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 < (0) and utility falls to zero for ever after time T. Imagine that there is a social planner who has to choose either of the two paths. The presentvalue of each utility path, using a constant discount rater, is p~ = fVle- dt, o co rt T P V2 = f v 2 e-rt dt o If the social planner applies present-value maximisation as the decision criterion, he or she will prefer path two to path one if and only if T o f V 2 e -rt dt co > 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...
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