Let us consider one partial case when the functions
have been estimated. In accordance to Nordhaus[5] and
Leimbach's[6] econometric estimation, the relative loss
of the Gross Domestic Product (GDP) for the i-th country,
(which are connected with the expenditures on CO
reduction) depends only on the relative reduction of
emission 
, so that
Nordhaus and Leimbach suggested the following form for
R: 
. Later on Leimbach[6] suggested using
the linear form 
. Unfortunately, 
for both forms, but this is an artefact of regression
analysis used in econometrics. Further on we shall use a
``pure'' linear form where the coefficient b has some
intermediate value (for instance, b = 0.1). (We think
that we do not commit any great crime in respect to
econometrics). Then
and the equations (13) are written in the form (for m =
0):
Let us suppose that all 
are known, i.e. all the
actors (countries) can be ranked along the axis ``altruism
- egoism''. Then the solution of (17) can be represented
as
where
Let us introduce new variables: the relative reduction of
emission for the i-th actor, the relative
contribution of the i-th actor, 
, to the total
current emission. Then (18) can be re-written in a very
simple form:
Substituting from (20) to (19) we get
