2. Labor productivity is defined as Y/L, the amount of output divided by the amount of labor input. Start with the growth-accounting equation and show that the growth in labor productivity depends on growth in total factor productivity and growth in the capital–labor ratio.

In particular, show that

= +a .

Hint: You may find the following mathematical trick helpful. If z = wx, then the growth rate of z is approximately the growth rate of w plus the growth rate of x. That is, Dz/z ≈ Dw/w + Dx/x.