Someone Has to Remind Bryan Caplan That No Such Thing as Utils
One of the issues in Bryan Caplan’s famous “Why I’m Not An Austrian Economist” essay (even though he had been one when he was younger) is the issue of cardinal utility functions. A lot of Rothbardians like to roll their eyes at the mainstream for thinking utility is a cardinal entity that can be measured in principle, whereas Austrians know that preferences are ordinal rankings. In a fit of exasperation, the Rothbardian might exclaim that the standard equilibrium conditions in a typical micro book involve dividing by marginal utility!!
But, as Bryan points out in his essay, such jabs misconstrue what the mainstream economists are doing. They don’t actually take a particular utility function seriously; it merely “represents” ordinal rankings over bundles of goods. There’s no special significance if someone has a certain utility function, because you could represent the same ordinal preferences with any monotonic transformation of that same function. (NB: If you’re doing von Neumann Morgenstern expected utility functions then it can only be a positive affine transformation.) Bryan is right, by the way: When I was a young punk down in Auburn my first year, I made sure everybody knew that I knew a bunch of math from NYU.
Anyway, somewhat apropos, today at EconLog Bryan says that there’s little doubt that a<1, when we model spouses' utility function as U=(Family Income)/(2^a). But Bryan wanted to know: "Where does a typically lie in the real world?” Daniel Kuehn reminded in the comments:
“Where does ‘a’ typically fall in the real world” isn’t a particularly meaningful question because it’s a monotonic transformation. Again I think the private/household good entering a utility function is the better approach.
So then the question is maybe something like what is the marginal rate of substitution between some representative (or bundle of… but I’d have to think about MRS’s of bundles) rivalrous and non-rivalrous goods.
Bob, out of curiosity, what is your opinion of vNM utility functions? Do you believe in the von Neumann-Morgenstern axioms, and do you believe that vNM utility functions measure intensity of preferences, in the sense that (u(x)-u(y))/(u(y)-u(z)) (which invariant under affine transformations) tells you how much you value x over y compared to how much you value y over z?
Is that actually the question here?
I thought we were trying to measure how much you value x over y, compared to how much someone else values y over z.
Who said anything about making interpersonal utility comparisons?
How can you have a concept of a “family income” without believing that utility between people is comparable?
If I add 5 meters to 10 seconds what do I get?
Income is all measured in green pieces of paper. I don’t see where the IUC comes in, Tel.
That’s not strictly true, if the wife cooks dinner she exerts effort and produces something valuable. No green paper involved.
You could decide to come up with an hourly rate to translate that into monetary terms, but it would be a rate based on your preferences, not her preferences.
The husband may spend the weekend gardening, or working on the car: effort spent, goods produced, and no green paper.
The presumption that the family consumption is neatly divided by two is impossible:
This statement in itself believes that the benefits they get are automatically split equally… which implies there is a way that such things *can* be split equally in a meaningful way.
We can split by price of course, but the married partners might not value the same things. The guy might value tools while his wife values perfume or something. Then you need to measure how much “utility” each person gets in order to know how much to spend on tools and how much to spend on perfume.
Just picking from your article. You said
But then do Austrians also not hold that marginal utility is the subjective appraisement of the usefulness of the marginal unit and not the increase in utility resulting from an additional quantity of the good? Wouldn’t Austrians object to the very phrase increase in utility as devoid of meaning?
No, because “increase in utility” refers to the ranked order of possible ends. An increase in utility means a higher ranked good is attained (technically speaking, in action it is always the highest ranked end given the available alternative ends).
I am nothing if not a firm defender of the intellectual legacy of Carl Menger.
From the linked article:
But on the left hand side (the ratio of marginal utilities) we do not simply have one cardinal number divided by another.
(…)
With this in mind, it is easy to see that for our example, the “utils” dimension cancels out on the left hand side (as Hülsmann has already done for “dollars” on the right)
The utils dimension only cancels out if you treat the division as a division of cardinal numbers.
Utils are cardinal. Preferences are ordinal.
Which is exactly what Bob tried to prove (with his article) is not the case.
Ummm, no.
Yes:
we do not simply have one cardinal number divided by another.
I acknowledge completely the existence of that sentence fragment.
Care to add anything else to your case or is this really what you’re going on?
The division it refers to is:
(6 utils / 1 bananas)
divided by
(2 utils / 1 hamburgers)
If this isn’t “one cardinal number divided by another”, then either (6 utils / 1 bananas) or (2 utils / 1 hamburgers) is not a cardinal number (probably both are not).
If (6 utils / 1 bananas) is not a cardinal number, then 6 utils is not a cardinal number.
Therefore utils are not cardinal.
He’s just saying that Hulsmann forgets that the units cancel on both sides, not just one. In other words, it’s not just one cardinal number divided by another cardinal number. It’s one cardinal number divided by another cardinal number divided by another cardinal number which is divided by another cardinal number.
I reread it and you’re right: the part I cited is addressed at the argument that you cannot compare prices to utility ratios because the units would be different, which isn’t true because (as Bob argues) the units cancel each other out.
I thought the canceling out was supposed to justify dividing 6 utils by 2 utils (the unit “utils” in the numerator and the same unit in the denominator canceling each other out).
“you could represent the same ordinal preferences with any monotonic transformation of that same function”
I’ve heard this claimed many times, but the explanation never really made sense to me. Taking your example of the spouse’s utility function:
U = (Family Income)/(2^a)
Then you will still have a one to one function, determined by income. How does that map into something like this:
…
$70
Videogame for the kids
$60
$40
Hour massage
$30
…
Caplan is actually presenting what’s called an indirect utility function rather than a utility function… I think Bob is referring to a proper utility function here.
Doesn’t make a huge difference – you can derive one from the other if you have the price vector – but I do think that obscured the point I was trying to make that his “a” is meaningless and that he should think about the issue in terms of the MRS between rival and non-rival goods.
Perhaps. Although I don’t know that the MRS would really matter here, either. Mostly because I find it incredibly pointless to try to empirically determine what it seems like a couple with the same income has “multiplied” their income by marrying and sharing their incomes. It is enough, in my mind, to point out that some goods are “sharable”, particularly things like subscriptions (cable, internet, etc.) or basic living expenses to some degree. To what degree that happens is basically irrelevant to my mind.
I’m still not really seeing how the indirect utility function maps to an ordinal preference list, even with a price vector transformation to a direct utility function. It seems to me that any addition of empiricism to obtain “bundles”, etc., necessarily aggregates away from the individual making the decision, abstracting away some of his choices you didn’t think of, adding ones he didn’t think of, and necessarily warping the preference structure as a result.
Ordinal preference list ranking of indirect utility function is:
$70
$60
$50
$40
$30
Ordinal preference list ranking of utility function is:
House
Running water
Food
Keynesian econ books
Cable TV
Austrian econ books
Goods are not in the former and income is not in the latter.
How can you decide what price you would be willing to pay for goods if the goods are not comparable with the income?
I’m not sure I follow. The income is the numeraire.
If you want to at “one dollar’s worth of liquid cash” in there I as a Keynesian would love to see that.
Actually there are money demand models that do just that in their microfoundations (they are inflation models… I’m not sure they draw out all of Keynes’s consequences for the interest rate).
I may be missing your point. The assumption USUALLY is money has no value and you spend all of it according to marginal principles.
Anyway you decide because your real list will have “first book”, “second book”, “third book”, etc. so any given amount of income will get you to a certain bundle.
Perhaps I wrote the list unclearly because I didn’t have the numbers in there. Sorry about that.
Let me start over, Tel. Let’s say three goods: A, B, and C. A costs 1, B costs 2, C costs 3. You rank them in descending order:
3rd C
3rd A
2nd A
3rd B
2nd C
1st A
1st C
2nd B
1st B
If you have an income of 8 you will get 1 A, 2 B, and 1 C.
If you have an income of 15 you will get 3 A, 3 B, and 2 C.
What we could call the indirect preference ranking would be:
18
15
14
13
11
8
7
4
2
The problem with all of this and with the strict Austrian approach is that it’s clunky.
I’d REALLY like to do calculus on the first ranking, and I’d like my marginal utilities as a function of the other goods in a clear way.
I’d really like continuity in the second preference ranking.
Make a few very reasonable assumptions and you can do that with utility functions without doing any violence to the primitive concepts.
If you guys manage to settle your differences on utility theory in the comments at someone else’s blog, I would next ask you to solve the mind/body problem.
I should add that if you think one of the important primitive concepts here is that you rank units of homogenous goods, then the move to utility functions WOULD hurt that (well, I’m 98% positive it would).
But that seems like a ridiculous thing to care about to me. In the sense that we consume over time you could say we consume sequentially like that, but people have budgets with bundles of goods in mind when they consume. We should compare bundles.
On that point, Menger struts and frets his hour upon the stage and then is heard no more. An important part of the revolution, but something we can dispense with.
“A costs 1, B costs 2, C costs 3.”
Ah, THERE’S the fatal error. Assuming prices prior to the existence or investigation of prices.
Preference and utility precedes pricing. If I value a bundle of goods (although I disagree with using bundles like this as they aggregate different ends and means together), that DOES compare against how much I value holding on to a certain some of money income for other uses. (That evil saving Keynes was always on about.) And that, itself, determines a large factor in how prices are set – my demand for a good relative to my demand to hold money or use it elsewhere.
One consumer won’t change market prices, Tanous.
I don’t even know how this gotcha is supposed to play out or why the hell you’re talking about Keynes.
Call “A” a future good if you want.
Irrelevant. The consumer changes her individual prices, if the offer is too high she simply does not buy.
That’s the whole point of having a method of decision making, to know when the offered price is higher than you would be willing to pay. Without that, forget about any price theory.
Tel –
re: “That’s the whole point of having a method of decision making, to know when the offered price is higher than you would be willing to pay.”
“higher than you would be willing to pay” is defined in terms of opportunity costs. I don’t see how this point poses any problems. Could you explain?
One of the opportunity costs of spending the $10 today is that I can’t spend it tomorrow… but I don’t necessarily need to know precisely what I’m going to spend it on tomorrow, nor for that matter do I know whether I might decide tomorrow to hold the money yet again… thus an infinite chain of future decisions is stored behind the decision to hold onto the cash.
Alternatively, relate spending to earning (on a subjective basis)… if a person is getting paid $10 per hour (after tax) then buying an object for $30 means they exchanged 3 hours of their life for that object. Another person betting paid more would be exchanging less of their life for that object.
If it makes you feel better, take the money out of the ordinal scale and insert hours worked. I think it comes to the same thing, but if that fits your theory better then keep money right out of the picture and presume we have a barter system that is merely facilitated by money.
Tel –
Your first paragraph, sufficiently developed, gives you a lot of the General Theory of Employment, Interest, and Money.
Your second and third paragraph gives you a very standard labor supply model.
I’m genuinely not seeing what problems this is supposed to pose for standard thinking on ordinal preference ranking.
Actually this evening your puzzlement over my presentation of Menger here has lead me to think a lot about precisely this – building up some fundamental points of Keynesian macro from Mengerian microfoundations.
Might do some good spreading the gospel among the heathens.
Keynes pre-dated modern labor supply models, so whereas you sort of intuitively present a labor-leisure trade-off (with leisure as a good), Keynes was old school and talked about the disutility of work (so work is a bad that you trade-off against income).
Functionally of course it works out the same. Equimarginal principal (plus some continuity assumptions) ensures that the marginal value of a unit of leisure is equal to the negative of the marginal disutility of a unit of work.
I would like to make something more clear. In reality, people do not sit around and think up value scales. As Mises said,
“People have often failed to recognize the meaning of the term “scale of value” and have disregarded the obstacles preventing the assumption of synchronism in the various actions of an individual. They have interpreted man’s various acts as the outcome of a scale of value, independent of these acts and preceding them, and of a previously devised plan whose realization they aim at. The scale of value and the plan to which duration and immutability for a certain period of time were attributed, were hypostatized into the cause and motive of the various individual actions. Synchronism which could not be asserted with regard to the various acts was then easily discovered in the scale of value and in the plan. But this overlooks the fact that the scale of value is nothing but a constructed tool of thought. The scale of value manifests itself only in real acting. It is therefore impermissible to contrast it with real acting and to use it as a yardstick for the appraisal of real actions.”
Scales of value are manifestations of actions. It would be more accurate to say that these scales do not exist. If I choose to do something, the only thing I can infer is that the marginal utility of this action was higher than any other action I could have done.
But how do I know whether I value getting cable TV if the dollar amounts and the goods are not on the same scale? I might value Cable TV more than $30, but less than $40. Then I can examine the price and determine whether it is “worth it” to buy.
To have no comparison is not feasible. Worse, it assumes a mapping of goods as prices, which is incorrect – utility preferences determine prices, not the other way around.
The only reason why you would value cable less than $40 is if there was something else you wanted the money for more – now, in the future, or just to hang on to for liquidity. What maters is the ranking of those alternatives.
Your second paragraph is confused – I’m not sure how you’re drawing those conclusions. This is standard stuff – I’m not trying to pull a fast one on you. Pick up a basic price theory treatment or read the equivalent from a Mengerian perspective on Mises.org.
Well, I’m not an Austrian economist since I find praxeology to be dubious. Likewise, the claim that socialism is “impossible” seems a bit far fetched. Difficult to maintain, sure, but physically impossible? Well, that’s just nonsensical.
It is interesting to note, however, that Leon Trotsky made a similar-sounding criticism of the Soviet Union’s planning mechanism.
“Difficult to maintain, sure, but physically impossible? Well, that’s just nonsensical.”
Physically impossible? No one claimed such. You just won’t be able to direct resources via a central plan, while a market automatically directs resources towards the most desired goals of the consumers. If you’re fine with shortages and gluts of everything under the sun, and bread lines as far as the eye can see….
Could you clarify what you mean here?
Always or some of the time? If the latter, then I can readily accept the claim. If the former, then I’m afraid that’s unclear.
What Mises meant when he said that is that a socialist economy is not an economy because it is incapable of doing any economizing. That’s the sense in which he meant it was impossible. Sure you can make people do anything if you have enough force behind you, but the practice of economic calculation that an advanced civilization depends on is impossible without property and prices.
I am a serf because I can’t rob people.
I agree, Socialism is quite possible if you happen to have a very benign dictator who is also highly competent, completely trustworthy, and capable of understanding the broad diversity of business that goes on in any economy.
In practice though, the leaders we get are not like that.
That’s an understatement.
What Mises was criticizing was pure, utopian socialism, not the semi-socialist countries we see now. Note that, in this sense, no pure socialist state has ever existed (and could never exist according to Mises).
Praxeology is irrefutable, because refutations are themselves actions.
Absolute truths are propositions that are necessarily true not only when trying to prove them, but trying to refute them as well. They should have that nature after all. Absolute truths are truths that are always true within us and outside of us, that we can do nothing to change, not even “idealistically” in our minds because our minds are of the same absolute truth
Also, Mises never claimed socialism is “impossible”. He argued that economic calculation in socialism is impossible, because there is no price system for the means of production. Not even the most staunch Marxists could refute that argument, which is why folks like Lange made strained (and failed) attempts to show that calculation in socialism is possible after all.
Just going back to the left margin here… FWIW I can make perfect sense of Matt’s scale:
This means I can quickly decide that if I see the video game on sale for less than $60 I should buy it, and if it see it on sale for more than $70 I should certainly not buy it. That’s easy from a decision making point of view.
Daniel Kuehn splits this up into two ordinal lists, one with money and the other with goods. How to go about relating money to goods when they are on separate scales? I don’t get how to use Daniel’s design for making a decision, should I buy the game or not?
The differences are settled. When Daniel attempted to explain it a few more times it still makes no sense, just like the first time. We have reached an equilibrium condition, or a plain state of rest if you prefer.
However, that still leaves a more difficult problem. Let’s suppose the husband’s personal utility calculation values the video game as somewhere between $40 and $50 but the wife in her estimate values the video game at somewhere between $80 and $90… then they see the game on offer for $60, so should they buy it?
Bryan Caplan claims that the combined family income should be used to buy goods which are then divided equally, but if they but the video game the husband would feel that the household utility is going backwards, and the wife feels like it is going forwards. Then you need to either split the household income again, or you need to resolve a unified all household ordinal utility preference list which is a very difficult thing to calculate from separate husband and wife ordinal utility lists.
“Let’s suppose the husband’s personal utility calculation values the video game as somewhere between $40 and $50 but the wife in her estimate values the video game at somewhere between $80 and $90… then they see the game on offer for $60, so should they buy it?”
I’d say that what is then being evaluated is, for the husband, whether keeping $60 is worth more than getting the game and bringing his wife that small pleasure, and for the wife, the opposite.
OK to be clear this isn’t “my” presentation. This is price theory that everyone from Austrians to mainstream economists agree on.
re: “However, that still leaves a more difficult problem. Let’s suppose the husband’s personal utility calculation values the video game as somewhere between $40 and $50 but the wife in her estimate values the video game at somewhere between $80 and $90… then they see the game on offer for $60, so should they buy it?”
See the household bargaining literature.
Two lists is problematical. In the combined one I can see I should prefer to hold $30 and get a massage and holding $60. Can I get that from separate lists?
One list is problematic. You only care about a given amount of money based on its opportunity costs. If you want to hold cash, make one of the goods either a future good or liquidity.
This is how it’s been done for almost 150 years in mainstream and heterodox traditions alike.
But “liquidity” isn’t a simple item, you can have a bit more liquidity or a bit less liquidity. By the time you have enumerated all of those possibilities and slotted them into the list, you now have one ordinal list again.
Which is where Matt started from.
I don’t think so:
5th liquid dollar
3rd C
3rd A
2nd A
4th liquid dollar
3rd B
2nd C
1st A
3rd liquid dollar
2nd liquid dollar
1st C
2nd B
1st B
1st liquid dollar
The indirect preference ranking is now:
23
22
19
18
17
16
14
11
10
9
8
5
3
1
And given a budget you choose in the exact same way.
I promise this is not something I’m just thinking up.
This is the Mengerian approach. Other neoclassicals use bundles. That’s the better way.
“One list is problematic. You only care about a given amount of money based on its opportunity costs.”
But then the supposed list you initially had in mind, was actually incomplete, for it did not include the opportunity costs (i.e. alternative ends) that you just mentioned.
Your argument doesn’t show any problem with a single list. It actually shows the problem of having an incomplete single list.
Any opportunity costs can be coherently slotted into any previously established, and incomplete, single list of alternative ends (including both goods and medium of exchange).