4.9. Increasing returns in a model with human capital. (This follows Lucas, 1988.)

Suppose that Y(t) = K(t)

α[(1 − aH)H(t)]β, H˙(t) = BaH H(t), and K˙(t) = sY(t).

Assume 0 < α < 1, 0 < β < 1, and α + β > 1.20

(a) What is the growth rate of H ?

(b) Does the economy converge to a balanced growth path? If so, what are the growth rates of K and Y on the balanced growth path?