考量最大願付價格下巡迴計程車市場最佳空車率與費率之研究

OPTIMAL VACANCY RATE AND FARE FOR A CRUISING TAXI MARKET WITH CONSIDERATION OF MAXIMUM WILLINGNESS-TO-PAY

針對以往雙邊取對數之計程車市場需求函數必須在需求之價格彈性絕對值大於1下求解之限制，提出考量消費者「最大願付價格」之處理方法，以解決當價格彈性絕對值小於或等於1時，無法求解最佳解之狀況；同時，研究中以社會福利極大為目標，求解在此最大願付價格下，計程車市場之最佳空車率、補貼率與費率。研究分析結果證明，本研究所提之方法較傳統方法更具一般性，並可有效克服傳統方法之限制；最佳化結果則顯示，在考量最大願付價格下，最佳空車率與補貼率為價格彈性、等車時間彈性、最高願付價格及邊際成本之函數，而最佳費率則發生於每車公里費率等於邊際成本時。以臺北都會區實例分析結果則顯示，最佳空車里程、載客里程、及空車率均較未考量最大願付價格下之最佳化結果為低；就2005年9月底臺北地區登記之58,488輛計程車數量而言，分析結果顯示當計程車平均每日營運時間超過 7.44 小時，大臺北地區之計程車市場有超額供給之現象，若以每日營業9小時分析，則會有一萬零一百餘輛之超額供給。就損益兩平次佳解加以考慮，則只要計程車平均每日營運時間超過5.71 小時，大臺北地區之計程車市場即有超額供給之現象，若以每日營業9小時分析，則會有二萬一仟三百餘輛之超額供給。

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 commonrestriction of the conventional log-linear demand function that the priceelasticity has to be restricted to be less than -1. This study also proves that themathematical model formulated in this study is more generalized than the conventionaltaxi model. The optimization results show that the optimal vacancyand subsidy rate are the functions of the price elasticity, the waiting-time elasticity,the maximum willingness-to-pay around the taxi market and the marginalcost. 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 vacancymileage, occupancy mileage and vacancy rate are higher than the results withoutconsidering 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 marketof the Taipei metropolitan area would be excessively supplied when the averagedaily operating hours of taxi drivers is more than 7.44 hours, while thereis an excessive fleet size of 10,100 when the average operating hours of taxidrivers is 9 hours. In the second-best environment, the excessive supply wouldhappen as long as the average daily operating hours of taxi drivers is over 5.71hours, while there is an excessive fleet size of 21,300 when the average operatinghours of taxi drivers is 9 hours.