The effects of contract mechanisms between the government and private hospitals on the social utility

In this work, we deal with a real healthcare system, in which public and private hospitals with different characteristics co-exist. While public hospitals have lower costs, they also suffer from long waiting times, diminishing the perceived quality of care for patients. Conversely, private hospitals, with their higher fees, offer shorter waiting periods, resulting in a more favorable perception of quality. A balanced healthcare system could offer societal benefits. Pricing strategies greatly influence a patient's hospital selection. For instance, reduced fees in private hospitals attract more patients, consequently reducing overcrowding in public facilities and elevating the overall quality of services provided. This study aims to develop pricing models to foster a balanced and socially advantageous healthcare system. Within this system, private hospital pricing is determined through contract mechanisms with the government. Thus, we delve into the ramifications of various contract models between the government and private hospitals on social utility. Our findings underscore the communal advantages of contract mechanisms. Furthermore, we generalize the proposed models to be applicable to similar systems.