In this study, a welfare maximization objective for the maximum willingness-to-pay has been analyzed for a cruising taxi market to deal with the common restriction of the conventional log-linear demand function that the price elasticity has to be restricted to be less than -1. This study also proves that the mathematical model formulated in this study is more generalized than the conventional taxi model. The optimization results show that the optimal vacancy and subsidy rate are the functions of the price elasticity, the waiting-time elasticity, the maximum willingness-to-pay around the taxi market and the marginal cost. The numerical results also show that, with the maximum willingness-to-pay, the optimal fare should be equal to the marginal cost while the optimal vacancy mileage, occupancy mileage and vacancy rate are higher than the results without considering the social maximum willingness-to-pay. Regarding fleet size, 58,488 taxis were registered in Taipei Metropolitan till the end of September, 2005; it is shown in the scenario of the first best environment that the taxi market of the Taipei metropolitan area would be excessively supplied when the average daily operating hours of taxi drivers is more than 7.44 hours, while there is an excessive fleet size of 10,100 when the average operating hours of taxi drivers is 9 hours. In the second-best environment, the excessive supply would happen as long as the average daily operating hours of taxi drivers is over 5.71 hours, while there is an excessive fleet size of 21,300 when the average operating hours of taxi drivers is 9 hours.