1.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+f)b, where f is the growth rate in human capital. One way to think about this is that technological progress, e.g. development of computers, makes us more productive in the workplace.

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 model behaves.