Taxi Vacancy Rate, Fare, and Subsidy with Maximum Social Willingness-to-Pay under Log-Linear Demand Function

A maximum welfare objective with maximum social willingness-to-pay (MSWTP) under log-linear demand function for a cruising taxi market is proposed to address the common restriction of the conventional log-linear demand function that the price elasticity has to be restricted to be less than -1. The closed forms for optimal vacancy rate, fare, and subsidy are also derived under consideration of MSWTP. The optimization results show that the optimal vacancy and subsidy rate are functions of the price elasticity, waiting time elasticity, MSWTP, and marginal cost. The empirical estimation shows that MSWTP in Taiwan is NT$78.38 (US$2.31 per vehicle kilometer). Additionally, the numerical results show that with consideration of MSWTP, the optimal fare should be equal to the marginal cost, and the optimal vacancy mileage, occupied mileage, and vacancy rate are lower than the results without consideration of MSWTP.