Countries that seek to provide universal health coverage deal with considerable publicly funded expenses. This article discusses if a private health insurance subsidy policy can reduce the expenses covered by the public system. A theoretical model is developed in which individuals are characterized by two dimensions: inherited risk of illness and preferences for prevention activities. It is shown that when beneficiaries of a voluntary plan have lower risk, i.e. advantageous selection scenario, a subsidy raises heath expenses if articulation between coverage is complementary. On the contrary, in adverse selection scenarios a subsidy reduces expenditure if articulation is supplementary. Intermediate scenarios are also considered where articulations between coverages have both complementary and supplementary components, which is apparently the case for the Colombian health system. Calibrated numerical simulations are provided using the Colombian system data. The calibration strategy employed reveals that selection is adverse in the Colombian voluntary health insurance market. Furthermore, we identify the level of subsidy and changes in articulation (towards supplementarity) that could lead to a reduction in public spending.