Suppose that total capital and labor both increase by the same percentage amount, so that the amount of capital per worker,k, doesn't change. Writing the production function in per-worker terms,y=f(k), requires that this increase in capital and labor must not change the amount of output produced per worker,y. Use the growth accounting equation to show that equal percentage increases in capital and labor will leave output per worker unaffected only ifaK+aN= 1.

NOTE:aKandaNare the capital and labor exponents of the Cobb-Douglas production function and represents the factor shares.