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Discounting for optimal and acceptable technical facilities involving risks

R. Rackwitz
Technische Universität München, Munich, Germany

Technical facilities should be optimal with respect to benefits and cost. Optimization of technical facilities involving risks for human life and limb require an acceptability criterion and suitable discount rates both for the public and the operator depending on for whom the optimization is carried out. The life quality index is presented and embedded into modern socio-economic concepts. A general risk acceptability criterion is derived. The societal life saving cost (= implied cost of averting a fatality) to be used in optimization as live saving or compensation cost and the societal willingness-to-pay based on the societal value of a statistical life or on the societal life quality index are developed, the latter for three different mortality regimes. Discount rates γ must be long term averages in view of the time horizon of some 20 to more than 100 years for the facilities of interest and net of inflation and taxes. While the operator may use long term averages from the financial market for his cost-benefit analysis the assessment of interest rates for investments of the public into risk reduction is more difficult. The classical Ramsey model decomposes the real interest rate (= output growth rate) into the rate of time preference of consumption and the rate of economical growth multiplied by the elasticity of marginal utility of consumption. It is found that the rate of time preference of consumption should be a little larger than the long term population growth rate if used for the determination of parameters in the acceptability criterion. The output growth rate on the other hand should be smaller than the sum of the population growth rate and the long term growth rate of a national economy which is around 2% for most industrial countries. Accordingly, the rate of time preference of consumption is about 1%, which is also intergenerationally acceptable from an ethical point of view. It is also shown that given a certain output growth rate there is a corresponding maximum interest rate in order to maintain non-negativity of the objective function.

Key words: Optimum technical facilities, life quality index, risk acceptability, discounting