Patients might be willing to pay more to obtain better quality medical services when they recognize that high-level hospitals have better quality. However, published papers have not found solid empirical evidence to support this possibility. Therefore, the purpose of this study is to empirically investigate patients’ willingness to pay (WTP) for an outpatient copayment. The study aims to analyze the difference between the two WTP values: to implement a hierarchy of medical care and to improve the quality of medical services. This study administered a questionnaire using the contingent valuation method with a quasi-bidding game for patients’ WTP and the SERVQUAL scale for medical service quality. The Wilcoxon signed-rank test was employed to test the difference between the two WTP values, notably to implement a hierarchy of medical care and to improve the quality of medical services. Both of the WTP values are higher than the academic medical centre’s current copayment NT$420 (approximately US$14); the percentage of respondents willing to pay a higher copayment declined when the outpatient copayment was increased, and the patients’ WTP to have better medical service quality was significantly higher than that to implement a hierarchy of medical care. Patients’ desire to receive better medical services from higher-level hospitals might be stronger than their desire to implement hierarchical medical care. This study reported the relationship between the respondents’ perceived medical service quality and WTP for having better service quality by using regression models. The respondents’ perceptions of medical service quality, especially for “reliability” and “assurance,” would positively affect their WTP. Policy makers should focus on improving the quality of medical services.