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Labor markets are financial markets

In support of my last post, there was another point that I wanted to make.   One thing that I’ve found helpful when thinking about labor markets is specifically not to think of hiring/firing workers (i.e. economic agents with a mind of their own).   Instead, and I always worry that this isn’t very PC, we should think of labor markets as the buying and selling of an asset–employment contracts–which just happen to be backed by the real productive capacity (human capital) of human beings.

For example, I don’t believe in profit maximization.   When it comes right down to it, maximizing anything in the real world is an extraordinarily complex task which requires an immense amount of information (relatedly, if you have time you should read this).  What people do, though, is they exploit opportunities for arbitrage.

This is an important distinction.   An arbitrage is a decision problem that is “local”, while maximization is “global”.   It also explains how and why an economy can appear to be very classical even when it is anything but.   For example, if you recognize that as an empirical matter, marginal product of labor equals the real wage (it does, or at least it is close) than you might be tempted to think that labor markets must clear.   This is not the case, you’re thinking too “global”, there’s no reason that total output must equal the potential total output at any given time.

Consider a firm trying to decide whether or not to hire a new employee–i.e. buy another labor contract.   There is a going (nominal) price for that labor contract (W) on the open market as well as a (nominal) price of goods (P) on the market.   The ratio of these two things is the real wage (W/P).   For a labor force (current) of size L, the firm could in theory (sustainably) produce f(L) units of output at price p (standard concave production function).   Operating at full output, the firm then has an arbitrage opportunity if:

  • p[f(L) – f(L-1)]/P < W/P  ==>  MPL < Real Wage  ==>  sell labor contracts to increase profits (a.k.a. layoffs)
  • p[f(L) – f(L-1)]/P > W/P  ==>  MPL > Real Wage  ==>  buy labor contracts to increase profits (a.k.a. hiring)

In other words, we recover profit maximization in the limit that all arbitrage opportunities are exhausted.   But there’s an advantage to this approach, it is not identical to profit maximization.   I’ve assumed that the firm is operating at capacity and selling its output.   I’ve assumed Say’s law is true.

Instead, I can replace the LHS of the above conditions with the real value of marginal sales.   The arbitrage condition still holds, and at full employment of the firm’s capacity the real value of  marginal sales (RVMS) must equal the marginal product of labor.   However, this need not be the case since the only decision the firm makes (in the presence of competitive labor markets) is the hire/fire decision.   Wages and sales involve the entire market.   Without going into details, RVMS is the firm’s “contribution” to aggregate demand–adjusted for prices–while the MPL is the firm’s contribution to aggregate supply.  Why there is a wedge between RVMS and MPL is an interesting question, but from the firm’s perspective there’s just no there there.  From the firm’s perspective sales as just given, since finding the “correct” market price is hard.

When I taught Macro Principles last year, I made sure to explain “MPL = W/P” as an arbitrage condition which I think is a more natural explanation for new students than “profit maximization”.   On the other hand, RVMS might be too much for most students, but for the rest of us, I think it might help us get our minds around the microfoundations of macro.

Another useful application is CEO pay.   From the firm’s perspective, at full employment, MPL is driven towards W/P because the firm purchases/sells many “copies” of similar wage contracts.   It does so until the condition is met.   A CEO is different, in this perspective, because leadership/management positions in general are not replicate-able for the firm–they are unique.

The firm has neither the use for buying more CEO contracts nor would selling make sense, as the firm certainly needs some kind of leadership, without a (near) simultaneous buy..   If there is to be efficient pricing of CEOs, then, the market has to be well-served on the “supply” side; i.e. there must be free entry of potential CEOs.   This also has profound implications, but I think that’s a story for another post.

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  1. July 28, 2012 at 1:05 pm

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