Question 2

Suppose that we modify the Solow-Swan growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience, and that there is labour-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 unit of labour. Letting b' denote future human capital per worker, assume that

b'=(1+f)b

where f is the growth rate of human capital.

a) Show that the long-run equilibrium has the property that =k=KbN is a constant. At what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. (12 marks)

b) What is the effect of an increase in f on the growth in per capita income? Discuss relative to how the standard Solow-Swan growth model behaves. (8 marks)