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 b' denote future human capital per worker, assume that b' = (1 + j)b, wherefisthe 12. growth rate in human capital.
(a) Show that the long run equilibrium has the property that k** = ~ is a constant. At what rate does aggregate output, aggregate consumption, aggregate investment, and per- capita income grow in this steady statel Explain.