II? You know that you prefer a stuffed goat to both a vacuum cleaner and a calculator individually, and that you prefer both a vacuum cleaner and a calculator to a carrot. But if your value scale is purely ordinal, the question “by how much?” doesn’t make any sense. You can’t measure the distance between the utility derived from utilizing a stuffed goat and the utility derived from a vacuum cleaner or a calculator. And thus, you can’t decide which bundle is preferable.

When you are writing 58008 on your calculator, the joy you feel is not a joy relative to the pleasure you would have felt consuming a carrot. It is a thing in itself, that would yield the same enjoyment regardless of how much you enjoy or dislike carrots. It is this intensity of a feeling that cardinal utility seeks to portray, an intensity that is not ordinal, because you would experience it even in the abscence of any other alternatives.

Now, returning to the value scale above and your choice between two bundles, you could argue that there is no need to compare the expected utility of one good to the expected utility of the other goods, because your choice is not between four goods, but between two bundles, and that you simply need to decide whichever bundle is higher on your ordinal value scale. That still leaves the issue of your subjective evaluation of the two bundles. How can you determine which bundle ranks higher on your value scale? The utility derived from vacuuming your house is distinctly different from the utility derived from eating a carrot, using your calculator. They yield different types of emotions and they fill different practical purposes. In order to know which bundle ranks higher on your ordinal value scale, you first need to compare the utility derived from all the different ends the various goods can be used to attain. And just as with factors of production in an “economy” without money, there is no way to evaluate and compare the services (psychic benefit/utility) that different types of consumer goods (or services) yield without a common unit of account, without at least some sort of internal calculation based on “cardinal utility” or whatever you wish to call it.

*It should be noted that preferences and ordinal rankings are never in terms of consumer goods, but rather in terms of the utility derived from the services they provide. Each consumer good generally yields many different kinds of services, each evaluated differently on one’s value scale - making the need for a common unit of account even greater.

20

Again, remember that in any action you choose between “consumption packages”, and that value scales change all the time depending on the choices an actor faces. When making the decision, your value scale isn’t the above, but 1. Stuffed Goat/Carrot 2. Vaccum Cleaner/Calculator (or vice versa). Another example is You and a date need to decide what restaurant you go to. You can go to the Italian resturant, which has a nice ambient atmosphere and eat pasta. Or you can go to the Bar, which is a more rowdy atmosphere, and eat burgers and hot dogs. The goods you decide between are “Nice Italian Restaurant with Pasta” and “More laid back bar with less fancy food”. And how you make that decision is ultimately up to you and can only be expressed as rankings. The value scale above would be applicable only when you have the option of selling your bike for all four separate goods. The subjectivity of the “goods” is crucial here.

The question you pose, “how” you decide between either of the two bundles, relates to how you rank your ends. If carrots are more servicable than calculators, (your hungry) then you would choose the carrot. A unit of account like you suggest would be equivalent to saying “The calculator is .76carrot satisfactions, so I’m going with the carrot.” You don’t need a unit of account to compare goods, you just need to know (and you express this through action) which one is more preferrable depending on which distinct satisfaction ranks higher on your value scale.

The situation under money is different. Money is a physical good that is a medium of exchange. Whichever one earns you the most profit (difference of money revenues minus costs) is the avenue you will take. The money can be used to buy (theoretically) any consumer good, which all rank differently on your value scale. You don’t need a unit of account for utility measurements, since each satisfaction that the goods provide are distinctly different.