The Zen of aggregated value

The value of a well-functioning economy V(s) at the end of year 0 that invests a constant fraction s of its aggregated production Yi into capital goods at any given year i in the future is described by formula (4.24).

Y0 is the aggregated production of the economy in year 0 (present time) denoted in units labour of reference year 0, δ0 is the weighted average depreciation rate of all capital goods in the economy, δT is the depreciation rate of human time that is the average of the (negative) drifts of the expected remaining lifetimes of all individuals within the economy which are assumed to evolve as Brownian motions. The depreciation rate of human time reflects the fact that present time is more valuable to humans than future time  (our time today is given, tomorrow you might not be there). Finally, g(s) is the annual growth of the economy which is a function of the investment rate s. Note that part of the investment rate s0 is required as maintenance investments to avoid decay of the capital goods such that g(s0) = δ0. So real growth gr(s) which equals g(s) minus δ0 occurs if s is larger than s0. For formula (4.24) to be valid δT must be larger than the real growth gr(s) and the people must use all future time released by productivity increases as labour (and not leisure).

1.3 Diminishing marginal returns and the optimal investment rate