Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience, and that there is labor-augmenting technological progress, with a production function

Y = F(K, bN),

where b denotes the number of units of “human capital” per worker, and bN is “efficiency units” of labor. Letting boe denote future human capital per worker, assume that boe = (1 + f)b, where f is the growth rate in human capital.

(a) Show that the long-run equilibrium has the property that k** = K/bN is a constant. At what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain.

(b) What is the effect of an increase in f on the growth in per capita income? Discuss relative to how the standard Solow growth model behaves.