Obviously I’m getting a lot of reaction to my stuff on robots and all that. (My copy editor, last night: “Thank God, it’s not about the fiscal cliff!”) My sense is, however, that a lot of the reaction, both positive and negative, involves misunderstanding the economic logic, with some readers believing that technological progress can never hurt workers, others believing that rapid productivity growth always hurts workers; neither is true. So here’s an attempt to explain what’s going on in the theory; cognoscenti will recognize it as nothing more than an exposition of J.R, Hicks’s analysis of the whole thing in his 1932 Theory of Wages (pdf).

Start with the notion of an aggregate production function, which relates economy-wide output to economy-wide inputs of capital and labor. Yes, that sort of aggregation does violence to the complexity of reality. So?

Furthermore, for current purposes, hold the quantity of capital fixed and show how output varies with the quantity of labor. We expect the relationship to look like the lower curve in this figure (we’ll get to the upper curves in a minute):

Photo

Now, in a perfectly competitive economy (don’t worry, we’ll talk about what happens if not in a minute), we would expect the labor force to achieve full employment by accepting whatever real wage is consistent with said full employment. And what is that real wage? It’s the marginal product of labor at that point — which, graphically, is the slope of the aggregate production function where it crosses the vertical blue line.

Now suppose that we have technological progress. This manifests itself — indeed, in this context is basically defined as — an upward shift in the production function. I’ve shown two alternative curves, to make a point. Technology A and technology B are drawn so as to yield exactly the same level of output at full employment — which also says that both would lead to exactly the same rise in measured labor productivity. But they don’t have the same effect on real wages! Technology A is just a proportional upward shift in the original production function — which is “Hicks-neutral” technological change. As a result, the slope of the function where it crosses the blue line rises by that same proportion: real wages rise by the same amount as productivity.

But technology B is different — the gains are bigger at lower levels of employment, which is to say higher ratios of capital to labor (because the amount of capital is held fixed for this exercise). As a result, it is much flatter where it crosses the full employment line — which says that it would lead to much lower real wages than technology B A. In fact, as I’ve drawn it, it leads to lower real wages than under the original technology.

What we’ve just seen, then, is that the effect of technological progress on wages depends on the bias of the progress; if it’s capital-biased, workers won’t share fully in productivity gains, and if it’s strongly enough capital-biased, they can actually be made worse off.

So it’s wrong to assume, as many people on the right seem to, that gains from technology always trickle down to workers; not necessarily. It’s also wrong to assume, as some (but not all) on the left sometimes seem to — e.g., William Greider — that rapid productivity growth is necessarily jobs- or wage-destroying. It all depends.

What’s happening right now is that we are seeing a significant shift of income away from labor at the same time that we’re seeing new technologies that look, on a cursory overview, as if they’re capital-biased. So we could be looking at my technology B story above.

There are, however, other possibilities — including the possibility that the fact that we don’t actually have perfect competition is playing a big role here.

So that’s the story so far. And it’s important stuff.