TD 4: THE AK MODEL

Exercise: AK model

We consider an economy producing goods using the following technology:

Y_t = a.K_t, with a > 0

Furthermore, the growth rate of the active population (n) is constant and strictly positive,

capital depreciates at a constant rate (>0), and the savings rate of the economy

is also constant (0 < s <1).

1. Show that, despite the absence of technical progress, the economy can be

characterized by strictly positive long-term growth of capital per capita. Calculate

the growth rate of capital per capita and compare with the standard Solow model (i.e.

with constant returns).

2. We now assume that the production technology is of the form:

Y_t = F(K_t,L)_t, = a.K_t +b.K_t .L^1-

with 0< <1 and > 0 and b >0

Determine the value of the growth rate of capital per capita in a situation of balanced

growth. Under what condition is this growth rate positive? Study the special

case where A = 1, n = 0.05, = 0.1, s = 0.2 and = 0.5