Consider first a steady-state overlapping generations economy of identical individuals
without migration (Samuelson, 1958, 1975; Diamond, 1965). As before, let output
per head y be produced using labour and capital according to a constant returns to
scale production function, y = f (k) where k is capital per worker. Individuals live for
three periods. In the first, they require education at a cost of c. In the second, they
work and earn a wage w = f (k) kf 0
(k) from which T is taken in taxes and s is saved so
that consumption is