Capital investment literature implicitly assumes that exponential growthof consumption can last indefinitely into the future. However, in the context of climate finance with benefits on current investments deferred to centuries from now , this process is fundamentally constrained by finite biophysical resources of Earth. Similarly to a population dynamics, a negative feedback mechanism will eventually prevent unlimited growth of consumption and reduce its rate. 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. This dynamic effect becomes stronger than the well-known "precautionary" effect related to uncertainty of a social planer in future growth rates of consumption in the relatively near future, which has been estimated here as about 100 years from now (the lower boundary). Our formulation yields remarkably simple expressions for time-declining discount rates which generalize the classic Ramsey formula. The derived results can help to shape a more realistic long-term social discounting policy. Furthermore, with the obvious redefinition of the key parameters of the model, the obtained results are directly applicable for estimations of the expected long-term population growth curve in stochastic environments.
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount curve. The latter plays a critical role in, e.g., climate finance with benefits on current investments deferred to centuries from now . The growth rate of consumption is irregularly evolving in time, which makes estimation of an expected term-structure of consumption growth and associated 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 a social discount curve at the time horizon estimated here as about100 years from now (the lower boundary). The derived results can help to shape a more realistic long-term social discounting policy. Furthermore, with the obvious redefinition of the key parameters of the model, obtained results are directly applicable for description of expected long-term population growth in stochastic environments.
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Capital investment literature implicitly assumes that exponential growthof consumption can last indefinitely into the future. However, in the context of
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount curve. The latter plays a critical role in, e.g.,
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, this process is fundamentally constrained by finite biophysical resources of Earth. Similarly to a population dynamics, a negative feedback mechanism will eventually prevent unlimited growth of consumption and reduce its rate. We apply this basic insight to valuation of long-term
. The growth rate of consumption is irregularly evolving in time, which makes estimation of an expected term-structure of consumption growth and associated
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. 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
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
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Our formulation yields remarkably simple expressions for time-declining discount rates which generalize the classic Ramsey formula.
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