Effects of high-speed rail and air transport competition on prices, profits and welfare

► Airfare decreases in rail speed if the marginal cost of HSR with respect to rail speed is not too large. ► Whether rail fare increases in rail speed depends on the marginal cost of HSR and the weight of welfare. ► Welfare in the HSR system can be either higher or lower under price discrimination than under uniform pricing. ► The frequency of flights decreases, while the frequency of trains increases, in the weight of welfare. This paper investigates the effects of competition between air transport and high-speed rail (HSR). While airlines are assumed to maximize profit, HSR may maximize a weighted sum of profit and social welfare. We show that both airfare and HSR fare fall as the weight of welfare in the HSR’s objective function increases, while airfare decreases, and rail fare increases, in the airport access time. Furthermore, airfare decreases in rail speed if the impact of HSR marginal cost with respect to rail speed is not too large. On the other hand, whether rail fare increases in rail speed depends not only on the HSR marginal cost but also on the weight of welfare. We further compare prices, profits and welfare between “with price discrimination” in which airlines price discriminate business from leisure passengers, and “without price discrimination”. Welfare in the HSR system can be either higher or lower with price discrimination: In particular, it is higher under price discrimination when the difference of gain from travel is sufficiently larger than the time value difference between business and leisure passengers. Finally, a numerical study on China’s markets is conducted in which both price and schedule frequency are considered as decision variables.