Before revision:  We apply this basic insight to valuation of long-term social discount rates . Combining the Ramsey optimal growth framework with the marginal-utility approach and the Verhulst logistic model, we demonstrate that inevitable slowing down of consumption growth leads to a declining long-term tail of the discount curve.
After revision:  We apply this basic insight to valuation of long-term social discount rates a challenging task. Nonetheless, observations show that the problem at hand is perturbative with the small parameter being the product of an average strength of fluctuations in the growth rate and its autocorrelation time. This fact permits utilization of the cumulant expansion method to derive remarkably simple expressions for the term-structure of expected consumption growth and associated discount rates in the bounded economy. Comparison with empirical data shows that the dynamic effect related to the planetary resource constrains could become a dominant mechanism responsible for a declining long-term tail of the discount curve.