Life quality time allocation index - an equilibrium economy consistent version of the current life quality index

The definition the life quality index for a country as originally suggested by Nathwani, Lind and Pandey is based on the gross domestic product (GDP), the expected life in good health at birth, and the fraction of life time the anonymous citizen of the country is occupied with money making work. The LQI is invented to serve as a mean to evaluate how much money that reasonably can be allocated to safety improving investments by simply requiring constancy of the LQI. By choosing that the importance of increments in the two first variables should be measured relative to the current values of the variables themselves, the relative increment of the LQI becomes defined as a convex combination of the two relative increments. The combination parameter is obtained by an optimality argument about the anonymous citizen's distribution of his or her time between free time and work time. In the original definition this equilibrium economy principle is applied under the assumption that the GDP is directly proportional to the work time fraction. This direct proportionality has been relaxed by the first author in two earlier papers with an essential effect on the combination parameter. The present paper presents a further development casting the definition into dimensionless quantities that make the index get a pure unit of time and not the somewhat obscure unit as a power product of a money unit and a time unit. To avoid confusion, this new variant of the LQI is called the life quality time allocation index (LQTAI). Moreover, the Danish data from the period from 1948 to 2003 show good agreement with the relation between the productivity and the work time as obtained from the optimality argument. The data fitting leads to an estimate of the combination coefficient of c = 0.092 together with a reduction factor of r = 0.92 to be applied to the total life expectation at birth to obtain the expected life in good health. Among other infinitely many choices of (c, r) there are (0.085, 1.0) and (0.1, 0.85).