Suppose also
that if a gross investment of I(v) is made in year v, the amount surviving
in a later year t will be B (t - v). Under the further assumption
that labor and machines of various vintages are arranged in such a way
as to yield maximum output (or equivalently that all workers receive
the same wage regardless of the age of their equipment) it can be
shown that the stock of surviving capital goods of different vintage and
productivity can be summarized for production-function purposes in
an "equivalent stock of capital." The equivalent stock of capital adds
up the survivors of each vintage after weighting them by the appropriate
productivity improvement factor. To be precise, the equivalent
stock of capital in year t is