David R. Henderson  

Robert Murphy Helps Resolve an Economic Paradox

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If it's true that a worker gets paid an amount just equal to what he or she adds to total economic output, then how can there be any surplus left over to benefit the masses? In particular, suppose that an incredibly productive person decides to drop out of the workforce altogether. Should the rest of society even care, or is it all a wash?

It turns out that there's no contradiction between these principles: Even though a worker is paid the value of his or her marginal product, it is still true that the rest of society benefits from the worker's contribution to the economy. And look at it another way: If highly productive workers were suddenly to become monks, the rest of us would be materially poorer, even though those workers were paid the value of their marginal product before becoming monks. In this essay, I'll reconcile the apparent tension between these two standard principles, by explaining first the role of specialization and then the distinction between inframarginal and marginal units.

This is a key excerpt from Robert P. Murphy's Econlib Feature Article for January, "Does a Worker Help the Rest of Society?"

I highly recommend it.

By the way, Happy New Year to all.

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COMMENTS (17 to date)
Philo writes:

Murphy makes two points: (1) that an extra worker permits greater specialization in the whole workforce, and thus greater productivity on the whole, and (2) the value of marginal work determines wages, and inframarginal work may be worth more. In his chewing-gum example to illustrate point (2), if the factory operated with only four workers the wage rate would $20/hr.; but it adds a fifth worker, and the wage goes down to $9/hr. Indeed, if it had only one worker, the wage would be $100/hr. This conflicts with the first point. Furthermore, the example is completely unrealistic: if the facts were as presented, all chewing gum factories would operate with a single worker. (But the first point itself is quite valid.)

Bob Murphy writes:

Philo wrote:

"Furthermore, the example is completely unrealistic: if the facts were as presented, all chewing gum factories would operate with a single worker."

Can you elaborate?

john hare writes:

If I were that business owner and accepted that table as fact, I would likely go to 3 workers producing 230 packs of gum per hour. Then I could pay better workers $20-$30 and hour and still make $140.00 an hour profit. That way the competing owners paying the marginal $9.00 an hour as in the example would be training my work force for when I needed to hire.

The only thing more expensive than good help in my business is bad help. Bad help is what you get for bad wages.

I don't think the article makes the point well. I agree with the premise, not this presentation of it. Among other things, the table directly contradicts the coconuts on a desert island example.

Philo writes:

@ Bob Murphy:

Probably the example was presented without enough background information to enable a non-economist (me) to understand it. My thinking was that the one-worker factory produces 100 packs of gum/hour, so five one-worker factories would produce 500. Since the five-worker factory produces only 259 packs of gum/hour, would not a gum producer rather operate five one-worker factories than one five-worker factory? But this thinking ignores the cost of capital: five such factories would require five times as much capital as one. So even though five such factories with one worker each would produce more packs of gum/hour per worker (100) than one factory with five workers (51.8), the former set-up might be less efficient than the latter. My claim to the contrary was mistaken.

I still do not see how the marginal/inframarginal point contributes to countering any (halfway) plausible complaint that workers are being exploited, i.e., paid less than their contributions are worth. The gum factory evidently was designed to be operated by five workers, and presumably five routinely show up for work. If only one showed up, he *would* produce 100 packs of gum, but this does not actually happen, so how does the hypothetical constitute a remotely plausible basis for a claim of exploitation? Nor has it any evident value for explaining how (extra) workers contribute to the rest of society.

David R Henderson writes:

@john hare,
If I were that business owner and accepted that table as fact, I would likely go to 3 workers producing 230 packs of gum per hour. Then I could pay better workers $20-$30 and hour and still make $140.00 an hour profit.
Bob Murphy, like virtually any economist who would analyze this, is assuming profit maximization. 3 workers producing 230 packs per hour, and being paid $30 per hour each would, as you say, create $140 in profit per hour for the employer.
But having 5 workers producing 259 packs her hour and being paid $9 per hour would, by contrast, create $214 of profit per hour.
Since $214 is well above $140, the former is better.

john hare writes:

@David R Henderson,
An economist might make that assumption. As a business owner, The idea of training, dealing with, and trying to retain 5 $9.00 an hour people is likely to be time consuming and frustrating. Dealing with 3 $30.00 an hour people is likely to be much easier on the time and nerves, allowing me time and focus for running the actual business. $140 an hour profit might net more than the $214 an hour if there are excessive QC and HR problems. If there are too many returns from bad QC costing customers, or if HR problems eat up the management time needed for sales and paperwork, cheap people can be expensive

On this example, economic theory and business reality diverge. Trying to run a company with the cheapest help possible creates QC and HR problems that are unbelievable to one that hasn't tried it. If in the example, $9.00 an hour people are reliable, conscientious, and capable enough to do the work, then maybe it would work. I don't pay my best people multiples of minimum wage because I'm generous, but because that's what it takes to retain and motivate them. There is a 250% spread in the hourly wages of my field people, and they are not interchangeable numbers.

Also, the example shows worker productivity dropping as more are hired. To make the example match the desert island coconut example, worker productivity should go up as more are hired. If the one worker were having to jump between the cooker, extruder, wrapper, stacker, packer, and boxer, and shipper by himself, he might get 25 packs a day with the second worker increasing totals to 75 a day and the third bringing the total to 200 a day and so on until the law of diminishing returns does look more like that table.

My apologies to all for not being able to express myself clearly on this issue. It's just that the island example matches my experience while the table doesn't.

Anonymous writes:

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Jon Murphy writes:

@john hare

The economic theory takes all that into account. If we assume profit maximization and add in whatever adjustments you want, then the numbers may change but the concept underneath, the point of Dr. Murphy's article, does not. you're just adjusting the profit-maximization point, not the idea of Dr. Murphy's article.

In short, there is no divergence between the economic theory and business reality.

Bob Murphy writes:

john hare,

I love this scene from "Back to School" and I always told myself I wouldn't want to be the stuffy economist when challenged by a real-world businessman. So, I hope you don't take this as defensive, but I think your comments here need to be refined.

It sounds like you're saying that any real businessman would know that it never makes sense to hire people at $9 / hour. Is that your position? What about all the business people in the actual real world who hire people at even less than that?

So, since it's obviously true that *some* businesses find that it makes sense to hire at $9/hour, why are you telling me my example is wrong? This could be one of those businesses.

Also, it sounds like you are getting hung up on the specific dollar amount. Suppose I had chosen the numbers so that the firm hired 5 workers at $30/hour. Couldn't someone who runs a headhunter agency say, "Eh, in my line of work, I go for the person worth $100/hour. It's a waste of my time trying to chase down mediocrity and place them with clients at $30/hour. Better to focus on the white whales." ?

Bob Murphy writes:

Philo and john hare,

You are both suggesting that my factory numerical example contradicts the island example. That's a very interesting point; thank you for bringing that up.

Part of what is going on is that we are here referring to a single factory. It obviously can't be true that average output per worker continues to increase indefinitely; at some point, there wouldn't be enough volume in the factory to contain the bodies of all the workers.

So, since it has to be the case that diminishing marginal returns *eventually* kicks in, it is common in textbooks to show it kicking in right away, as I did in my table. (In fact, that was so natural that neither I nor my editor even considered that it could be confusing since it looks like it contradicts the tropical island example.)

One obvious reconciliation is that I could've made the numbers go up at first and then turn around, as john hare suggests. I have to ask around to see if there's any reason that would pose problems for something else we economists try to do with these stock illustrations, but that might be best.

So again, thanks, you definitely showed that my discussion wasn't as straightforward as I thought.

Bill writes:

When I began reading this essay, I immediately thought "What about consumer surplus?" and hoped the Nordhaus piece referenced near the end would be mentioned.

Charley Hooper writes:

Really interesting. Thanks. I'm still thinking about any questions I might have...

john hare writes:

@Bob Murphy,
You are quite right that I got hung up on the $9.00 an hour figure. It is around the number used locally by people that have the problems I mention. It seems quite possible that we would more agree than disagree in face to face discussion. Interesting scene you linked. It may be influenced by not being a Rodney fan, but I somewhat side with the professor in that a solid grounding in theory is a valuable tool to take to the 'real' world.

The table though still rings false to me with the single worker producing 1100% of his wage, two workers producing at 1,000%, and three at 850%. I would be quite wealthy if I had found any sector operating at that level of profit.

robc writes:

john hare,

You should rewatch the scene. The professor says at the beginning that he isn't going to waste their time with a bunch of useless theory.

I agree that a solid grounding in theory would be important, but the professor is claiming to be doing a real world example. And in that case, Rodney's character is dead on right.

Although having owned two businesses in flyover country, I have never had to deal with the mafia or kickbacks to inspectors. The above the board regulations were bad enough.

A Free Lunch writes:

@ Bob Murphy:

The first example is incorrect since each worker's marginal product is actually 20. This is because, if either were to stop working, then total output would fall from 30 to 10. Hence if each worker were actually paid their marginal product, neither person's existence would benefit society (contrary to what you claim in the essay).

Of course, in real life it would not be possible for both workers to receive their marginal product since they only jointly produce 30 coconuts! This illustrates the well known fact that marginal product theory does not straightforwardly apply to teams (a point noticed by e.g. Alchian and Demetz.)

So to summarise: while your example does point to a well known weakness in marginal product theory, it fails to serve its stated purpose (showing how someone's existence can benefit other people even if that person is paid their full marginal product).

Bob Murphy writes:

john hare wrote:

"The table though still rings false to me with the single worker producing 1100% of his wage, two workers producing at 1,000%, and three at 850%. I would be quite wealthy if I had found any sector operating at that level of profit."

Again, Mr. Hare, you are misunderstanding the table. It's not free to build a factory. The employer might just be breaking even when hiring the 5th worker.

Bob Murphy writes:

A Free Lunch,

Yeah, I was aware of that issue and debated whether to address it directly, but decided it was too much of a distraction. (I had limited space, which also sheds light on the other things that are confusing some people in these comments.)

Most normal people will not have a problem saying that if 2 identical people cooperate, then splitting the output down the middle doesn't involve exploitation. So I used that approach to make my first point about the division of labor and productivity.

Then in my second example I had to clarify what economists mean by "getting paid the full value of their marginal product."

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