In Samuelson’s model, people live for two periods only, so that the ongoing
economy is always populated by two age cohorts, one young and the
other old. Here I assume a constant population, so that per capita and economy-
wide magnitudes can be used interchangeably. At each year’s end, the
old die, the young become old, and a new young group arrives. It is important
for my purposes (as it was for Samuelson’s) to assume that there is no
family structure in this economy: no inheritances and no financial support
by one cohort for another. Suppose that a young person in this economy can
work and produce goods, while an old person likes to consume goods but
has no ability to produce them. Denote a person’s two objects of choice by
the pair (c, n), where n is units of labor supplied when young and c is units
of the good consumed when old. Assume that everyone’s preferences over
these two goods are given by