Exploring the Limits of Two Opposing Paradigms, Third Edition
Appendix 1: How Present-value Maximisation Can Lead to Extinction
Appendix 1 How Present-value Maximisation Can Lead to Extillction Here is an example that shows how applying present-value maximisation with a constant discount rate as decision criterion can lead to utmost unsustainability. Imagine that there are two utility paths available. The flrst one provides an inflnite stream of utility at a constant level VI' The second one provides a stream of utility at a constant level V 2• Assume that V 2 is higher than VI (V2 > VI), but that the second path provides higher utility V 2 only for a fmite time T (T fV r e -rt dt 0 V2 _rt]T > VI [--e r 0 r V 2 -VI e-rT <--=--....:... V2 196 Appendix 1 197 How is this result to be interpreted? Assume V 2 to be 10 per cent higher than VI and T to be 50 years. I Then r has to be just about 4.8 per cent per annum in order to choose utility path 2, that is to prefer human extinction in 50 years time for the sake of 10 per cent higher utility over the 50 years to an infmite, albeit lower, utility stream! That is, present-value maximisation can lead to utmost unsustainability. This might appear counter-intuitive to the reader, but is a compelling consequence of the logic of discounting which gives negligible weight to the distant future. Note, however, that this result depends on the discount rate being constant throughout. If the discount rate varies with the welfare level...
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