However, these market failures imply that competition alone is not sufficient to guarantee cost control and that measures are also needed to improve the functioning of the market both on the supply and on the demand side. This replaced a dual system where public insurance was mandatory for about two-thirds of the population while the other third relied on voluntary private insurance. In the new system, all citizens have to pay a flat rate premium (freely set by the insurer) to their chosen health insurer and an income-related contribution to a risk-equalisation fund, which covers 50% of total health expenditure.