I find it difficult to reply to Ajit's ope-l 5306, because it evinces a
serious lack of comprehension of what I've been trying to explain to him. All
I can do is try again, and guide him through the issues more slowly this time.
To begin:
Consider a variable G. As time approaches infinity, it is *not* the case that
G "explodes" (increases or decreases without bound).
Ajit, please answer each of the following, "yes" or "no":
(a) As time approaches infinity, is it necessarily the case that G converges
on a stationary state in which G(t+1) = G(t)?
(b) As time approaches infinity, is it necessarily the case that the average
value of G converges on a stationary equilibrium value, i.e., a value at
which, if G(t) has this value, then so will G(t+1)?
(c) Assume that some values of G are negative, and that the frequency of
negative values does not decrease as time approaches infinity.
(i) Is it necessarily the case that, after some time, all the values of
G are negative?
(ii) Is it necessarily the case that, as time approaches infinity, the
average value of G will be negative?
(iii) Is it necessarily the case that, as time approaches infinity, the
average value of G declines?
On this, the five-week anniversary of my challenge to Ajit,
Andrew Kliman