Optimal and Acceptable Technical Facilities Involving Risks

Economic cost-benefit optimization of technical facility requires suitable "life saving cost" and/or an appropriate acceptance criterion if human life and limb are at risk. Traditionally, acceptance criteria implicit in codes of practice, standards, or regulations for well-defined fields of application are calibrated against past and present practice. This is all but satisfying. It is unclear whether present rules are already optimal. Extrapolations into new fields of application are extremely difficult. Direct cost-benefit analysis is proposed as an alternative. Based on the recently proposed "life quality index" (LQI), a rational acceptance criterion and so-called life saving cost are derived. The classical life quality index is reviewed, modified, and imbedded in modern economics theory. The results are then applied to technical facilities. The relation between optimization and the LQI-based acceptance criterion is discussed. The relevant economics literature is reviewed with respect to discount rates applicable for long-term investments into risk reduction. They should be as low as possible according to a recent mathematical result. Modern economic growth theory decomposes the 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. The public benefit rate (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. Given a certain output growth rate there is a corresponding maximum financial interest rate in order to maintain nonnegativity of the objective function at the optimum. Finally, a simple demonstration example is added.