Home > economics community, Fallacies, foundations of econ > Frances Woolley does my work for me

Frances Woolley does my work for me

I enjoy reading Adam Ozimek,  but man does he have a couple of bad habits.  Take for example this post and this post.   I don’t have anything to say about Adam’s main points–which I think are fairly interesting but aren’t really directed at people like me–but in the course of making those points, Adam says–then repeats–that workers earn their marginal products, which he implies is a property of the worker.

This is just wrong, wrong, wrong–and I’m talking Econ 101 kind of wrong, not some deep mistake or subtle bit of theory.   For someone who fancies themselves a labor economist–and a public face of the profession–I have to say this is not really acceptable.

Fortunately, I don’t have to explain the mistake (although I addressed it briefly here), because Frances Woolley does it for me, much more succinctly:

Undergraduate students learn that, in a competitive market, wages are equal to the marginal value product of labour, that is, the dollar value of what the marginal worker produces. Formally, w=p*MPL where w=the wage rate, p=the price of output and MPL is the marginal product of labour.

The proof of this proposition is simple: if an additional worker produces goods and services worth, say, $12, and the wage rate is, say, $10, hiring more workers adds to the firm’s profits. Thus, if the marginal value product of labour is greater than the wage rate, the firm will hire more workers. Eventually, however, as more workers are hired, their productivity will start to fall. For example, the additional workers will take on lower and lower value tasks. Once the marginal productivity has fallen to the point where w=p*MPL, the firm stops hiring…

“The marginal product of labour” is an abstraction. The idea is simple enough – what an additional worker brings to the production enterprise – but the implementation is not.

For example, think about the simplest possible production technology: one worker + one shovel digging a hole. Without the shovel, the worker produces nothing. Without the worker, the shovel produces nothing. Together, they produce a hole in the ground. What is the “marginal productivity” of the worker? Of the shovel? It’s like the sound of one hand clapping – it’s impossible to tell what each member of the production process contributes.

Allocating the profits from hole digging between shovel owners and workers is like dividing a pie. When two parties are bargaining over who gets a pie, no one will ever accept less than their outside option –  the amount that she could get if she walked away. If the worker’s outside option is $10 per hour, he will never accept any wage less than $10 per hour; if the outside option is $2, a wage of $7 starts sounding pretty good.

Outside options explain why Apple can pay its workers a fairly low wage. If a typical Apple specialist or genius walked away from their job, their next best alternative might be an even worse retail position.

Marginal product is a property of the firm specific match while wages are a property of the market as a whole, which determines the outside option.   At no point does a employer give a [bovine excrement] what a worker’s “marginal product” might be, except to the extent that there may be a gap between the industry-wide wage and the nominal value of  firm-specific marginal production which thus provides an opportunity for arbitrage from buying and selling labor contracts.

This is standard theory and it implies that there is always a gap between the two so there is surplus to be split.  Frankly, this is not something that I even let my students get away with.

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  1. July 30, 2012 at 5:38 am

    “Marginal product is a property of the firm specific match while wages are a property of the market as a whole, which determines the outside option.”

    I like this way of putting it. The standard theory, of course, implies that firms hire workers until the two are equalized, but that assumes perfectly competitive output and input markets markets, and particular types of production technologies.

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