Simulation of ratio of old to young people in countries like Poland

Retirement gets difficult to support if everybody lives longer, the birth rates go down, and retirement age and immigration/emigration remain constant. This demographic change influences the ratio of people in retirement age to those of working age. These effects have been simulated by statistical offices in many countries, but also with detailed assumptions in journals and a book [1, 2, 3, 4, 5]; the latter two references give a complete Fortran program. These methods, with minor adjustments, were used to predict the future growth of this ratio for countries with low birth rates like Germany [1, 2, 6], intermediate birth rates like Algeria, [3] and high birth rates like the Palestinian territories [5], always ignoring special historical events which are particular for this country. Now we apply this method to a country like Poland where massive immigration may be less realistic; instead we simulate increases of birth rate and retirement age. Simulation details are shifted to an appendix. The decay of the birth rate (more precisely, the average number of children per women, unfortunately called the total fertility rate) came in Poland later but sharper than in Germany and is approximated by 2.3 − 0.55 ∗ [1 + tanh(0.15(year− 1993))], Fig.1. The total simulated population, normalized by the actual Polish population in 2002, agrees well with what the official Polish authority, www.stat.gov.pl, predicted: Fig.2. Fig.3 shows the ratio of people above retirement age of 63 to the people between 20 and retirement age (lower curve). (Our time units are years throughout.) The future looks less problematic if the number of people up to age 20 is added to those above 63, both groups needing public support. Then the ratio is approaching a minimum: middle curve in Fig.3. Thus for some time, according to Fig.3 until about 2030, the fraction of people needing support from the working population will not be much higher than it was in the past. THus one has some years time to think, discuss and agree on how to solve the future problems of demographic change. The upper curve there shows the effects of a net emigration of 0.1 percent per year, starting in 2010 (e.g. from Poland to Western Europe; some statistical data give higher values already now). In