Rationally discounting an uncertain future

J. Doyne Farmer & John Geanakoplos Assessing the relative value of a benefit (or harm) in the future vs. the present is a fundamental problem in economics1. The conventional approach is to discount the future exponentially. This can be motivated by the opportunity cost relative to an investment paying fixed interest2. In contrast, real interest rates vary randomly, so the resulting effective discounting function is no longer exponential, but is rather a function that gives more weight to the far future3, 4. We extend this by investigating a random interest rate model and showing that the effective discounting function asymptotically decays as a power law. This demonstrates that the proper way to discount over long time horizons is very sensitive to fluctuations in interest rates. It suggests that for problems such as global warming, standard exponentially based present value calculations might underestimate the economic impact of future harm by several orders of magnitude. In a broader context our results suggest that the nonexponential discounting used by humans and many other animals5, 6 may be rational.