26 Jul 2012

## More on Krugman and Marginal Product, Sans Calculus

By popular request, my new article at The American Conservative makes the same basic point that Karl Smith made back in November, but I think I spelled it out here very clearly to isolate Krugman’s mistake. Contrary to some of you guys in the comments, I don’t think the issue on this one was nominal vs. real, I really think it was marginal vs. inframarginal. I tried to show that by reproducing Krugman’s error in a story involving direct payment in apples. An excerpt:

In terms of our story, we can illustrate the problem by imagining that two more workers show up in town, looking for work picking apples. Through reasoning similar to that above, we conclude that in the new equilibrium, one of the newcomers goes to Smith’s orchard, the other to Jones’s, and they both get paid 10 apples per hour. However—and here is the crucial part—the original workers now only get paid 10 apples per hour, too. Because the four workers are all interchangeable, they have to get paid the same amount, and we know that the marginal product of the new guys is only 10 apples per hour.

Step back now and survey the whole picture. There are a total of 60 apples being harvested every hour among both orchards, while the four workers are only being paid 40 apples total. Thus the orchard owners are enjoying a “surplus” of 10 apples each, for every hour the laborers are at work. Thus, it is not true to say that the workers in this hypothetical world are “getting paid what they put in,” in the sense that Krugman means. Yet even so, the workers are being paid their marginal product, according to textbook price theory.

#### 29 Responses to “More on Krugman and Marginal Product, Sans Calculus”

1. Kevin Donoghue says:

Thus the orchard owners are enjoying a “surplus” of 10 apples each, for every hour the laborers are at work. Thus, it is not true to say that the workers in this hypothetical world are “getting paid what they put in,” in the sense that Krugman means.

You seem quite convinced that Krugman means something entirely different to what he actually says. In his words, which you quote: in “standard textbook microeconomics: in a perfectly competitive economy, factors of production are supposedly paid precisely their marginal product.”

They are “getting paid what they put in,” in precisely the sense that Krugman describes. They are getting their marginal product.

• Bob Murphy says:

KD if we take Krugman to be saying the correct thing about factor pricing, then his objection to Romney supporters falls away. The rest of the population does indeed suffer a decline in real income, if some suppliers of labor withhold more than 1 man-hour.

2. Kevin Donoghue says:

Incidentally, Karl Smith, the “Keynesian fellow-traveler economist” (Bob’s description) didn’t actually dispute Krugman’s point. He simply moved the goalposts:

The problem was with Paul’s period. He stopped with one person, one hour. However, most people suspect that we are dealing with more than a single man-hour here.

So, if we make a really substantial reduction in inputs, this distinctly non-marginal change will have more-than-marginal effects. No shit, Sherlock?

• Bob Murphy says:

KD you continue to make the same point as when you first showed up here. Are you telling us that Krugman thought right-wingers were worried about job-creators scaling back their inputs by a total of 1 man-hour? Or, was Krugman leading his readers to believe that even if we lost 2 or more man-hours, the effect on everybody else would be a wash?

Karl and I are actually being generous, and presuming Krugman made a basic mistake without realizing it. If he is actually correct because he was thinking what you have in mind, then he is a liar.

(Anyway, we don’t have to speculate. Krugman specifically said Wheelerdealer reduces his efforts by one-third. I.e. more than one unit.)

OK Watson?

• Kevin Donoghue says:

You’ve got your sequence wrong. In the November post which Karl Smith is responding to, Krugman explicitly refers to a one-hour reduction: “If a hedge fund manager gets \$60,000 an hour, and he works one hour less, he reduces GDP by \$60,000 — but he also reduces his pay by \$60,000, so the net effect on other peoples’ incomes is zip.” Karl Smith explores a much more dramatic reduction in supply: “contracting the supply of high income earners will cause the pre-tax incomes of those who remain to go up.” Obviously Krugman is not discussing a reduction large enough to have that effect.

In the July post the reduction is 1,000 hours at \$10k per hour, resulting in \$10m in income foregone. Krugman assumes this will have no impact on the wage-rate for wheelerdealers. That’s hardly unreasonable in an economy the size of the US.

• Major_Freedom says:

What good are nominal income increases if there is a lower productivity of labor and lower supply of goods to buy?

Why are we supposed to believe that as long as total nominal incomes don’t fall, people are no worse off?

If everyone but me spent money on consumption, then even though nominal incomes won’t fall, my standard of living would collapse, because the demand for labor and the demand for capital goods will fall to zero, thus collapsing the productivity of labor. I’d be able to go to the store with more dollars, but the store shelves will be empty, and the building would eventually become dilapidated.

3. Major_Freedom says:

I must insist that the issue is one of nominal vs. real.

Krugman said if Wheelerdealer’s capitalistic labor is reduced from 3000 hours a year down to 2000 hours a year, then because Wheelerdealer is earning \$10 million fewer dollars from non-Wheelerdealers, it means non-Wheelerdealers can earn \$10 million more dollars, and are hence no worse off.

The reason why I think the issue is between nominal vs. real, is the following analysis:

Krugman wrote:

“So, imagine a Romney supporter named John Q. Wheelerdealer, who works 3000 hours a year and makes \$30 million. And let’s suppose that he really does contribute that much to the economy, that his marginal product per hour — the amount he adds to national income by working an extra hour — really is \$10,000.”

Here the word “income” clearly refers to real goods, which are represented as “\$10,000 worth per hour”. Marginal product per hour is hourly produced real goods that have a value of \$10,000.

Krugman said Wheelerdealer makes \$30 million, and then “let’s suppose that he really does contribute that much to the economy”. This is clearly saying that we should suppose that \$30 million in money earnings Wheelerdealer makes is not just “exploitation”, but that he really is producing goods that can be represented by \$30 million. This is of course to distinguish Wheelerdealer’s nominal \$30 million earnings, from Wheelerdealer’s real productivity. For if the “makes \$30 million” was real all along, then “And let’s suppose he really does contribute that much to the economy” would have been redundant and grammatically awkward. It would be like saying “I earn \$100 in dollars. And just for argument’s sake, let us suppose that that I really do earn \$100 in dollars.”

Krugman then writes:

“According to marginal productivity theory, this does in fact shrink the economy: Wheelerdealer adds \$10,000 worth of production for every hour he works, so his semi-withdrawal reduces GDP by \$10 million. Bad!”

So at this point, he’s still talking about Wheelerdealer’s real output, specifically, he is supposing it fell, which Krugman represents as a fall of “\$10 million in GDP.” This I think is the source of confusion, because he is presenting real output as synonymous with how much money is spent on it. Most economists do this, because real goods are heterogenous, and it is difficult to add those up to get a single representative concept. It’s a lazy way of saying “The real goods that were purchased for a total of \$10 million”.

Then Krugman continues:

“But what is the impact on the incomes of Americans other than Wheelerdealer? GDP is down by \$10 million — but payments to Wheelerdealer are also down by \$10 million.”

At this point, it is absolutely clear that by “income” Krugman means real output, and by “payments to Wheelerdealer”, he is referring to nominal payments. People don’t pay Wheelerdealer in apples, they pay him in dollars. Krugman is saying that because Wheelerdealer’s nominal income “really does” signify that much output, meaning it wasn’t just exploitation of the workers, then it follows that nominal payments to Wheelerdealer will decline by \$10 million.

Then he writes:

“So the impact on the incomes of non-Wheelerdealer America is … zero. Enjoy your leisure, John!”

And there you go. From the statement “payments to Wheelerdealer are also down by \$10 million”, Krugman infers “the net impact of incomes to non-Wheelerdealer America is … zero.”

How is that NOT a conflation of nominal and real income? Anyone, please tell me.

The concept “income” was deftly switched from real output in the preparatory analysis, to nominal income in the conclusion, without so much as a blink. He did EXACTLY what Keynes often did, which is equivocating “income” between real and nominal.

This IS an issue of conflating nominal and real, for that is exactly what Krugman did when he went from treating “income” as a real concept, to “income” as a nominal concept, as if unchanged nominal incomes means everyone is no worse off!

Clearly however, if we always keep clear the difference between nominal and real income, then we can see exactly where Krugman made his mistake. He made it when he deftly switched from real to nominal. He made it when he said that if non-Wheelerdealer nominal incomes increase by \$10 million to the extent that Wheelerdealer’s real output declined by an amount that can be represented by \$10 million GDP, then supposedly non-Wheelerdealers are no worse off.

4. Major_Freedom says:

I don’t think the apple example can provide us with enough practical information to make sense of the error Krugman made in the Wheelerdealer scenario. In the Wheelerdealer scenario, there were differences in productivity, and differences in nominal incomes. That’s what Wheelerdealer and non-Wheelerdealers is meant to describe.

We should take into account differences in types of output, and hence differences in how different types of output affect the productivity of labor going forward.

Maybe you can tweak the apple example so that there are differences in productivity, as well as types of output:

Imagine 1 of the 4 workers is not a producer of apples, but a producer of ladders that are used to pick apples.

It would be wrong to say that the 3 workers can produce the same apples as before if the 1 producer of ladders reduces his output. For the production of 30 apples per hour depended on the assistance of the ladder capital. With fewer ladders, the 3 workers can only pick fewer apples, DESPITE the fact that the same nominal quantity of apples as medium of exchange are being exchanged.

It is almost a certainty that examples in which the output is also the medium of exchange, will lead to confusion. We must separate nominal versus real in a monetary economy where people earn nominal for the purposes of buying real goods. If everything is apples, then it would make little sense to say that 10 apples were produced and then sold for…10 apples.

If in the example apples and ladders are produced, and apples are the real output but a different commodity than apples is the medium of exchange, a commodity that is durable, homogeneous, divisible, and highly valued, then I think you’ll see how Krugman’s mistake was conflating nominal with real, and not marginal versus submarginal, which leads, I think, to contradiction of saying there is no change at the margin, but somehow a change when lots of people change at the margin (which is a praxeological impossibility), as well as anti-economic concepts such as infinitely differentiable and continuous “function” type analysis which human actors do not take into account when investing, producing, and consuming.

• Bob Murphy says:

MF wrote:

It would be wrong to say that the 3 workers can produce the same apples as before if the 1 producer of ladders reduces his output.

Right, and Krugman never said that.

• Major_Freedom says:

But he did. Krugman said Wheelerdealer reduces his output from what 3000 capitalist labor hours produced, to what 2000 capitalist labor hours produced. He said there is a fall in real output that is represented by “\$10 million GDP”

Krugman is saying the worker’s “incomes” (which was equivocated) won’t fall because they can make more nominal dollars that no longer goes to Wheelerdealer.

• Major_Freedom says:

How is that not saying 3 workers can produce the same as before with the 1 worker producing fewer ladders?

• Bob Murphy says:

But he did.

No, he’s agreeing that total apple production would fall if the ladder is no longer involved. But he’s saying the new production would be equal to old production minus how much the ladder owner was previously paid.

So yes, of course total apple production falls, but total apple payments to everyone-except-the-ladder-owner is the same.

This is still a false claim, but you seem to be repeatedly attributing views to Krugman that he doesn’t hold, and then knocking them down.

• Major_Freedom says:

No, Krugman is saying there will be no net change. He didn’t say there will be new production equal to old production minus how much the ladder owner was previously paid. He only said total nominal income would be unchanged. That’s what he meant by “enjoy your leisure John!”

Total apple production DOES fall, you can’t see this if you keep using apples as both real output and as medium of exchange. If ladder production falls, then apple payments to everyone except the ladder owner must also fall, precisely because their initial apple payments depended on the use of the ladders.

You have fewer ladders, you produce fewer apples, and apple payments will go from 30 to something less.

But in a monetary economy, we have to separate medium of exchange from real output, and notice that even if total nominal spending doesn’t fall, it doesn’t mean, contrary Krugman, that everyone-except-the-ladder-owners are just as well off.

I am not falsely attributing views to Krugman that he doesn’t hold. It’s right there in black and white. He switched from real income to nominal income. He said there is a drop in real output, but non-Wheelerdealers are no worse off because they experience an increase in nominal income on account of Wheelerdealer earning less nominal income.

I think you might be falsely attributing views to Krugman that he did not write. Nowhere did he write that new production would be equal to old production minus anything. He said “So the impact on the incomes of non-Wheelerdealer America is … zero.”

An impact of zero means there is no “minus” going on here.

• Major_Freedom says:

Krugman even doubled down on this point when he wrote:

“OK, there’s a catch: Wheelerdealer pays taxes, and when he chooses to work less, he pays less taxes. So there is in fact a welfare loss to the rest of America, but it comes only through the fact that revenue falls.”

See? Only if NOMINAL incomes fall, can Krugman even see non-Wheelerdealers being worse off.

• Major_Freedom says:

Make that TRIPLE down. He then writes:

“Now, obviously the Romney fans have a very different view. They seem to believe that John Q. Wheelerdealer somehow adds much more to the economy than even the lavish amount he gets paid; he’s an engine of growth! ”

Krugman is equivocating real and nominal AGAIN. Here, he is saying that Romney fans are foolish to think, what he believes they are thinking, that someone could add more ladders than the dollars they receive.

Huh?

Who thinks of real output and dollar spending in this way other than someone who conflates real output with dollars? Who can even say it makes economic sense to say that someone produces the same quantity of ladders as the dollars they earn doing so? It doesn’t make any bloody sense.

Only if one views dollars as equivalent to real goods, can one say that consuming fewer apples but earning more dollars is not a loss of any kind.

No capitalist produces less than, more than, or equivalent to, the money they earn. Money and real goods are incommensurate concepts. Those who pay money gain the goods, and those who pay the goods gain the money (from which they can then gain goods). There is nothing here to even make a difference concept or a sum concept.

Krugman is not getting the “Galt” argument. He believes that the Galts are saying cepitalists produce MORE than the money they earn, which makes no sense, when in reality the Galts are saying that capitalists are increasing real wealth by increasing the productivity of labor, through which they are rewarded with money income from the customers. If he did well, he makes a profit, if he didn’t, he incurs a loss.

Nobody is saying that capitalists produce MORE than the money they earn, except those who are conflating nominal and real.

5. Major_Freedom says:

Krugman is basically saying this:

“Hey all you liberal proletariat hard working altruist do gooder readers of mine, don’t worry about the greedy, selfish, immoral capitalist exploiters fear mongering about what will happen if they reduce their “productivity” (which by the way is a term I use very lightly, but I will go along and play the game on the bourgiosie’s terms, to really stick it to them, because I got them nailed on this one!). For if the capitalists do reduce their “productivity” (which again is a term I use lightly), then they will get paid less dollars, right? Well, if the John Q. Wheelerdealers get paid less, then that means all you liberal proletariat hard working do gooders can make more money for yourselves! Join with me and let’s mock the capitalists! Enjoy your leisure John! We don’t need you capitalist exploiters anyway! You do nothing but hoard cash and extract profits that rightfully belongs to the liberal proletariat hard working altruist do gooder class anyway! And we have the “economics” argument to prove it!”

6. D. F. Linton says:

Why work so hard to refute this foolishness? Clearly if the rest of us lose nothing if anyone else drops out of the system of division of labor and free exchange, then after a few iterations Robinson Crusoe is as well off as any American city dweller. He certainly wouldn’t gain anything if some guy named Friday showed up. By Krugman’s logic, none of us lost anything by Steve Job’s death and indeed we would be equally well off if he had never been born.

• skylien says:

What if Krugman dropped out of the system of division of labor?

• Major_Freedom says:

Then many individuals would be worse off and many individuals would be better off.

• Dave says:

I think it’s different because his job is to advocate for more state power. Legally that should be the equivalent to like giving advice on how to do stick-ups efficiently.

7. Jonathan M.F. Catalán says:

Frank H. Knight undermined Krugman’s argument in 1942 in “Profit and Entrepreneurial Functions;” see this quote,

To begin with a general abstract answer, it will be evident to anyone with a rudimentary understanding of economic processes and analysis that profit (always in the sense of pure profit) would be absent under the conditions of equilibrium with “perfect competition,” (which may be defined in more than one way). The”tendency” of the competitive processes of buying and selling and the control of production is to impute the whole product to the productive agencies which create it, leaving nothing for entrepreneurship as a distinct function (except for monopoly gain, referred to below). This means that under the conditions of ideal equilibrium (stationary or moving) the function of entrepreneurship itself is entirely absent from the economy.

8. Tel says:

I completely support your explanation of why 4 guys picking a total of 60 apples per hour and only getting paid a total of 40 apples per hour can still exactly match their marginal productivity. However, I think your conclusion from this doesn’t really work, although it might take a much longer article to explain it properly.

Now a Marxist might conclude from our story, “Aha! The capitalist system skims product out of the effort of workers into the hands of the fat cats.” Yet that would be an odd way to describe the situation, since the owners in this story are supplying the orchards and equipment.

In tabular form then:

2 orchards + 2 pickers => wages of 20 apples per hour per picker + 0 apples per hour return per orchard.

2 orchards + 4 pickers => wages of 10 apples per hour per picker + 10 apples per hour return per orchard.

2 orchards + 6 pickers => wages of 5 apples per hour per picker + 20 apples per hour return per orchard.

Only in the first scenario is the Marxist happy, when return on capital is exactly zero and the workers keep everything they pick. However, the exact same marginal theory is at work in every scenario so what is it that makes one situation more or less “fair” than another? How much does the orchard owner really deserve, and how much do the workers deserve?

You can see why workers in the first scenario feel ripped off when more workers come along because now they work just as many hours for half the wage! Then another two workers come along and their wages drop by half again, while the orchard owner does nothing and his wages have gone up through the roof. As more pickers come along the gap between rich and poor gets wider and wider… all of which feels really unfair to the people concerned.

What I’m getting at is, although the marginal productivity theory does tell you what each economic component is worth in a system, it says nothing about what makes the system fair or unfair. How would we feel if the pickers formed a guild and decided amongst themselves that only a maximum of 4 pickers could be tolerated? The marginal productivity theory will tell you the effect of the guild is to keep their wages higher than they would otherwise be, but tells you nothing about whether that would be a respectable way to behave.

You actually need a moral theory as well as an economic theory, if you see what I’m getting at.

For example, the owners of agricultural land earn a lower income than the owners of diamond mines, even though food is essential to life. This is because the marginal value to consumers of an additional bushel of crops is lower than the same amount of diamonds, simply because diamonds are relatively scarce. Yet even though agricultural owners are currently paid according to the value of the marginal bushel of crops, it would be silly to conclude that if all owners withdrew their farms from production, that the effect on everybody else would be a wash.

Sure, the relative scarcity of one against the other drives the relative price… hardly a surprising conclusion (except to a Marxist) but it still does not answer the moral question. Point is that the owners of agricultural land could sell all their land to one guy who then produces only enough food to make apples sell for the same price as diamonds. Would that be “fair” though, or should that owner produce plenty of cheap food because it’s just the decent thing to do? We have laws in place for precisely the purpose of making sure markets are “competitive” and no one can create an artificial scarcity… and yet those laws have been observed to be abominable failures, and scarcity still exists, with the definition of what is “artificial” scarcity vs “natural” scarcity being highly arbitrary (and subject to corruption).

By the way, when you have a positive feedback situation (like the production advantage of an assembly line, vs individual craftsmen) the outcome gets even stranger. Let’s suppose some sort of assembly line can produce enough goods for 50 people to consume but requires only 10 people to do the work. Since 40 people are sitting idle, and all workers are interchangeable, their marginal productivity is zero! Then again, if their wage is zero, who buys the stuff?

However if those workers all work individually they are massively less productive and there is employment for all 50. Not only are they more equal, but they are all employed, and at least they get to keep what they make. Overall though, they work a lot harder to produce the same output (which is just dumb).

• Mark says:

How do you put in those vertical blue lines?

• Kevin Donoghue says:

Mark, use the HTML blockquote tag:

http://www.w3schools.com/tags/tag_blockquote.asp

• Mark says:

Thanks!

Just to let you know I am not that lazy, I did check that website, but they don’t show the vertical blue bar when you “Try it yourself”, so I wasn’t sure.

• Tel says:

Welcome to stylesheets. The “blockquote” is considered semantic layout, so it describes a piece of text that is quoted, but it does not describe what a quote should look like.

The vertical blue bar is merely one way to present a quote, some people use a quote sign, others put a box around it. Your blog posts inherit the style chosen by the blog owner.

Believe it or not, intense philosophical debate rages over the deeper meaning of this, and whether people like you should be able to mix in a red line amongst those blue lines.

• P.S. Huff says:

The correct answer is that they should not.

• Dave says:

“You can see why workers in the first scenario feel ripped off when more workers come along because now they work just as many hours for half the wage! Then another two workers come along and their wages drop by half again, while the orchard owner does nothing and his wages have gone up through the roof. As more pickers come along the gap between rich and poor gets wider and wider… all of which feels really unfair to the people concerned.”

Yeah but the part you’re skipping is where the price of apples comes down because there’s more apples being produced for less money. So the reduced wages ultimately end up not being reduced in terms of value/purchasing power. In fact the trend of laissez faire’s history is that wages regularly go up in terms of purchasing power. So paying the workers themselves in apples in the analogy kind of evades that reality. Yeah it *feels* unfair when you leave out that part of it, which is what leftists do deliberately.