The paper aims to create a mathematical model of a social security program taking into account the mixed pension system introduced in Poland in 1999. The author subsequently uses this model to show how pension systems may be affected by the so-called Laffer effect – an effect intuitively predicted by various authors and involving the relationship between possible rates of taxation and the resulting levels of government revenue as a possibility in the economy. The econometric modeling carried out in the article is based on neoclassical growth models, especially one based on research by American economist Peter Diamond, who suggested that people’s lives should be divided into two main periods: professional career and retirement. The analysis conducted by Chrzonstowski combines basic economic values that influence the functioning of the pension system. The study aims to demonstrate the possibility of the occurrence of the Laffer effect in relation to a basic driver of economic growth – “a product constituting remuneration for production factors: capital and human labor”, the author says. The article confirms that the Laffer effect, indicating a specific optimum, can occur in any economy with an institutional pension system, according to Chrzonstowski. The occurrence of such a point of maximum efficiency of the economic system should encourage politicians to search for a permanent path of sustainable growth taking into account this optimum, the author concludes.