1、CH33 Growth and Accumulationfocus of the chapter In this chapter we study how potential outputthe output that would be produced if all factors were fully employedgrows over time. To better accomplish this, we learn growth accounting and the fundamentals of neoclassical growth theory. Together, they
2、tell us that output growth results both from improvements in technology and from increases in one or more of the inputs to the production processcapital, labor, and natural resources. Neoclassical growth theory also tells us that in the long run, growth in potential output results entirely from tech
3、nological improvement. * Note: The authors in this chapter and the next use the term “long run” in a way that is inconsistent with the rest of the textbook. They should be saying “very long run.” section summaries1. Growth AccountingOutput grows because of increases in factors of production like cap
4、ital and labor, and because of improvements in technology. The production function provides a link between the level of technology (A), the amount of capital (K), labor (N), and other inputs used, and the amount of output (Y) created. The generic formula for the production function is:Y = AF(K,N)The
5、 Cobb-Douglas production function, a more specific formula, is frequently used as well, as it provides a good approximation of production in the actual economy. The formula for the Cobb-Douglas production function is:Y = AKN 1 pronounced “theta”, represents capitals share of incometotal payments to
6、capital, as a fraction of output, or (iK)/Y. (1 ) is labors share of income, given by (wN)/Y. To derive these results algebraically, you need one more fact: When the markets for capital and labor are in equilibrium (i.e., when the supply of capital equals the demand for capital, and the supply of la
7、bor equals the demand for labor), capital and labor are each paid their marginal product. For the Cobb-Douglas function, the marginal product of capital (MPK) is AKN. The marginal product of labor (MPL) is (1 )AKN 1 We can express our production function in terms of growth rates rather than levels:Y
8、/Y = (1 )x N/N + x K/K + A/AThe symbol pronounced “delta” means “change in”. The term Y/Y, then, should be interpreted as the growth rate of output. The terms N/N and K/K should be interpreted as the growth rates of labor and capital, respectively. The last term, A/A is the rate of improvement of te
9、chnology, often called the growth rate of total factor productivity (TFP). It is the amount that output increases as a result of technological progress alone (plug in N/N = K/K = 0, and youll see why).Because growth in GDP per capita (output per person) tells us more about increases in the standard
10、of living, it is useful to subtract the rate of population growth (N/N) from both sides, and write the above equation in per capita terms:y/y = (x k/k) + A/AThe terms y and k represent output and capital per person: y = Y/N, k = K/N. (There is an implicit assumption here that the fraction of the pop
11、ulation in the labor force is constant. This is why we can get away with using the terms “population” and “labor supply” interchangeably.) The terms (y/y) and (k/k) are the growth rates of output and capital per person: y/y = Y/Y N/N, and k/k = K/K N/N. The term K/N is often called the capital-labor
12、 ratio.2. Empirical Estimates of GrowthSince 1929, U.S. economic growth has averaged about 2.9 percent a year. Of this, estimates suggest that about 1.09 percent has been due to increases in the labor supply, 0.32 percent has been due to capital accumulation, and 1.49 percent has been the result of
13、technological progress.Physical capital and labor are not the only inputs to production. Two other important factors of production are natural resources and human capitalthe skills and talents of workers. The shares of income (also called factor shares) of physical capital, human capital, and raw la
14、bor are estimated to be roughly 1/3 each.3. Growth Theory: The Neoclassical ModelNeoclassical growth theory studies the way that growth in the capital stock per worker affects the long-run level of per-capita potential output. A key result is that, while the rate of saving has a significant impact o
15、n the level of per capita potential output in the long run, the rate of improvement in technology entirely determines its growth rate. Figure 31the per-capita production function To build our model, we begin with a few simplifying assumptions: (1) the level of technology is fixed, so that there is n
16、o growth in total factor productivity; (2) the production function has constant returns to scale (see Review of Technique 4), so that increasing the amount every input used in production will increase output by the same amount. A consequence of this second assumption is that all factors of productio
17、n must have diminishing marginal productsas more of one input is added, and the others are held constant, each unit contributes less to output than did the previous one. (Buying more tractors for your construction company without hiring any more workers to drive them will not help increase your outp
18、ut much.) We also need to write our variables in per capita form; as before, y = Y/N and k = K/N. We write the per capita production function:y = f(k)Figure 32steady-state in the neoclassical modelWe then consider the flows into and out kthe stock of capital per worker. Investment increases the tota
19、l stock of capital (K), which increases k. It can be thought of as a flow into each workers pool of capital. Both depreciation and population growth decrease kdepreciation because it decreases the stock of functional capital, and population growth because it increases the number of workers sharing t
20、his capital. Both depreciation and population growth can be visualized as flows out of each workers pool of capital. When the flow into this pool is greater than the flows out, k grows. When the flows out of this pool are greater than the flow in, k shrinks. And when the flows in and out exactly bal
21、ance, the level of capital per worker will remain fixed. We call this last case the steady-state, because it is the point at which the level of capital in each workers pool remains steady, or stable. It is the point of equilibrium in our model; we will find that the capital stock per worker grows or
22、 shrinks toward this point, and that once it gets there it stays. At least until some shock forces it to move.It is not difficult to express the dynamics described above as an equation. We know that saving must equal investment. If we assume that people save a constant fraction (s) of their incomes,
23、 we can write the flow into k as (s x y), or, using our per capita production function, as (s x f(k). The standard assumption about depreciation is that a constant fraction (d) of the capital stock becomes obsolete each period. Using this assumption, we can express the flow out of each workers pool
24、of capital that result from depreciation as (d x k). Similarly, when population grows at a constant rate (n), we can express the flow out of this pool resulting from population growth as (n x k). Putting all of these terms together, we get the following equation:k = sf(k) (n + d)kWe find an expressi
25、on for the steady-state by simply plugging in the requirement k = 0:sf(k*) = (n + d)k*k* represents the steady-state value of k. The steady-state value of y is y* = f(k*).The growth process can be studied graphically as well. Figure 32 graphs the flows into and out of k against the level of k. The o
26、utflows are graphed as a straight line, with slope (n + d). This is often called the investment requirement line, as it shows the amount that must be invested, if the capital stock is to remain constant. The slope of the line that represents the flow into k shrinks as k increases, because we have as
27、sumed it to have diminishing marginal returns. Where these two lines intersect, the flows into and out of k balance, and k is at its steady-state. Whether the savings line lies above the investment requirement line, so that k is increasing, or the investment requirement line lies above the savings l
28、ine, so that k is decreasing, k always moves toward the steady-state. Using this graph, we can examine the consequences of changes in s, n, or d. An increase in the savings rate (s) will shift the savings line, sf(k), upward, increasing the steady-state capital-labor ratio, and hence the steady-stat
29、e level of per capita potential output. It will also, temporarily, increase the growth rate of both y and k (remember, the growth rate of k is zero at the steady-state, and without improvements in technology per capita, output has no other reason to grow). An increase in either the rate of depreciat
30、ion or the rate of population growth will increase the slope of the investment requirement line, decreasing the steady-state levels of k and y, and causing both to “grow”, temporarily, at a negative rate.steady-state,lower ssteady-state,higher sFigure 33a decrease in the savings rate reduces the ste
31、ady-state capital-labor ratioWhen the level of technology is permitted to change, we add in another term: “g”, or the growth rate of technology. Technological improvement is represented on our graph as an upward shift in the savings line, now written s x Af(k). Notice that it causes the steady-state
32、 levels of k and y to rise. Notice also, though, that with the addition of technological growth our production function no longer has constant returns to scaledoubling capital and labor will more than double output. In order to fix this problem, growth theorists often assume that technology has a very particular characteristic: It is assumed to be labor augmenting, so that technological improvements increase the productivity specifically of labor. The production function, under this assumption, is written as follows:Y = F(
