# [OPE-L:5307] Re: x+a = revenue

andrew kliman (Andrew_Kliman@msn.com)
Tue, 24 Jun 1997 20:42:18 -0700 (PDT)

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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).

(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