Economics 3307

Key Points of Chapter 5

Chapter 5 extends the model of Chapter 4 (the Solow model with population growth) to allow for technological progress.

The model assumes that technological progress is labor-enhancing -- that is, technological progress has the same effect on output as additional labor. It turns out that this assumption about the form of technological progress is needed to explain the basic facts of economic growth outlined at the beginning of the Chapter 4 "Main Points" memo. We therefore focus on efficiency units of labor, LxE, where L is the number of workers (or hours worked), and E is the efficiency of labor. (LxE) can increase either because of population growth (a rise in L) or technological progress (a rise in E).

Once we allow for technological progress, we interpret y as output per efficency unit of labor -- that is, y = Y/(LxE). Similarly, k = K/(LxE), or capital per efficiency unit of labor.

In steady state equilibrium, k and y are constant. The condition for steady-state equilibrium is that s·f(k) = (d+n+g)·k. Because s·f(k) = i = I/L, if s·f(k) < (d+n+g)·k, actual investment is less than break-even investment (the level of i needed to keep k constant) and k tends to fall. If s·f(k) > (d+n+g)·k, actual investment is greater than break-even investment and k tends to rise. Thus when k is not constant, it tends to move toward the level at which it is constant (the steady-state equilibrium level). When k is constant, there is enough new capital produced to do three things: (i) replace worn out capital; (ii) equip new workers with capital, and (iii) accommodate the new capital required by technological progress.

If k and y are constant, this means that K and Y grow at the same rate, which accords with fact that (K/Y) is constant. If y is constant, Y grows at the same rate as (LxE), which grows at rate (n+g), where n is the population growth rate and g is the rate of technological progress. Thus Y grows over time. (Y/L) grows at the same rate as E, which grows at rate g. The fact that (Y/L) grows at rate g means that we have explained the fact that output per worker grows over time.

The Golden Rule savings rate maximizes consumption per efficiency unit of labor in equilibrium. It seems clear that the U.S. savings rate is well below the Golden Rule rate. The government can promote savings by reducing the government deficit (increasing government saving) or by changing incentives for private saving. Economists disagree about how responsive people are to changes in the incentives for savings.

When applying the growth model discussed above to the real world, it is helpful to think of "capital" in broad terms -- i.e., as including human capital (knowledge) as well as physical capital (machines and buildings). Economists disagree on whether government should pursue policies aimed at influencing the kind of capital the economy produces.

Though technological progress is the source of long-term growth in output per capita in equilibrium, economists do not understand the determinants of technological progress very well.

Productivity growth fell dramatically in the mid-1970s. Though many possible explanations for this decrease have been proposed, none has been accepted by a majority of economists. Thus the productivity slowdown remains something of a mystery.

Economists have constructed models that go beyond the Solow model we have been studying. Unlike the Solow model, these models assume that capital does not have a diminishing marginal product. (This assumption is most reasonable if we interpret "capital" as including human capital, i.e., knowledge.) In these models, a rise in the savings rate can permanently increase the growth rate of output. Recall that in the Solow model, a rise in the savings rate increases output growth only temporarily (during the transition to the new equilibrium).

On balance, it seems to be the case that the social return to research is higher than the private return. This is an argument justifying government funding for research, though in practice it is not clear that government money allocated for these purposes will always be used wisely.