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Mathematical Problems in Engineering
Volume 2017, Article ID 5192968, 11 pages
Research Article

Optimal Fare, Vacancy Rate, and Subsidies under Log-Linear Demand with the Consideration of Externalities for a Cruising Taxi Market

Department of Tourism, Aletheia University, New Taipei City 25103, Taiwan

Correspondence should be addressed to Chun-Hsiao Chu;

Received 25 June 2016; Accepted 5 December 2016; Published 15 January 2017

Academic Editor: Chaudry M. Khalique

Copyright © 2017 Chun-Hsiao Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Externality is an important issue for formulating the regulation policy of a taxi market. However, this issue is rarely taken into account in the current policy-making process, and it has not been adequately explored in prior research. This study extends the model proposed by Chang and Chu in 2009 with the aim of exploring the effect of externality on the optimization of the regulation policy of a cruising taxi market. A closed-form solution for optimizing the fare, vacancy rate, and subsidy of the market is derived. The results show that when the externality of taxi trips is taken into consideration, the optimal vacancy rate should be lower and the subsidy should be higher than they are under current conditions where externality is not considered. The results of the sensitivity analysis on the occupied and vacant distance indicate that the relation of the vacant distance to the marginal external cost is more sensitive than the occupied distance. The result of the sensitivity analysis on the subsidy shows the existence of a negative relationship between the marginal external cost and the optimal subsidy.