Optimal pricing and budget decisions in public health systems with delay sensitive patients

The congestion of public hospitals for elective treatment in some countries and regions, such as Canada and Hong Kong where the free health policy is implemented, is a serious issue. The main reason is the excessive demand generated by the provision of free service. In response, the government can set appropriate service price and budget for public hospitals to moderate such demand. This is often referred to as the charging policy, implemented in countries such as China. A Stackelberg game is established for a health system consisting of a government, a public health provider and delay sensitive patients. The results show that when the customers' waiting cost is low (e.g., the market demand, the patients delay sensitivity, or the unit capacity cost is low), the free health policy outperforms the charging policy; otherwise, the charging policy is better. Moreover, we find that the equilibrium waiting time and the equilibrium price decrease with the market demand when the funder attaches more importance to patients’ welfare than the budget surplus and the total budget is sufficient.