Walmart reports that its recent wage hike is paying off via reduced turnover, which produces cost savings that offset the direct expense of the higher wages. In other words, efficiency wage theory is vindicated. What are the political/policy implications? What follows is a slightly wonkish note, largely to myself.

Efficiency wage theory is the idea that for any of a number of reasons, employers get more out of their workers when they pay more. It could be effort, it could be morale, it could be turnover. The causes of the efficiency gain could lie in psychology, or simply in the fact that workers are less willing to risk better-paying jobs with bad behavior. The details can matter a lot in some contexts, but in this note I just want to assume that worker productivity is increasing in the wage rate. And I want to focus on the decisions of an individual employer, not the full market equilibrium.

In the absence of an efficiency-wage effect – and also of monopsony power in the labor market, which I’ll come back to another time – an employer can be thought of as choosing employment L to maximize profits, which are equal to the value of sales (net of purchased inputs) generated by the work force minus wages paid:

(1) P = V(L) – wL

where the wage rate w is given by the market, and is outside the employer’s control.

With efficiency wages, we can think of each worker’s productivity E as being an increasing function of the wage paid, so that this problem instead becomes one of maximizing

(2) P = V(L*E(w)) – wL

where the employer gets to choose both L and w.

Let’s assume that the employer actually gets this choice right. That is, I am not going to suggest that Walmart has been making a mistake with its always-low-wages policy, that it would have been more profitable all along if it had been following a Costco-like strategy. Even so, efficiency-wage effects can make a lot of difference.

To see why, suppose that the employer finds itself under some kind of pressure to raise wages – the threat of union organizing, a boycott from consumer groups, politicians looking at it funny. How will it respond to this pressure?

Well, in the absence of efficiency wages the employer has a strong incentive to resist this pressure, because raising wages has a clear negative effect on profits:

dP/dw = -L*

where L* is the initial level of employment. Induced effects on L don’t show up here because of the envelope theorem – L was already chosen to maximize P, so small changes have no further effect.

But if there is a significant efficiency-wage effect, a small rise in wages has a negligible effect on profits:

dP/dw = 0

Why? Envelope theorem again: because w was already chosen to maximize profits, a small change has no further effect. When you’re at the top of a hill, a single step in any direction doesn’t change your elevation much.

And what this suggests in turn is that a relatively small amount of pressure can nonetheless have relatively big effects on wages: the employer may well be willing to raise wages by, say, 20 percent to avoid a consumer boycott or 40 percent to avoid a strike because it knows that it can make up most of the direct cost of the wage hike via reduced turnover and increased productivity.

Or to put it differently, efficiency wages suggest right away that the invisible hand’s grip on labor is a lot looser than people imagine, that wages are relatively easy to shift with social and political pressure. And this is one important reason attempts to reduce inequality can and should involve working on the distribution of market income as well as ex-post redistribution through taxes and transfers.