The results of the last two chapters can rapidly be combined.
They lead to a statement of the necessary conditions for the
General Optimum of Production and Exchange--due essentially
to Pareto, but implicit in much of Pigou's 'particular equilibrium'
analysis. ^† Indeed, it might be said that Pigou's treatment is in
a sense the more 'general', since he is the more aware of external
effects--especially in production.

Before we start it is as well to note that we require a well-
defined horizon. Our social transformation function is defined
with reference to it, and so are the individual utility functions of
the members of the community. Moreover, the observing econo-
mist is assumed to know the composition of the community--
the tastes of the men who will die and of the men who will be
born--during the whole course of future time this side of the
horizon. Only on this assumption can we proceed. The problem
of actually determining the horizon we leave for Chapter VI. We
shall also postpone till then discussion of the amounts of terminal
capital equipment to be left over when the horizon is attained.
For the present we shall assume them given.

In Fig. 8 the BB curves are social indifference curves (of the
'Bergson frontier' type) corresponding to any Paretian welfare
function. TT is the social production frontier, assumed to be
independent of the distribution of wealth. In the first diagram both
X and Y are outputs; in the second, X is an input--but the
argument is quite general. What are the conditions for maximum
welfare?

Let us start by abstracting from excessive external effects in

-55-