Comparison of the costs of the defined-benefit and the defined-contribution schemes under an actuarial methodology

The goal of this work is to use basic tools of actuarial analysis to prove for the first time that the cost of financing pure defined-benefit scheme is equal to that of a pure defined-contribution scheme whenever these plans grant equal benefits in terms of the amount and conditions to obtain them, and it is calculated using the same financial and biometric hypothesis. We state our results in terms of an individual computation and of a group model (for in the second case, the defined-benefit scheme requires the calculation of a general average premium); and in both scenarios, we study the possibility of an early retirement with full and partial portability. Our overall recommendation is to drop the discussion on which scheme is more expensive. The main limitation of this research is also its greatest asset: we have proven that there is no dominance of either plan over the other when there are no other labor market distortions; which means that the discussion could be in order should we consider the presence of such disruptions.