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Does Rothbard Contradict himself with regards to the Law of Diminishing Marginal Utility?

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BlackNumero posted on Tue, Aug 3 2010 11:21 PM

In Chapter 2 of MES, while utilizing the Law of Marginal Utility to explaing Supply and Demand schedules (and ultimately price formation), Rothbard states that "the supply must always remain unchanged or increase with an increase in price" (MES 124). This is derived from the Law of Marginal Utility, because as the supply of a good X decreases (Actor exchanges good X for Y), the utility ranking of the marginal unit of X increases (since it serves ends higher on the value scale) while as the supply of Y increases, the utility ranking of the marginal unit of Y decreases (since it serves ends lower on the value scale).

Therefore, in order to supply an additional unit of X (and forgoe a higher utility ranked X), he will only sell it at an equal or higher ranked price of Y units. He uses this to say that at each hypothetical price an individual will supply a certain amount of good X because at that price an individual will supply up to the marginal unit. At a higher price, an individual will supply either the same or more because the larger amount of Y recieved ranks higher then the forgone utility of the marginal unit.  With the laws of supply and demand deduced, Rothbard moves on to describe various types of exchanges along with an Austrian analysis of the Structure of Production (using these theorems to describe price formation of factors of production, the interest rate, etc etc).

However, in Chapter 9 when discussing land and labor incomes, Rothbard discusses the possibility of a "backwards bending supply curve of labor" (MES 573). No longer an increase in price require the quantity supplied to stay the same or increase, now an increase in price can cause the quantity supplied to decrease! Either I'm not understanding the backward bending supply curve, or this small concession has grave consequences for Austrian theorizing. Doesn't the possibility of a backwards bending supply curve refute the laws he derived in Chapter 2, that the supply of a good will either stay the same or increase at a higher price? If the "laws of marginal utility" have exceptions, then the Austrian analysis of price formation is incorrect because it is not true in all scenarios. One cannot describe apodicitically certain deductions when there are blatant exceptions.

Interestingly enough, Bryan Caplan levels the same criticisms againist Austrian economics in "Why I am not an Austrian Economist" and states Rothbard makes ad hoc concessions after his value scale approach cannot explain certain economic phenomenon (such as the backward supply curve). I find neither Block or Hulsman defenses really satisfactory, as Hulsmann seems to outward deny it while Block says it won't occur if we hold income constant (but isn't every change in price a change in income?).

Anyone have any thoughts?

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Depending on how you talk about it; yes, labor will have a backward bending supply curve, because an increase in wages can, in fact, mean that people provide less of it, because, in their opinion, the oppurtunity cost may rise faster than the wage they are getting. 

I 'really' want to make 1000 dollars a month, relatively independent on how much I have to work. I know i provided lest labor last year after a wage increase because of this. 

I don't see the grave implications for the 'whole' of Austrian economics though, because looking at it like that violates ceteris paribus. 

The state is not the enemy. The idea of the state is. 

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Haha, is that the best Caplan can do?

Rothbard on Labor [MES page 573]:  One of the complications in the
analysis of labor is the alleged occurrence of a “backward supply
curve of labor.” This happens when workers react to higher wage
rates by reducing their supply of labor hours, thus taking some of
their higher incomes as increased leisure. [emphasis mine].

To possibly help understand this, if you were able to take two possible jobs, one paying more but with only two weeks annual vacation time, another paying less but with a two month vacation, would you not spend some time thinking about it before deciding? Leisure is a consumer good, and so being "paid" in leisure is a possibilty  some people may consider.

Rothbard on land: A backward supply curve might conceivably take place for a
land factor as well, when the owner has a high reserve demand
for the land in order to enjoy its unused (in the catallactic sense)
beauty.

This one is a bit deeper. Let's say someone owns a refrigerator factory. As prices rise, he will sell more and more refrigerators because he loves that profit. But will he also sell the refrigerator in his own kitchen, if he cannot get another one, even if the price of refrigerators skyrockets?  Maybe, maybe not. Depends how desperate he is for the money. 

In other words, the law of supply and demand assumes the very common situation, that if a person is out there selling product X, it means that X is not really that important to him. He is out there selling it in the first place because he would rather have money than the object X he is selling. 

But say a sports lover has two autographed Michael Jordan basketballs, unique in the world. He doesn't really want to sell either of them. Then he suddenly needs money very badly, to pay for an expensive operation. If selling one of them will pay for the operation, he will only sell one. If the price he can get is lower, he will of course sell both. This does not contradict the law of supply and demand, for the reason explained in the previous paragraph.

What Rothbard is saying is that on rare occasions, people treat land like those Michael Jordan basketballs. They only sell it because they really have to, but would prefer having it lying around as their pretty back yard.

 

 

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Thanks for your replies.

I'm having a hard time understanding your post smiling dave, mainly because I feel like the example with the basketballs still violates the laws of supply and demand. The Law of Supply states that an increase in price will either keep the quantity supplied constant or increase it (value scales constant). An individual will only supply an additional unit of a good if the money price for it is higher, as "the operation of the law of marginal utility serves to reinforce the rule that the supply cannot decrease at higher prices, but must increase or remain the same" (MES 124). Your previous paragraph stating "the very common situation" that a person sells a product X because it is not really important to him misses the point. Unless the person has no reservation demand for X (and the supply curve would be vertical), each additional unit the person supplies will become more valuable to him because of the Law of Marginal Utility (the decrease in supply will raise the utility ranking of the marginal unit). The Law of Marginal Utility is a Law, it can't apply only to common situations but to every situation (or else it wouldn't be a Law, and then the Austrian's couldn't explain price formation).

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Hi BlackNumero.  Do you have the links available for Block and Hulsmann?

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Hello, ThinkBlue, we meet again :D

Starting with Caplan's essay: http://econfaculty.gmu.edu/bcaplan/whyaust.htm

Rothbard's rejection of the utility function approach led him to make strange ad hoc concessions to it elsewhere in his writings. Using his value scale approach, Rothbard was able to derive the laws of demand and supply as theorems.[11] But then inexplicably in his later discussion of labor and land, Rothbard conceded the theoretical possibility of "backward" bending supply curves.[12]

Then Block's reply: http://mises.org/journals/qjae/pdf/qjae2_4_2.pdf

This criticism, too, misses its mark. Of course, downward sloping demand and
upward sloping supply are exceptionless propositions, given the ceteris paribus
assumption of no income changes. And, obviously, when this assumption is
relaxed, as in the case of the backward bending supply curve (or the Giffen good),
and income changes are allowed into the analysis, then it is theoretically possible
for such exceptions to occur. But why should neoclassical economics be granted a
monopoly position regarding this rather basic “insight”? Surely, the Austrians, too,
without any by your leave tugging at the forelock, may take note of the fact that
when price changes, income, too, can be impacted.

Then Hulsman's reply, which IMO, is ridiculou, as he states that the shape of supply curves have nothing to do with price formation: http://mises.org/journals/qjae/pdf/qjae2_4_1.pdf

There are probably few Austrian economists who would claim that nothing of
value could be learned extra muros. However, Caplan’s conclusion is premature.
The fact that Rothbard occasionally refers to income and substitution effects does
not warrant the claim that these effects correspond to anything real. And it does
not make the Austrian theory of the price formation of land and labor dependent
on neoclassical insights. We have already pointed out that Mises did not bother
about the shape of supply curves or the underlying motivations of market participants.
His price theory stresses a much more fundamental feature of price
formation, for example, that all exchanges are (at least ex ante) beneficial for both
parties and that entrepreneurs appraise factors of production in terms of their
expected relative contribution to the monetary income generated by the production
process. It follows that consumers steer the allocation of resources in a market
economy. Nothing of this depends on the shape of supply curves, or on the
existence of income and substitution effects.

Then there is Caplan's reply to both of them: http://mises.org/journals/qjae/pdf/qjae4_2_6.pdf

Caplan (1999) maintains that Rothbard contradicts himself by introducing
income effects and backward-bending supply curves after purporting to
prove that the laws of supply and demand are exceptionless theorems. Block
denies the charge; Rothbard is perfectly correct, given the “ceteris paribus
assumption of no income changes” (1999, p. 29). There is a fundamental
problem with Block’s reply, though. It hardly makes sense to invoke an “all
else equal” condition in cases where all else is of necessity never equal ! The
key neoclassical insight is that price changes ipso facto change income.
Income effects do not happen at the same time as price changes by miraculous
coincidence. They are inherent in the nature of price changes. Block’s
defense of Rothbard makes about as much sense as a “theorem” that “no one
ever dies of starvation,” which is apodictically true “given the ceteris paribus
assumption that no food is nourishing.”
Hülsmann, in contrast, amazingly declines to either (a) defend Rothbard’s
use of income and substitution effects, or (b) argue that this was an unfortunate
neoclassical corruption of Rothbard’s thinking. Instead, he remarks only
that “Mises did not bother about the shape of supply curves” and that relatively
little depends on this.18 Bear in mind that “shape” here is not just slope, but
sign! “The fact that Rothbard occasionally refers to income and substitution
effects does not warrant the claim that these effects correspond to anything
real” (Hülsmann 1999, p. 11). True enough; but Rothbard did claim to have
strictly deduced the conclusions that supply slopes up and demand slopes
down from the axiom of action. Why doesn’t Hülsmann say that Rothbard’s
supposed proofs warrant the rejection of the income and substitution effects?
If he thought Rothbard’s proofs were valid, he would. And if Rothbard’s proofs
of the laws of supply and demand are not valid, the remaining ten chapters of
Man, Economy, and State—everything from interest-rate determination to monetary
economics to the theory of price controls—rest upon error. If these are not
“fundamental feature[s] of price formation” (Hülsmann 1999, p. 11), what is?

Subsequent replies to Caplan deal exclusively with Probability (links can be found here: http://mises.stackexchange.com/questions/134/whats-the-best-austrian-response-to-bryan-caplans-essay). Block says he replied to the rest of Caplan's article in an unpublished manuscript, but I cannot find that.

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in this thread http://mises.org/Community/forums/t/10309.aspx

Jon posted this Garrison article http:// http://www.auburn.edu/~garriro/j7rheiner.htm

Where there is no property there is no justice; a proposition as certain as any demonstration in Euclid

Fools! not to see that what they madly desire would be a calamity to them as no hands but their own could bring

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I wrote a long reply, but somehow it didnt get posted.

Since it's toil and trouble to rewrite it, I'll just indicate the reply.

Rothbard writes that supply and demand only apply when all the things being sold have the same disutility [=grief to the seller] when he sells them.

I think it's on page 105, where he talks about selling to someone hated. Then the disutility of selling to him is greater than the disutility of selling to a friend, and will lead to the hated one being charged a higher price, and a willingness to sell to the friend at a lower price.

He goes on to say that this does not mean that the laws of supply and demand have been violated, but rather that "object X sold to hated one" and "same object sold to friend" are to be treated in theory as TWO DIFFERENT KINDS OF OBJECTS.

Now if you reread page 574 where he talks about not selling all ones land because one wants to have visual benefit from it, he says that selling land [on rare occasions] has "increasing marginal disutility". Meaning selling the second basketball brings greater grief than selling the first one.

OK, that should give an obviously intelligent fellow like you enough to go on to figiure it out.

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Once again I can't figure out how to quote again, so I'll separate replies with spaces. Thanks for replying guys.

 

Thanks for the links NirgrahamUK, although I don't know if the links were a vindication of Rothbard or to say that Giffen goods don't exist (see below).

I understand the neoclassical notion of Income and Substitution effects (different optimal points among multiple indifference curves when a change in price occurs) and how Neoclassical economists use these diagrams to derive demand and supply curves. I understand that, in this context, for a normal good, when the price of a good decreases, the substitution effect causes people to consume more as well as the income effect. For an inferior good, the substitution effect causes people to consume more while the income effect causes people to consume less. When the Substitution effect is greater than the income effect, the demand curve is still downward sloping. When the income effect is greater than the substitution effect, then the demand curve slopes upward and the elusive Giffen Good rears its ugly head. The same thing can be said of supply curves, when the substitution effect is greater than the income effect the supply curve slopes upward, while when the income effect is greater than the substitution effect the supply curve slopes backwards.

Now aside from the fact that this method is incorrect because it assumes indifference, continous utility scales, cardinal utility, and the very unrealistic "budgetline two goods bundle" etc etc, Austrians must critcize the notion of income and substitution effects in order to sucessfully defend their value scale approach and the Laws of Supply and Demand. The argument could still hold that when price decreases people consume more of the good because 1)the price of the good has changed and 2)the income has changed.  However, from my understanding for the Austrians, this type of analysis doesn't work with the value scale approach because a change in "income" violates the ceteris paribus assumption as the perception of the good has changed (I believe this is the correct reasoning), For demand curves, once income changes the value scale changes as well and then the good becomes evaluated differently. In the case of the backwards bending supply curve, a change in income means the good is evaluated differently as the marginal utility of leisure is allowed to rise and each additional work unit is evaluated differently in the context of higher income (ditto).

As Salerno notes in the link above, "the ceteris paribus qualification is construed as precluding any other AUTONOMOUS change in the economic data until full adjustment of the overall economy has been made...endogenous changes in the demand curves and prices of  related goods (substitutes and complements), in the purchasing power of money and in the distribution of wealth induced by this change in supply of a given good may cause some low-income people as well as others to purchase less of the good at the lower price than they did at the higher price in the new final equilibrium.  But this is hardly evidence that demand curves can ever be upward sloping. Rather it is an illustration of the fact that all prices are interconnected and that every single change in the fundamental economic data brings about a "revolution" in the structure of demands, incomes and prices."

However, while all of this information is certainly helpful (and strengthens the Law of Supply Rothbard laid out in Chapter 2), it doesn't really help him in Chapter 9, and my question still stands about him contradicting himself. Rothbard's notion of a backwards bending supply curve could conceivably exist if "the marginal utility of money falls rapidly enough and the marginal disutility of leisure forgone rises rapidly enough as units of labor are sold for higher prices in money" (MES 574) just as a upward sloping demand curve could exist with the same reasoning if the income effect outweighs the substitution effect. But as Salerno notes in his reply and along with everyone elses replies in that thread, that line of reasoning violates the ceteris paribus assumption and instead connects two separate demand curves as if they were one. The same must be said for the backwards bending supply curve, as it would be incorrect reasoning to ever assume such a schedule existed using ceteris paribus assumptions Rothbard developed earlier in the book. So, as much as Iove Rothbard and am enthralled by his writing, I feel like his concession is an incorrect line of reasoning.

 

Smiling Dave:

I understand that a two objects might represent different goods depending on whom they are sold to. And when two objects are differerent goods, then they no longer belong on the same demand schedule. So if they are different goods and belong on different schedules, then why are they drawn on the same curve?

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I understand that a two objects might represent different goods depending on whom they are sold to. And when two objects are differerent goods, then they no longer belong on the same demand schedule. So if they are different goods and belong on different schedules, then why are they drawn on the same curve?

LOL, did I draw them on the same curve?

But if you press me to explain "what was he thinking?", I'll say that since the two basketballs are physically identical, it is interesting to see what a curve showing them both would look like, as well as important to explain why its shape does not contradict supply and demand. Rothbard explained it in a few words added on as a tail to a sentence [mumbled under his breath, probably], so it may pass right by someone not looking for it.

Let me just add that not only are they different goods depending on who they are sold to. Any reason that in the seller's mind adds significant grief [disutility] to one of them that does not exist in the other also makes them two different goods. Which was what Rothbard said in those few words "increasing marginal disutility".

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I never said that you drew them on the same curve but only wanted to highlight that (I least I thought) you only include one good on each schedule (of course a value scale can have multiple goods, but thats not what I'm talking about. I can see how it can be "interesting" to include them on the same graph but it can be very misleading for people when its not clearly explained that this isnt a violation of the law of S/D and only a relaxtion of the ceteris paribus rule.

And not to sound nitpicky, but doesn't "increasing marginal disutility" happen when any good is given up, per Law of Marginal Utility? Now if one good is evaluated psychically different like you suggested then all is fine and well, but in the plain sense it occurs among units of a good.Selling the second unit of cows will have a higher opportunity cost then the first unit of cows because the second unit of cows serves ends higher on an actor's value scale.  When Rothbard says "increasing marginal disutility" he uses it for visual enjoyment forgone in the case of land and leisure forgone in the case of labor, but both of these are different goods from the marginal units of land/units of work and using ceteris paribus in the strictest sense would not allow either of these to move up a value scale when determing price formation for the plot of land/job (they can and probably will move up, but from what I'm understanding of Salerno's comment-see what I posted as well as whats in that thread-they should have no influence on the construction of a curve for a particular good).

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Increasing marginal disutility need not happen always. Think about it. Say you own 100,000 copies of a book. Do you feel worse when you sell one, and only have 99,999 left?

Even if we concede that it always happens, it happens by very small increments indeed, so small they can be neglected. But with those two autographed rare basketballs, the increased grief is HUGE. Same thing on rare occasions, says Rothbard, with land.

And let us remember that the whole value scale thing with the cows always talks about the first couple of cows, not about cow number 10,000. And those cows were not bought with the intent of being sold in the usual descriptions, right? They are used to feed the family etc. It's a whole nother story with goods produced in huge quantities for the express purpose of selling them, or fish caught by the boatfull for the purpose of selling.

I regret that I cannot read the respected Prof. Salerno's no doubt incisive comments, cause the ole brain aint what it used to be.

 

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A supply curve could be completely vertical (Rothbard talks about it extensively) as he explains that a supply curve will only be sloping forward because of reservation demand and speculation. So for the owner of a bookstore who sells 10,000 books a day, since he has to rank the books on his value scale, the first book sold must be lower than the second book sold, ectera. The utility could still be nothing in the form of its decreasing supply will not provoke an increasing in price (as seen in a forward sloping supply curve), or as Rothbard puts it "of course, if the marginal utility of the stock to the supplier is nil, and if the marginal utility of money to him falls only slowly as he acquires it, the law may not change his quantity supplied during the range of action on the market, so that the supply curve may be vertical throughout almost all of its range."(245). The utility ranking of marginal units will still increase, but it just won't be enough to provoke an increase in price. Decreasing marginal utility and increasing marginal utility of goods will always occur because of the ordinal ranking of goods.

But if we stick to the basketballs here, increasing marginal disutility on the same schedule just means in order for the person to exchange a second one a much higher money price will be needed. If for some reason then the objects become two different goods, then they are no longer on the same schedule and on the same supply curve.

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I'll start with a personal note, that I've developed great respect for your knowledge and intelligence. More power to you.

I'm very glad we agree about all you said in the first paragraph.

As for the basketballs, let's give everything numbers and hopefully things will become clear. Even though it is a big no no in AE to assign numbers to the benefit something gives a person, let's do it just this once, the better to clarify an idea.

Say a guy owns those two totally identical valuable basketballs, and suddenly needs a lot of money for an operation, He will be confined to a wheelchair, deaf and blind, if he doesn't have the operation. The market price of the operation is $100,000. But he would have it even if it cost $100 MILLION, so important is his health to him.

Parting with the first of the balls gives him a million dollars worth of grief. Parting with the second hurts much more, and gives him ten million dollars worth of grief.

OK, if he can get 100K for both of them together, his balance sheet looks like this: Total happiness: $100 million dollars, [because now he can have the operation]. Total grief: $11 million. Bottom line: $88 million net happiness.

If he can get 100K for one basketball, meaning 200K for both of them together, the situation is like this:

If he sells one ball, the balance sheet is Total Happiness: $100 million Total Grief: $1 million. Bottom line: $99 million happiness.

If he sells both balls, we have Total Happiness: $100 million from health and $100K in cash. Total Grief: $11 million. Bottom line: $88.1 million happiness.

Obviously, he is better off selling only one ball.

I confess I lost the thread a bit, about whether we need to consider them as two goods or not after this analysis. In any case I think this clears up the situation without contradicting the law of supply and demand.

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I appreciate your comment.

As much as I enojy your example, I'm a little bit confused as to what its trying to explain and a little confused as to the cardinal utility dollars of happiness. From my understanding the problem cannot exist without the numerical utility values associated with each good (which according to A.E can't exist). 

If I'm reading your example correctly, the individual's value scale would look something like this:

Operation

100 million dollars

10 million dollars

2nd B.B

1 million dollars

1st B.B

 

The individual values the operation the most, even if it cost him 100 million (I don't know if 101 million is too much, so I left it out). Each larger money amount ranks higher than smaller sums because of the law of total utility. Now since selling one "gives him 10 million dollars worth of grief", 10 million dollars ranks higher than the 2nd B.B sold because selling the actor would not sell the B.B at a lower price since the disutility of forgoing the B.B ranks higher than the monetary sum of less than 10 million dollars. The same thing goes for the 1 B.B, as it gives him "1 million dollars worth of grief". In the strictest sense of the value scale approach if the going price for the B.B's was 100,000 he would not sell them because the opportunity cost of selling the B.B (1 million dollars) is greater than the 100k. If then for some reason he says "screw it I need the operation" and sells them for the going price (100K), then the value scale looks differently. In any case, there are never "net dollar amounts"

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