The Evolution of Welfare Economics
Edgeworth defines
exact utilitarianism to entail
the
greatest quantity of happiness of sentients, exclusive of number and
distribution — an end to which number and distribution are but
means.
Utility, as Professor Jevons says, has two
dimensions, intensity and time. The unit in each
dimension is the just perceivable increment. The implied equation
to each other of each minimum sensibile is a first principle,
incapable of proof.
Mathematical
Psychics (1881) p.7
Problem.—To find $(\alpha)$ the distribution of means and $(\beta)$ of labor, the
$(\gamma)$ quality and $(\delta)$ number of population, so that there may be the greatest possible
happiness. … Greatest possible happiness is the greatest possible integral of
the differential 'Number of enjoyers${}\times{}$duration of enjoyment${}\times{}$degree
thereof '….${}^2$
${}^2$ The greatest possible value of $\int\int\int dp\,dn\,dt$
(where $dp$ corresponds to a just perceivable increment of pleasure, $dn$ to a sentient
individual, $dt$ to an instant of time).
ibid. pp. 56–57
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