[Gretl-users] Re: Gretl-users Digest, Vol 148, Issue 8 (Ramsey model - no hope for the lazy)
On Wed, May 8, 2019 at 9:49 PM Alecos Papadopoulos <papadopalex(a)aueb.gr> wrote:
In fact Ramsey (1928) originally formulated the problem with zero
discount rate.
Interesting, I need to go back and read him.
If sigma is the parameter of the CRRA utility function u(c) =
[c^(1-σ)-1]/(1-σ), I would suggest to try a Ramsey model with
Cobb-Douglas production function, and also for simplicity zero exogenous
efficiency growth, and the parameters of the model satisfying
(delta + rho) /σ = alpha * (n+δ),
where delta is the depreciation rate, rho is the time discount rate,
alpha is the exponent of capital in the production function, n is the
growth rate of population. rho can be set equal to zero if you like.
You should obtain that in such a case obeying the Euler equation gives a
constant savings rate from the beginning.
Indeed, it's a special case. Another way of stating the requirement is
that the sigma in the utility function happens to equal the reciprocal of
the steady-state saving rate.
Allin