# 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