We are interested in the growth rate of labor productivity, Y/L. To look at productivity, we return to the production function that we used in the growth accounting lesson.
[8] (Y/L) = (K/L)0.25E0.75
where E is the efficiency of labor. When we took logs of both sides, we obtained an equation for the growth rate of productivity. If y is the growth rate of output and n is the growth rate of the labor force, then the growth rate of productivity is y-n. Letting g be the symbol for the growth rate of E, the efficiency of labor, we have
[9] y - n = 0.25(x - n) + 0.75g
When we made numerical assumptions in equation [7], we found that x-n = 4%. Plugging this into equation [9] and assuming that the growth rate of the efficiency of labor, g, is 2%, we have
[10] y - n = 0.25(4%) + .75(2%) = 2.5%
Thus, the assumptions about saving rate, depreciation, and so forth imply growth in labor productivity of 2.5% per year.