8. Growth accounting

The appendix to this chapter shows how data on output, capital, and labor can be used to construct estimates of the rate of growth of technological progress. We modify that approach in this problem to examine the growth of capital per worker.

Y = K^1/3 (AN)^2/3

The function gives a good description of production in rich countries. Following the same steps as in the appendix, you can show that

(2/3) gA = gY - (2/3) gN - (1/3) gK = (gY - gN) - (1/3)(gK - gN)

where gy denotes the growth rate of Y

a. What does the quantity gY - gN represent? What does the quantity gK - gN represent?

b. Rearrange the preceding equation to solve for the growth rate of capital per worker.

c. Look at Table 12-2 in the chapter. Using your answer to part (b), substitute in the average annual growth rate of output per worker and the average annual rate of technological progress for the United States for the period 1985 to 2009 to obtain a crude measure of the average annual growth of capital per worker. (Strictly speaking, we should construct these measures individually for every year, but we limit ourselves to readily