Given recent concern about technological change and how it is wrecking the middle class, I thought I’d share a simple illustration of what classical economic models* imply about the relationship between productivity growth and the returns to workers and capital owners.

It is especially interesting to think about which assumptions we may want to relax and how these alterations affect the classical conclusion that workers fully benefit from productivity improvements (in the form of higher long-run wages).

Classical Incidence of Technological Change

On the production side, equation 2 shows that output growth results from three sources: increasing productivity A, increasing labor L (scaled by its share), increasing capital K (scaled by its share).

In the classical model with constant returns to scale, revenues are divided between labor and capital as shown in equation 3. Combining these two simple observations (about the structure of production and the division of income) enables us to understand the link between productivity growth and increases in the real returns to capital and to labor.

Equation 4 shows us how capital owners and workers benefit from productivity improvements.

- In the short run, when the supply of labor and capital don’t have time to adjust, a one percent increase in productivity growth results in a .67 % increase in real wages and a .33 % increase in the real return to capital (if labor’s share is two thirds).
- In the long run, however, labor and especially capital can adjust to the new higher productivity conditions. Suppose labor doesn’t adjust (say if effects on population growth and labor supply are small). And suppose the supply of capital elastically increases until the real return to capital equals its original level. Then you arrive at the conclusion that the incidence of technical change fully benefits labor. In terms of equation 4, a 1% increase in productivity will result in a 1.5% increase in real wages since the change in real returns to capital are zero in the long run (due to higher levels of capital).

Assumptions to Consider Relaxing

This post is getting a bit long, but here are a few assumptions that we may want to consider altering:

**Elasticity of Factor Supplies**: Notice that the long run paragraph assumed that labor supply was perfectly elastic (and hence bears all of the incidence) and that capital supply was perfectly inelastic (and hence bears none). The slopes of these supply curves are crucial in terms of thinking about incidence. Evidence on the latter is much weaker than it should be.**Production**: We assumed that a change in A doesn’t affect the level of labor L in equation 1. We also assumed homogenous labor, despite the fact that the marginal products of high and low skill workers are clearly different.**Income**: Note the absence of markups or rents.

*This simple set up is based on Kevin Murphy’s lecture on how Malthus’s views on technological change were backwards. To oversimplify, Malthus thought that the supply of capital was land (and was thus constant) and that the supply of labor would fully adjust via population growth to prevent increases in real wages. Thus, his conclusion about equation 4 was backwards.