Question

Production Function: Yt = 10Kt^0.4 Lt^0.6 Consumption Function: Ct = 0.7Yt Depreciation rate: 10% (i.e. δ= 0.1) Population growth rate: 3% (i.e. n= 0.03) With this production function, it can be shown that MPK= 4Kt^-0.6Lt^0.6 = 4kt^-0.6 and MPL= 6Kt^0.4 Lt^-0.4= 7k^t0.4

What kind of policies would an economist recommend in order to reach the golden rule capital stock? (Hint: think about saving rate)

Answer 1

Divide the production function by L_t to get the per capita production function.

Now the investment equation is.

At the steady state, LHS becomes 0. So

So 10sk_t^0.4=0.13k. So k^0.6=1000s/13

So k*=(1000s/13)^5/3

At the golden rule, we have the tangent to the production function, that is the MPK is equal to

MPK=4/kt0.6. So

So this will give us the golden level of capital stock. This level of capital stock can be reached by setting the savings rate at the appropriate level.

(400/13)^5/3=(1000s/13)^5/3

So s=0.4. Thus the golden rule level of k can be reached by setting the savings rate=0.4, while it is currently only 0.3