President Obama’s recent remarks about business owners have intensified the national debate over the proper relation of the individual to the rest of society. Economist and pundit Paul Krugman has entered the fray from a different angle, analyzing the rhetoric of conservatives: On the one hand, they praise the free market for paying individuals according to their contribution to the economy, yet on the other hand they also love entrepreneurs for creating jobs and new products, thereby showering benefits on everyone.

Krugman claims that these two principles contradict each other. Yet Krugman is making a basic mistake in economic theory. There’s nothing wrong with standard conservative attitudes toward the meritocracy of the market and the social benefits of high achievers.

To set the context, let’s reproduce Krugman’s argument from July 9, when he thought he caught Romney supporters contradicting themselves:

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. This is, by the way, standard textbook microeconomics: in a perfectly competitive economy, factors of production are supposedly paid precisely their marginal product.

Now suppose that President Obama has reduced Mr. Wheelerdealer to despair … [s]o Wheelerdealer decides to go Galt. Well, actually just one-third Galt, reducing his working time to just 2000 hours a year so he can spend more time with his wife and mistress.

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!

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

 …
 So there’s a huge contradiction in the whole position of the self-regarding rich—a contradiction that I’m quite sure bothers them not at all. More champagne?

Thus, Krugman thinks that very high income-earners—according to textbook economic theory—take out from the economy exactly what they put into it. Therefore, it won’t do for conservatives to lambaste soak-the-rich policies on the grounds that they will hurt middle-class and poor workers, because (Krugman claims) the total income of everyone besides the high-income earners will be unaffected if the super-achievers withdraw from the economy.

Krugman is saying that conservatives need to get their story straight: Does the market really pay workers according to their marginal productivity, as the free-market economists tell us with glee, or do the super-rich entrepreneurs actually add more to the economy than they take out in terms of their enormous earnings?

There’s actually no contradiction here: Krugman is botching basic price theory, as even a Keynesian fellow-traveler economist pointed out last year when Krugman made the same mistake. I’ll illustrate the confusion with a simple tale involving apples. In order to pinpoint Krugman’s error, I’ll have to use a few numbers, but I’ll keep it relatively painless.

Imagine Smith, the owner of an orchard who is considering hiring some day laborers to pick apples. If just one man shows up, Smith lets him use his ladder (the only one Smith owns) to go up and down from tree to tree, filling up baskets with apples. If it’s one man working by himself, he can fill 20 baskets per hour.

However, if two workers show up, then one guy will climb up the ladder, and start dropping apples down to the other. The man on the ground will catch each apple and place it carefully in the basket. This approach cuts out much of the ladder time, and so two men working in this fashion can fill 30 baskets of apples per hour.

Finally, if three workers show up, then two of them proceed as before. The third will ferry the sole basket back and forth to the barn, where Smith stores the apples. This change makes the operation even more efficient, so that three men working in tandem manage to fill 35 baskets of apples per hour.

There’s one final wrinkle: Down the road a few miles is another orchard, owned by Jones, who also owns one ladder and one basket. All of the numbers would be the same for Jones’s apple operation.

Now the fun part. Suppose initially there are two workers total, who are both equally agile and competent at the various tasks, and they don’t have any preference for one task over the other. They are aware of both Smith and Jones’ operations, and are trying to find work picking apples. In a competitive labor market, what will be the “real hourly wage” of the workers, if they are paid directly in apples?

An economist would solve this problem by first calculating the “marginal product” of each subsequent worker’s efforts on a given orchard. Recall that with one worker, either orchard owner reaps 20 apples per hour, while with two workers, the total harvest jumps to 30 per hour, and finally with three workers the total jumps to 35. Therefore, the marginal product of the first worker is 20 apples per hour, the marginal product of the second worker is 10 apples per hour, and the marginal product of the third worker (if there were one) would be 5 apples per hour.

Now back to our scenario with just two workers. If both of them for some reason were working at Smith’s orchard, then Jones would be willing to pay up to 20 apples per hour to hire one of them to come work for him. But Smith can’t afford to pay 20 apples per hour to both workers, since together they only harvest 30 apples total. We know that in equilibrium, therefore, Smith and Jones will hire one worker each.

But how much will they pay these workers? Whatever the number is, we know that it must be the same number. To see why, suppose that Smith paid his worker (say) 15 apples per hour, while Jones paid his worker 18. Then the worker getting 15 from Smith would approach Jones and say, “Hey, you should fire that clown you’ve got working for you now at 18, because I’ll do the same job for 17.”

We could add more complications to the story, involving collusion between Smith and Jones to hold down wages and so forth, but in the spirit of textbook theory (which assumes there are a large number of potential employers and workers), let’s assume that things settle down with Smith and Jones each paying his worker 20 apples per hour, i.e. their marginal product. Thus, the workers pick 40 apples total per hour at the two orchards, and that’s exactly what they consume as their wages. Smith and Jones, the orchard owners, aren’t hurt by their decision to hire the workers, but they aren’t helped either.

At this point, we seem to have justified Krugman’s argument. Here we have workers earning their marginal product—20 apples per hour—but they are consuming exactly as many apples as their labor added to the harvest. So it seems as if Krugman was right, that when someone joins the economy, he doesn’t really affect anybody else’s standard of living.

Ah, but the problem here is that marginal productivity theory applies—as the name suggests—on the margin. It tells us that workers get paid according to how much the last unit of extra input raises the total output. Once we take that into account, we see that Krugman’s “insight” collapses.

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.

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. Although his observation doesn’t justify higher taxes and other federal regulations, President Obama was right in pointing out that no individual can produce in our economy without contributions from others.

Finally, to underscore the point that there is nothing sinister here involving the exploitation of workers, realize that this same phenomenon occurs with the prices of goods and services, too.

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.

By the same token, entrepreneurs and other high-income earners really do contribute to society; the rest of us have a higher standard of living because of their participation in the economy. This is true, even though their compensation tends to equal the market value of what they created on the margin.

Krugman’s elementary confusion on what “marginal product” means, led him to falsely accuse conservatives of a contradiction. There is no dichotomy in praising the meritocracy of the market, while also acknowledging the social benefits of successful entrepreneurs.

Robert P. Murphy is author of The Politically Incorrect Guide to Capitalism. His blog is Free Advice. Follow him on Twitter.