Hyperbolic Discounting and the Time-Consistent Solution of Three Canonical Environmental Problems

Holger Strulik

doi:10.2139/ssrn.3022578

Abstract

In this paper I propose a time-consistent method of discounting hyperbolically that contains the discount rate implied by Gamma discounting as a special case. I apply the discounting method to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, (iii) economic growth and pollution. I then compare results with those for conventional exponential discounting using the normalization that both methods provide the same present value of an infinite constant flow. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the Modified Green Golden Rule.

Highlights

Economic scholars agree that the appropriate choice of the discount rate is of preeminent importance in the evaluation of policies that matter for the distant future
For these reasons a panel of leading economists in environmental economics recently came to the conclusion that the discounting of costs and benefits of long‐horizon projects should best be done at a hyperbolic rate (Arrow et al, 2014)
I proposed a time‐consistent method to discount at a declining rate and applied it to three canonical environmental problems

Summary

Introduction

Economic scholars agree that the appropriate choice of the discount rate is of preeminent importance in the evaluation of policies that matter for the distant future. The reason is that, irrespective from whether the discount rate is constant at all times or declining, that is, irrespective of whether an exact or an asymptotic steady state exists, the adjustment dynamics follow a saddlepath along which the growth rates of x and c vanish but are never exactly equal to zero. The unique solution path under hyperbolic discounting, according to (2), leads asymptotically to steady‐state consumption of the maximum sustainable yield.

Results

Conclusion