How does the decision of high-speed rail operator affect social welfare? Considering competition between high-speed rail and air transport

We analytically examine the decision of high-speed rail (HSR) operator from the social welfare-maximizing perspective under quantity competition, price competition, quantity competition with train speed determination (quantity-speed competition) as well as quantity and frequency competition between air transport (AT) and HSR, respectively. A basic Assumption underlying each competition model is that the AT aims at maximizing its profit, while the objective function of HSR which can be manipulated by the government is given by a weighted sum of HSR profit and social welfare. It is demonstrated that under quantity, price and quantity-speed competition between AT and HSR, the socially optimal objective weight of HSR operator depend mainly on both the potential market size of the AT-HSR transportation system and the attractiveness of HSR. However, under quantity-frequency competition, the socially optimal decision weight of HSR operator has nothing to do with the market size and the attractiveness of HSR. These results offer some important insights for government which has the power to influence the decision of HSR authority and aims to maximize the social welfare.