关键词: 在线极速问诊, 非线性, 参考价格, 极大值原理

Abstract: Online medical consultation service is a critical feature offered by online medical service platforms. The service enables patients to receive medical consultation via the Internet, helping them to manage their conditions efficiently while minimizing transportation and time costs. As a result, the service enhances people's quality of life and promotes the better social governance level. The online speedy telemedicine service is a subtype of online consultation service that stands out due to its rapid matching of doctors for consultation based on patients filled-in information. It offers lower price and faster response to medical problems than the traditional online expert medical consultation.
Despite in-depth research on service price by scholars globally, there is still a lack of exploration of service price strategy for online medical services. Previous research on price models of online service platforms has mainly concentrated on traditional industries such as education, catering, and insurance. However, medical consultation service pricing requires consideration of costs, profits, patient acceptability of prices, and satisfaction with services. Moreover, existing online service price models frequently use linear cost functions, which often overlook the impact of psychological price level and decreasing unit variable cost on price. As a result, such models are challenging to apply directly to medical service price strategy. In this paper, we explore the price problem of speedy telemedicine services on online medical platforms based on the reference price utility and the Pontryagin's maximum principle. We establish a price model of online speedy telemedicine services based on the interaction of user demand, reference price, and platform cost. This model focuses on the improvement of the cost function, takes into account the refund problem due to the poor quality of doctor's service, and proposes a price strategy that differs in long and short periods. Our research results can help online medical service platforms better establish price mechanisms, avoid revenue loss due to excessive price changes, and provide a theoretical basis for medical service price reform.
This study introduces a cost function with feedback into the price model for the first time, improving the original price model study and more accurately describing the demand-cost relationship in online medicine platforms. By combining the specificity and development trend of the online medical field, we establish a dynamic price model based on the interaction of demand, cost, and reference price. We also conduct a numerical analysis in terms of the level of reference price effect, price sensitivity, and the possibility of refund. Our proposed price model can describe the nonlinear and dynamic change process of reference price utility level, including the structural characterization of steady-state prices and the monotonicity of the optimal price strategy. Our study has five main conclusions: (1)The service price setting can increase with the increase of the reference price, but the rate of change is less than the increase of the reference price. (2)The greater the user's loss aversion, the more slowly the platform needs to adjust the service price. (3)When the user's reference price utility level is high, the platform will needs to adopt a cautious price strategy. (4)Online medical service platforms need to improve their service quality to avoid excessive refund rates, thus avoiding excessive user churn when raising service prices. (5)Long-term price strategy needs to slow down price changes for stable profits compared to short-term price strategy. Above all, online medical platforms need to raise prices carefully and adopt a price strategy of gentle rise. The platforms also need to pay attention to the change of users' psychological expectation price to avoid the loss of a large number of users due to excessive increase in service price. It should ensure the quality of the services they provide, encourage doctors to communicate better with users and ensure user satisfaction.
Our study investigates the price model of speedy telemedicine service in the context of online medical platforms based on the reference price utility, filling the research gap of the service price model of online medical platforms. Our proposed model can help the platform solve the dynamic price strategy problem for the reference price-dependent demand model. However, our study has several limitations: First, our price model is constructed in a no-competition context, ignoring the effects of price competition and realistic contexts such as tax rates and inflation rates. Second, we only propose a market-based price model for speedy telemedicine service and do not focus on the price of online expert medical consultation in online medical platforms. Future studies can explore the price of expert consultation by introducing a reference price model.

Key words: speedy telemedicine, nonlinear, reference price, maximum principle