04 Feb 2015

Reconciling Marginal Productivity Theory of Factor Payments With No-Profit in Equilibrium

My latest Mises CA responds to a reader who thought he had discovered a contradiction in Rothbard. An excerpt:

Notice that in this outcome, it is still true that an entrepreneur earns a “surplus” on the inframarginal units. However, such an entrepreneur is starting out with a bunch of fixed costs (based on other expenditures necessary for the operation), and by optimizing the amount of units to buy of the particular factor under examination, the entrepreneur is simply reducing his loss down to \$0. For example, holding all other expenditures at their optimal amount, and starting with 0 units of labor, the entrepreneur might suffer a loss of \$1 million per year. Then if the entrepreneur hires 1 unit of labor at \$10/hour, where that first worker has a MVP [marginal value product] of \$20/hour, then for a 2,000 hours / year work schedule, the loss now drops to (\$1 million – \$20,000) = \$980,000 per year. The marginal benefit of hiring each new worker exceeds the marginal cost, meaning that total profit increases, up until the point at which the last worker hired just pays for his own wages. At that point–if we’re in a long-run equilibrium–the loss has been whittled down precisely to \$0.

28 Responses to “Reconciling Marginal Productivity Theory of Factor Payments With No-Profit in Equilibrium”

1. Transformer says:

Good post !

While this explains how the profit on the store would be pushed back to the average for the economy, it doesn’t explain the landlords “profit”. The extra competition increases his revenue from \$10000 to \$17000.

I suppose you could go one-step back and show that more people will open stores seeing the big profits that landlords are making , and this will force rents down – but ultimately if land to build stores is in short supply – landlords may earn above average profits (using the term loosely) just becasue they own the land. I think this is actually the conclusion Rothbard comes to.

This makes sense form an economic theory perspective nut not so much from a social-justice one.

Its pretty obvious that a lot of global land and natural resources are owned by people who have just stolen them (Russian oligarchs, Middle eastern oil sheik’s etc, plus examples closer to him). Rotbardians are very good at highlighting the economic inefficiencies and injustices inherent in statism (and I agree with them). However (and correct me if I am wrong) they are less good , or at least less vocal , at highlighting the injustices arising from the fact that some significant part of global income is based on outright theft of natural resources in the recent or more distant past.

(Have I been reading too much Piketty?)

• Bob Murphy says:

Transformer, I think you anticipate my response, but it’s not profit if the owner of a piece of real estate rents it to somebody. If there is new information and the rental price jumps, the difference in capitalized value of the land is a one-shot capital gain that we can book as profit, but the continued flow of rent is rent. Indeed that’s the quintessential form of rent, which is where the label comes from.

• Transformer says:

Yes, I see there is a difference between profit and rent, and I was being loose in my comment. But I think I was really trying to get at the justification behind some forms of rent, particularly those based on illegal or arbitrary ownership of natural resources.

• Bob Murphy says:

Transformer that was a big thing in Kevin Carson’s project. If you look at the issue of the JLS in which this article appeared, you’ll see a whole debate on this topic.

• Transformer says:

Thanks, that looks interesting – I will check it out.

• Harold says:

Does this make income from rights to a ebook, for example, more like rent than profit? The distribution of electronic books is essentially costless.

• guest says:

“However (and correct me if I am wrong) they are less good , or at least less vocal , at highlighting the injustices arising from the fact that some significant part of global income is based on outright theft of natural resources in the recent or more distant past.”

Nothing is a resource – “natural” or otherwise – until an individual utilizes it as a means toward satisfying his own personal preferences.

If nobody else wanted agricultural land but one guy who then homesteads it, then its value in trade would be nothing.

Here is an extremely important point: ALL prices consist of the subjective values of individuals, and the supply of a good factors into the price only insofar as any given individual deems that there is marginal utility in an extra unit of that good.

(Or, in other words, costs are subjective, too. It may take X number of Factor A to make a good that someone wants, but the only reason the number of Factor A is relevant is because it has been chosen as a means to fulfill the preferences of individuals for a finished good.

(Factor A could be extremely rare and useful as a means to fulfill all sorts of preferences if employed for those purposes, but if nobody knows about its usefulness, or, due to some philosophical reason no one cares to utilize it, then it has no use-value, and therefore no price.)

There’s no such thing as an optimal or fair price for something. The price for land, for example, goes up because other people want it – that’s what prices *are*: subjective values.

Prices are *supposed* to be high for rare goods that many people want. Other people bid up the price by offering something of higher value to the seller relative to other bidders.

And then, because there’s logically no value in doing more than is necessary to acquire something, the seller ought to feel perfectly good about himself if he charges the highest possible price he can get. Anything less would be to place an unnecessary burden on himself.

(Now, if alieviating a particular person’s stated uneasiness is part of the *goal* of the trade, then he should feel just as good about lowering the price, because that, too, would be an example of maximization of profit.)

I highly recommend this video, if you haven’t watched it, already:

The Birth of the Austrian School | Joseph T. Salerno

• Major.Freedom says:

Pretty sure Transformer was talking about outright theft of resources from homesteaders.

He is saying that setting private property rights now would invariably be “tarnished” by past violations of them.

I think…

• guest says:

Yeah, I forgot to get to that point after setting the foundation.

• guest says:

Yes, there has been theft, but if the people from whom it was stolen died before giving their belongings to someone else, or no one deliberately accepted the offer from the owner, then it rightfully belongs to the next person to homestead it, since no one else has a legitimate ownership claim.

Also, given that holding each individual criminal responsible for what they did to each of their individual victims would be impossible (there are no group rights or group crimes), if only because nobody has all of those answers, the most just thing that could be done is, from this point forward, to let the free market reward those who provide value without violating others’ rights, hold individuals accountable to individual victims (if you have been delegated that authority by an individual who has the legitimate right to do so, himself), and, when a specific individual can prove his right to a piece of land, then respect that individuals’ private property right.

It’s too bad that Mises.org restructured their site in such a way as to result in the removal of past article comments, because there was a really good one which explained that even if someone “inherets” ill-gotten gains, he still has to buy stuff, so as long as there’s no government there to forcibly prevent competition, he has to sink or swim on his own merits.

And if, through employing his ill-gotten gains, people are still willing to trade with him, then, whatever else can be said about his unfair starting advantage, other people are making a profit off of him, and he is actually having to dispense with some of his ill-gotten gains.

It’s also not likely that every single thing he has was stolen; So good luck figuring out those particulars.

The individuals who have a right to the stolen goods should try and take them back, but it would be economically destructive to prohibit voluntary trade with him.

• Transformer says:

Yes, MF is right about the intent of my comment.

I feel a bit uncomfortable with the “as its impossible to tell which wealth is legit and which is stolen, we should let sleeping dogs lie” argument (hope that’s not a wild mis-characetization). Control over resources combined with control over the state could well have allowed the thieves to have legitimized their wealth and covered up the historical trail. Specific individuals may have been totally screwed in this process but have 0% chance of proving their claims. Such individuals may find it a hard sell as to why they should respect the property rights of those they suspect stole from them, or even whose ancestors stole from their ancestors.

• guest says:

“Specific individuals may have been totally screwed in this process but have 0% chance of proving their claims.”

If their claims cannot be proven, then forcibly taking things from suspects more likely than not will violate yet another individual’s rights.

“Such individuals may find it a hard sell as to why they should respect the property rights of those they suspect stole from them, …”

Same thing as above.

“… or even whose ancestors stole from their ancestors.”

This case would be irrelevant, since you can’t own something simply by being born. You have to homestead it, or deliberately accept it from the previous owner.

If the victim is dead, then there’s no one that exists who has a legitimate claim to restitution; If the criminal is dead, then there’s no one that exists from whom restitution may legitimately be exacted.

• Major.Freedom says:

That is all well and good, but the main problem once you get to that point is the efficacy of implementing it. Lack of definitive proof via evidence may not always overlap with absence of injustice. Real victims may go without justice. This is of course true for any body of laws.

Then there is the problem of the burden of proof being placed only on those alleging an injustice. This is consistent with the very effective and morally fair axiom of “innocent until proven guilty”, but there might be cases of real victims not knowing an injustice was had, which will result in cases of ” well nobody is complaining here so that means land ownership distribution in those cases will be just.”

I think the issue is that because the state has existed for so long, the ability to accurately and efficiently trace back proper ownership claims and how they came to be and how they were transferred, voluntarily or otherwise, in order to come to a universally fair conclusion today, would be next to impossible.

Then there is the problem of why sons and daughters automatically have “first dibs” on lands identified as properly belonging to “this” set of parents, given that many parents in practice sometimes forbid and do not wish lands to be bequeathed to their children.

2. Transformer says:

“plus examples closer to him” should be “plus examples closer to home”

3. Tel says:

It bothers me a bit to say “entrepreneur” in relation to the Evenly Rotating Economy. After all, the whole point of an “entrepreneur” class is risk taking and getting involved in new areas of business.

Suppose the MVP of the first worker is \$20 per hour and this worker knows as much about the business as Joe the owner of the business… the employee can just work for herself and earn \$20 per hour instead if the \$10 that Joe offers.

There might be reasons why this doesn’t work, possibly Joe has a license issued by government and those are hard to get, but then the license becomes an asset. Maybe this type of business is only viable with a minimum of 5 employees, because of some structural concerns (maybe they offer 24 hr service for example) but in that case you can’t really say what the MVP of the first employee is, because it is discontinuous (no derivative exists until after the minimum size is reached). Maybe costs and economy of scale are nonlinear, but then MVP is more complex, a group of just the right size can organize some complex cost sharing scheme and still get paid more than they do working for Joe. Maybe Joe just has an excellent reputation and customers would never switch, but that’s not quite ERE.

• guest says:

“… but in that case you can’t really say what the MVP of the first employee is …”

The MVP of the first employee is zero since the unit of concern is “5 employees”.

The MVP is only relevant for at least the first set of 5 employees with certain skills:

Toward a Reconstruction of Utility and Welfare Economics [by Murray N. Rothbard]
Ordinal Marginal Utility and “Total Utility”
http://mises.org/library/toward-reconstruction-utility-and-welfare-economics-0#2a

“There is, however, no reason why marginal utility must be conceived in calculus terms. In human action, “marginal” refers not to an infinitely small unit, but to the relevant unit. Any unit relevant to a particular action is marginal. For example, if we are dealing in a specific situation with single eggs, then each egg is the unit; if we are dealing in terms of six-egg cartons, then each six-egg carton is the unit. In either case, we can speak of a marginal utility. In the former case, we deal with the “marginal utility of an egg” with various supplies of eggs; in the latter, with the “marginal utility of cartons” whatever the supply of cartons of eggs. Both utilities are marginal. In no sense is one utility a “total” of the other.”

• Tel says:

Well the example states the MVP of the first employee is \$20 so the presumption is that a solo business must be workable.

• Harold says:

Tel, I don’t get what you are saying here. If she could earn \$20 for doing the same work, then she would do so. However, the entrepreneur has to do all the business stuff as well as do the work. Joe prefers to do this, the employee does not, even if she knows as much as Joe. Or maybe Joe has access to capital the she does not, or is prepared to risk a loan. I don’t see the need to introduce permits or minimum viable size.

• Tel says:

If there’s risk involved, it is not an Evenly Rotating Economy.

As for access to capital, that would imply privileged positions in the capital market structure which may well happen, but then you have a hidden asset (much like licensing). I guess in societies where the “who you know” becomes more important than “what you know” you can say the hidden asset of access to that old boys’ network pays a tangible return. Most economists would probably be dissatisfied with that explanation.

So it could be down to preferences, and I guess this covers you in any case, mind you would all employees think that way? Out of 10 employees any one of them could double their wage by breaking out and starting a solo business, I think one of them would go for it.

The problem comes back to the Evenly Rotating Economy, which is a very specialized construct, not intended to closely model a real economy.

Think of it this way, in a real economy two things are happening at the same time: goods are being produced, exchanged, consumed, and also information regarding those goods is being processed. Thus, I sell apples by physically exchanging the apple for some sort of payment, while I simultaneously haggle over the price of apples, and discuss with the buyer about the quality of the apples, how the supply side is looking, what type of apples they like, etc.

In an Evenly Rotating Economy there’s no point haggling because no new information ever turns up. Everyone knows what everyone else knows. Whole industries cannot exist under an ERE, advertising and market research for example.

• Harold says:

OK, thanks for more details about the ERE. Having looked at it a bit now, the concept of “entrepreneur” makes no sense in the ERE -according to Mises Inst. “future prices will be the same as current prices and the entrepreneur has no reason to combine factors of production anew based on the anticipation of future prices; there is no future price as different from the current price, and therefore, no entrepreneur.” So I see where your initial comment came from.

• guest says:

Is a government-mandated license an asset?

This reminds me of the saying that the government wants you to be thankful for the crutch it gave you after it broke your leg.

Government-mandated license requirements impede wealth creation rather than aid in the process.

• Tel says:

Thankful or not thankful is irrelevant.

If I have a license such that I’m the only one allowed to sell apples then it’s a big advantage to me… and a big disadvantage to everyone else. No doubt that operates as a type of asset. It would have a sale price (presuming I’m allowed to sell it). Letters patent operate like that.

Now, there’s another issue whether such a device is a nett advantage or disadvantage to the economy as a whole (i.e. whether the privilege to the license holder outweighs the problem caused by granting such a privilege). But how do you go about measuring that? How do you compare utility across a group of people?

• guest says:

“Now, there’s another issue whether such a device is a nett advantage or disadvantage to the economy as a whole (i.e. whether the privilege to the license holder outweighs the problem caused by granting such a privilege). But how do you go about measuring that? How do you compare utility across a group of people?

(An excellent question, by the way.)

Since the economy is always about the individual (economic activity – “human action” – happens only by individuals, and only for their own purposes – even if the personal preference is in regard to another person), such devices can be said to be a net disadvantage to the economy if a single person’s personal rights were violated.

I think the term is “Pareto negative”, or something to that effect.

To be sure, since utility is subjective, it cannot be compared across a group of people.

• Tel says:

Imagine a smallish country with just a million people, and in order to get any law passed you needed to get unanimous agreement from all of those people. Would be kind of tricky, hmmm?

That’s the problem with Pareto optimisation.

Then when you finally do pass your first law, the country next door can always veto that because Global Warming, or whatever they can think of.

• guest says:

“Imagine a smallish country with just a million people, in order to get any law passed you needed to get unanimous agreement from all of those people. Would be kind of tricky, hmmm?”

Gridlock is a feature, not a bug – the goal of legitimate government isn’t to pass laws.

Legitimate law is based on private property rights, which are logically prior to government.

When individuals choose to not agree to be contractually bound together, laws should not be passed, and governments should not be created.

• Tel says:

Fine in theory, but the nation next door, which can organize itself to raise an army will take away the property rights from those individuals who cannot get their act together. No nation has ever operated on the basis of 100% consensus, nor even close to that.

Legitimate law is based on private property rights, which are logically prior to government.

When individuals choose to not agree to be contractually bound together, laws should not be passed, and governments should not be created.

The property rights are only “logically prior to government” while everyone agrees. It only takes a handful to say, “No sorry, that’s not your farm, it belongs to us,” then someone needs to settle that, and ultimately such settlement has to be backed by violence at some point (even if the violence is only a threat and one side backs down).

Regardless of who wins and how they do it, you have already failed to get 100% agreement.

• guest says:

“Regardless of who wins and how they do it, you have already failed to get 100% agreement.”

You need 100% consensus for contractual obligations, not self-defense.

“Fine in theory, but the nation next door, which can organize itself to raise an army will take away the property rights from those individuals who cannot get their act together.”

If you’re not violently preventing cheap imports from individuals from the nation next door (so-called “free-trade” agreements or sanctions), it won’t be in their interest to take away property rights from individuals.

Besides, the solution to preventing the nation next door from using an army to take away my property rights isn’t to empower my own government to take them before the other nation can.

If there isn’t 100% consensus on contracts such as governments, then the laws of such governments aren’t laws at all.

• guest says:

Check this out; It’s awesome and timely:

How Economic Aggregation Hides the Problems of Interventionism
http://mises.org/library/how-economic-aggregation-hides-problems-interventionism