marginal utility confusion from HA

Economics Economics Questions
1

From pg 120 of Human Axtion, Mises says:

“A man owns five units of commodity a and three units of cornmodityb. He attaches to the units of a the rank-orders I, 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 Iose 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.”

I think I understand the first example, it seems fairly clear that both commodities ranked 7th and 8th would be valued less than those ranked 5th and 6th. But his 2nd statement confuses the hell out of me. How would it necessarily follow? He even states that we cannot perform operations to “find” the value of these bundles, so how does it follow that if you know the rankings of 3 of one commodity a as 4, 7 and 8, and with b as 5 and 6, that it must necessarily follow that the 3 of a are valued more. Even though 5 and 6 are valued less than a individually, couldn’t it be the case, that “as a bundle they are valued” more than the 4th ranked commodity, and that this information could not be revealed through a value scale which only reveals information about the “unit” quantities of each commodity?

Or have I missed something?

2

bump.

3

… I agree with your analysis…

I’m somewhat surprised…, maybe its an editorial oversight sort of thing.. (but we have been through quite a lot of editions by now!)

4

It’s from the scholars edition, and whats worse is he seems to contradict(at least for me) his later statements about the impossibillity of deriving the valuations of bundles from comparisons of the valuations of marginal units. The dude is amazing, but he isn’t perfect. There are plenty of other areas, I feel are a little unclear or incorrect. I greatly respect him, but sometimes I feel Austrians hero worship him too much, along with Rothbard and Hayek.

5

Mises is correct. I think that the part you’re missing is that as each unit is lost, the remaining units of that commodity move up in rank to replace it.

In order to verify this, I sketched a chart with two columns, one representing commodity A and the other representing commodity B. I then listed units 1 and 2 in consectutive rows in column A, unit 3 in the next row in column B, unit 4 in column A, units 5 and 6 in column B, and units 7 and 8 in column A.

When the man loses two units of commodity A, each remaining unit moves up in rank. So, what were previously units 4 and 7 become units 1 and 2 and the previous unit 7 becomes unit 4. He can still satisfy utility levels 1 through 6. If he had lost two units of B, unit 6 would become unit 3 and he could only satisfy levels 1 through 4 before wanting to satisfy levels 5 and 6 with commodity B.

If he loses three units of commodity A, he only has two units left. The unit that was originally ranked 7 now moves up to rank 1 and what was originally ranked 8 now becomes 2. He would now only be able to satisfy utility levels 1 through 3. Conversely, if he loses two units of commodity B, what was previously unit 6 moves up to unit 3. He can then satisfy utility levels 1 through 4.

This might not be very clear from my explanation but I think that if you set up a chart as described it will be clearer.

6

It’s from the scholars edition, and whats worse is he seems to contradict(at least for me) his later statements about the impossibillity of deriving the valuations of bundles from comparisons of the valuations of marginal units. The dude is amazing, but he isn’t perfect. There are plenty of other areas, I feel are a little unclear or incorrect. I greatly respect him, but sometimes I feel Austrians hero worship him too much, along with Rothbard and Hayek.

This isn’t a contradiction. In the first instance Mises is explaining a thoretical construct. In the second, he is explaining that we can’t observe this concept directly in empirical experience. It’s similar to supply and demand curves. We can state, as a theoretical concept, that as price goes up, demand decreases and supply increases, but we can’t observe this phenomenon directly because we can’t isolate this from all of the other things that might be taking place at the same time. What we can observe is the price that is achieved in a particular transaction. In a similar manner, we can’t observe marginal utility but we can derive it from economic theory.

7

Doug M, I’m going to try to create a ‘simpler’ example of the question of intrigue here, abskebabs correct me if I go wrong.

Lets say you have the following rank ordering of preferences:

  1. riding services of a horse

  2. milking services of a cow

  3. companionship services of a dog

now it will be trivial to pick between any two from the above 3. one will be higher up the scale than the others.

If I have a cow and no horse but could trade it for the horse then I would.

So…, what if Iwho have zero animals am offered either

1 horse, or (a cow and a dog)

If it is possible to have the following value scale :

  1. milking services of a cow and companionship services of a dog

  2. riding services of a horse

  3. milking services of a cow

  4. companionship services of a dog

… then…

8

His whole point is that what counts is the individual in the current situation.

And what counts for the individual is not 3 bananas versus two apples. What counts is his needs and desires, ordered by importance.

Those numbers 1 through 8 should be thought of like this

  1. Most important to me, more than anything, is feeding my little child. who only likes food a.

  2. next in importance, more than anything except number 1, is feeding my dog, who also only likes food a.

etc.

Lets say that 4, 5, and 6 are tossing food a [a cream pie] at his unfriendly neighbor, giving food b to charity, and putting some of food b [lemon juice] in his bathwater. I think you are asking that perhaps giving food b to charity and putting it in his tub, taken together, is more important to the individual than tossing a cream pie in the face of his neighbor. Or that maybe if he can have 2 through 8, he will forget about 1 altogether.

The answer is very simple. It may be the case that he prefers having both 5 and 6 rather than 4 alone. But remember, we are talking about a hypothetical person, made up by Mises to illustrate a point. So Mises is free to give this imaginary persons preferences anything Mises feels like.

And Mises made up a person who wants to have any lower number satisfied, even if it means giving up ALL the higher numbers after it.

The reason he made up that particular person is to bring out the point that in such a case, he prefers losing 2 a’s to two b’s, but prefers losing 2 b’s to three a’s, [given that he starts out with 5 a’s and 3 b’s].

I guess the importance of having such a case is that to figure things out, you don’t add subtract multiply or divide some number value . You look at the positioning of the objects on the list.

9

If A > B > C, it does not follow A > B + C.

10

Okay, I’ll state my point as simply as possible using Smiling Dave’s example of cream pies. If this fellow has six cream pies, he’ll use them as Dave specified (and he sounds like a pretty bizzare dude). If he loses two of his cream pies, so that he now has only six, he will forgo giving one to charity and putting one in his bathwater. If he has only two, he will forego tossing any at his neighbors and just serve one to himself and one to his dog. The point is that this is a commodity, so if he loses the one that he had initially earmarked for eating himself he will substitute one of the others for it and forego the uses for cream pies that gave him the lowest utility. If you work through Mises formulation keeping this in mind, you’ll find that he is absolutely correct.

11

(In response to Doug’s first 2 posts)

I see… I’m not sure I’m “happy” yet, I just tried drawing those charts. I didn’t include the it about “moving up” levels, which I thought was superfluous, since if we just imagine the least valued units are removed we attain the same result. I understand how clear this appears when we break up the action of giving up 2 of b for 3 of a, into first exchanging 2 of a, before our value scale then shows a higher rank of 4 and 1 and 2 for the ones remaining.. You could go one step further and analyse the one action as a combination of exchanges choosing between marginal units of a and b.

But in doing so, aren’t we utilising a construction that requires us to break up an individual action, which is keeping one bundle over another into several different actions? Mises correctly censures(in my opinion) the neoclassical for assuming several different actions to be synchronous under the same value scale, emphasizing its limitations as a tool to understand but not appraise action, in the chapter on time, helping dispel confusion over what is referred nowadays as the “transitivity of utility.” Yet if we carry out the above, aren’t we committing a similar error? In order to demonstrate our conclusion we are positing that we can break up a single action into several, which we know for which we cannot necessarily assume a constant value scale.

I was thinking as soon as I made my post of a solution similar to the one you’ve sketched out, and instead of thinking of levels of utility, I simply thought of ends. I did so, because I see it as the way of resolving other similar puzzles, for instance Robert Nozick’s confusion over an alleged contradiction in utility theory.

This is since what are actually exchanged are possible ends, not means. Action is a demonstration preference of one end over another, it is perfectly consistent therefore, that means are equally substitutable for one another in the actor’s point of view, if they can produce the same ends to the same efficacy. Since the value of objects is ultimately evaluated by the subjective use value perceived by the individual, which may or not be dependent on their objective use value, it is therefore perfectly possible that 2 different means could be viwed as equally serviceable for the execution of an end, just like we reason 2 of the same means probably will be seen in such a way(though they may not be). It doesn’t follow from this however, that action is a demonstration of indifference, since it is still a demonstration of preference over alternative ends.(I should probably put this in the Nozick thread…)

Back to the subject at hand, when we break down our analysis into the achievement of ends, at first things seem clear, depriving the person the a ranked 4th over the 5th or 6th ranked b would clearly result in a state of affairs he values less. But this is when we have broken down our analysis into these units surely? It is perfectly possible that we can conceive ends 5 and 6 as one end, which can then con be compared to 4, 6 and 7 collectively, or even 4 individually. But this denies us a way to solve this problem cognitively, since as Mises himself notes, we lack a means of ratiocination to calculate the utility of a bundle from an individual unit, and similarly to derive the valuation of a unit from a bundle.

Mises correctly censures the classical economists in making such an error in conceiving the value of one unit of a supply to be derivable from that of the entire supply. Shouldn’t we, as honest Misesians, censure him for appearing to do the same in comparing 2 bundles of different magnitudes?

I also don’t think doing so would somehow invalidate the marginal theory of utility, in fact I think it should make it more consistent. The key idea is that one is not exchanging the highest valued “unit” of a supply, whatever magnitude it may be, but comparing the individual marginal units in question that are being traded. Hence it is perfectly feasible that a man in our society would prefer to exchange a glass of water for a trinket of gold, in evaluating the services he can derive directly or indirectly from either. A similar man encountered in the desert with the same choice would probably do the opposite, unless he does not wish to be long for this world, and this results precisely from our analysis of marginal utility. Yet this results precisely from always evaluating our answer in terms of the actual units of quantities being traded. Hence a “value scale” can only inform about a trade involving precisely units of this size being traded, in this sense it is really a means of visualisation, just like supply and demand curves aim to be.

I also don’t think we as Austrians should be bothered by the minimal amount that can actually be rigidly derived from value scales. After all, it is not us that try to derive everything by trying to squeeze the dry apparatus of indifference curves, utility functions and value calculus as far as it can go. I welcome your thoughts and engagement Doug. Please let me know how and where I am wrong, if you feel I have unfortunately strayed again into error.

(edit: @ Nirgraham, that’s the idea I had stated in more straightforward terms, and also what I showed above in terms of comparing ends)

12

to DougM’s most recent post

a’s and b’s are objects that fall into two classes, unlike homogenous cream pies.

13

But in doing so, aren’t we utilising a construction that requires us to break up an individual action, which is keeping one bundle over another into several different actions? Mises correctly censures(in my opinion) the neoclassical for assuming several different actions to be synchronous under the same value scale, emphasizing its limitations as a tool to understand but not appraise action, in the chapter on time, helping dispel confusion over what is referred nowadays as the “transitivity of utility.” Yet if we carry out the above, aren’t we committing a similar error? In order to demonstrate our conclusion we are positing that we can break up a single action into several, which we know for which we cannot necessarily assume a constant value scale.

I agree that it would be incorrect to assume several different consecutive actions under the same value scale. However, my understanding is that this is example is meant to represent several alternative actions that might take place at a single point in time under a single value scale. In other words, our man ios walking down the street with 5 units of A and 3 units of B when a robber points a gun at him (and assuming that he values his life more than any of the commodities). He figures that he can satisfy the robber by giving him 2 units of A or 2 units of B. We can now tell strictly within the confines of this example which one he would choose. Then we turn back time to the point that the man is first held up. Everything else is the same but this time he figures that the robber will require either 3 units of A or 2 units of B.

I agree, and I’m sure that Mises would, that this is completely unrealistic. The only purpose in this exercise is to demonstrate the lump of clay from which the marginal utility sculpture will emerge as we begin to refine it.

But this is when we have broken down our analysis into these units surely? It is perfectly possible that we can conceive ends 5 and 6 as one end, which can then con be compared to 4, 6 and 7 collectively, or even 4 individually. But this denies us a way to solve this problem cognitively, since as Mises himself notes, we lack a means of ratiocination to calculate the utility of a bundle from an individual unit, and similarly to derive the valuation of a unit from a bundle.

If we bundled 5 and 6 perhaps assuming that both units were in a single package and could not be seperated, it wouldn’t make a great deal of difference in this analysis. The marginal utility of our man having this package would still be 6 and the marginal utility of not having it would still be 4.If you bundled 3 and 5, you’d have a more interesting question. In this case, You’d have to compare the 3 and 5 bundle to 4, which cannot be solved within the eonfines of the example. We’d have to know how the 3 & 5 bundle compares to 4 in terms of marginal utility.

Mises correctly censures the classical economists in making such an error in conceiving the value of one unit of a supply to be derivable from that of the entire supply. Shouldn’t we, as honest Misesians, censure him for appearing to do the same in comparing 2 bundles of different magnitudes?

He’s not doing that at all. The 1st unit of A is clearly worth more to our man that the 5th unit of A.

I agree completely with the rest of your post. The only reason for addressing value scales is as a learning/teaching tool for the concept of marginal utility. You seem to have a thorough understanding of it at this point.

14

a’s and b’s are objects that fall into two classes, unlike homogenous cream pies.

A’s and B’s are two different types of physical objects but they both fall into a single value scale for our man. In real life, everyone deals with hundreds of goods and services but everyone must constantly place and replace them in their constantly shifting value scales.

15

yes, but my point is that Mises hasn’t furnished us with a complete value scale, there are unkowns in it (i.e, when the marginal unites are other than single a’s or single b’s but pairs of a’s and triplets of a’s etc.), so he can not justifiably says ‘that this means…’ as he seemingly does in the text.

16

“In other words, our man ios walking down the street with 5 units of A and 3 units of B when a robber points a gun at him (and assuming that he values his life more than any of the commodities). He figures that he can satisfy the robber by giving him 2 units of A or 2 units of B. We can now tell strictly within the confines of this example which one he would choose. Then we turn back time to the point that the man is first held up. Everything else is the same but this time he figures that the robber will require either 3 units of A or 2 units of B.”

I understand that, indeed it is the very sense we come to understand marginal utility when analysing the intended purpose of value scales in actually helping us understand the exchange value of the actually traded marginal units. I don’t see how though your analysis can be produced without splitting up the action into several, since our value scale compares only the units of value in question on a preference scale. In this example they are 4, 7 and 8 for a and 5 and 6 for b. Action can only rigidly only implies relative preference on a value scale of the specific units of quantities being exchanged, and we cannot know anything about magnitude of utility from a value scale. Hence how can we know for sure that 5 and 6 together may not be valued more than 4 alone?

“The marginal utility of our man having this package would still be 6 and the marginal utility of not having it would still be 4.If you bundled 3 and 5, you’d have a more interesting question. In this case, You’d have to compare the 3 and 5 bundle to 4, which cannot be solved within the eonfines of the example. We’d have to know how the 3 & 5 bundle compares to 4 in terms of marginal utility.”

Tbh, this baffles me, since it seems like the only case in which one could produce a legitimate answer in comparing bundles! 3 is valued more than 4 on its own. So why would there be a dilemma about giving up both 3 and 5 for 4? For the same reason, I have no problem with Mises’ earlier statement of 5 and 6 of b being preferred to 7 and 8 of a. In any case, regardless of our ultimate conclusion, this thread has certainly been intellectually engaging!

17

I think the problem here is that we’re trying to add up values, which is an impossible endeavor. The simple implication here is that individuals will always peruse their most highly valued ends first, which is tautological.

18

The two “value charts” below are consistent with the value scale described by Mises:

"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. "

Further, Mises states that from the value scale above we can make the two following statements:

“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.”

i.e., according to Mises, from the value scale above it follows that X > Y and Y > Z.

While it is possible that an individual values the bundles in such a way, it does not necessarily have to be the case.

The first value chart gives that Y > X and Y > Z

The second that X > Y and Z > Y

Edit: to clarify, the numbers in the value charts are the ranks of the different bundles, a higher number signifies a higher rank. The ranks are of course stricly ordinal. To find the value scale we find the path beginning from the top right, where at each step, the individual chooses the bundle with the highest rank.

19

I am not sure I understood the OP correctly.

Is your point that value of some goods is not fully independent from each other (complementary/substitutes), and this breaks the analysis of value scale in terms of individual goods as opposed to bundles/states of the world?

20

I must confess I find the above charts a little confusing, but I think I’m beginning to see what Esuric, Doug and others have been getting at, though I’m still not sure it’s correct. I’ll use a simple example of Mises’, which is much like nirgraham’s to illustrate, and you can tell me if and where I go wrong. Suppose we have a man with 12 dollars who can buy opera tickets to Aida, Falstaff and Traviata, each of which cost 4 dollars. We may suppose he has preferences among viewing the 3 operas as follows:

A

F

T

Hence in analysing the action assuming a value scale as so just before, we may conclude without controversy, if he only has 4 dollars, that he will purchase A. Now suppose he’s given 8 dollars, again, it’s not controversial that he will purchase A anf F. Now suppose that we tell him he has 12 dollars, so we may well expect him to purchase A, F and T, but if we then turn around and tell him that he can only purchase 4 dollars worth, he may now only purchase A. This is functionally equivalent to the first case in which he knows he only has 4 dollars to begin with. Yet I think one could claim it also displays a functional equivalence with the case where he has A, F and T to begin with, and we then tell him he has to lose 2. Ignoring the intermediary device of dollars, the actual opportunity costs are represented by forgone ends F and T in both the first and final case. Is this the kind of things you guys were pointing at?

I’m still a little uneasy, but I think it’s starting to make sense… I’d be interested to know nirgraham’s thoughts in light of the above.