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Congestion Pricing

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Transportation Economic and Policy
Congestion Pricing
Professor 邱裕鈞
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0453658徐郁涵、0453667羅巧容、0453660徐福君、0453668賴柏諺、0453217楊孟軒
一、定義
擁擠定價為一針對公共財額外收取費用之系統,而這些公共財通常是需求過大造成擁擠現象,並在其尖峰時刻收取費用。這種方式,可以透過以不增加供給為前提下,解決壅塞問題。而根據市場經濟理論,強迫使用者支付他們所引發的外部性成本,讓使用者能更清楚他們對於環境、市場所帶來的影響、衝擊。
二、通勤者行為模式

一般而言,針對瓶頸路段徵收擁擠費時,一般通勤者之決策與行為模式如上圖所示。以A為出發點,一開始決定去/不去(目的地),不去通常是以假日且觀光性質居多,若為平日上班時段,一般而言都還是要去(上學/上班)。然而下一階段擇是通勤者可選擇轉搭公共運具/維持私人運具。轉搭公共運具者,將可完全不用負擔擁擠費用,而維持私人運具者,則可以選擇改變路線/維持原路線。改變路線者,亦可避免擁擠費用。最後選擇維持原路線者,可以選擇是否改變出發時刻。改變出發時刻者,亦可避免支付擁擠費用,而最終選擇維持原出發時刻者,將支付擁擠費用。
三、本篇探討重點
探討最後一個選擇,出發時刻選擇。
四、文獻回顧
最早將瓶頸路段擁擠定價之問題提出來討論的開山鼻祖為Vickrey(1969),但該研究沉寂一段時間後,於西元1986年再度受到交通經濟學者之重視,刊登於知名國際期刊之相關文獻紛紛出籠:如De Palma and Arnott (1986), Cohen (1987), Newell (1987), Braid (1989), Arnott, et al. (1990a, 1990b, 1993), Tabuchi (1993), Laih (1994), Chen and Bernstein (1995), Yang (1997, 1998)等。其中在探討單一瓶頸路段之擁擠定價架構方面,最具代表性之著作乃為 Braid (1989), ARNOTT, et al. (1990a)及Laih (1994)。前二者不約而同地推導出玲等候最佳收費已完全消除通勤者在瓶頸路口前之總排隊等候時間。零等候最佳收費乃是隨著通勤者到達收費入口之時間不同而收取不同之等候費。又因該等候收費結構乃為連續變化之收費金額,實務上之可行性不高。有鑑於此,Laih 於1994年發展出一套階梯式等候收費結構作為零等候最佳收費之替代方案。
五、本篇選用之文獻
1. R Arnott, A De Palma, R Lindsey, “Economics of a bottleneck”, Journal of urban economics 27 (1), 111-130
2. Laih, C-H, 2004, “Effects of the Optimal Step Toll Scheme on Equilibrium Commuter Behavior”, Applied Economics, Vol.36, No.1, 59-81. (SSCI)
3. 賴禎秀、吳志仁,2002,高速公路實施匝道電子收費下最佳費率與經濟效益評估之研究,運輸計劃季刊,三十一卷,第一期,頁 37-58。 (TSSCI)
4. 賴禎秀、楊培俊、曾俊琳、白俊英,2003,開車通勤者時間價值之模式研究,運輸計劃季刊,三十二卷,第三期,頁 479-492。 (TSSCI)
5. 賴禎秀,2001, 階梯式擁擠收費體制下最佳階段數之研究,運輸計劃季刊,三十卷,第二期,頁 253-274。 (TSSCI)
六、假設說明
H1:成本守恆,在許多相關領域之文獻中,都希望透過擁擠收費進而降低社會總成本,然而相對於本此選用之文獻有著截然不同之觀點。為何這些文獻之研究都會在一開始假設總成本必須均衡不變呢?其實如同於在一封閉系統內,質量守恆為同一道理,質量不變,體積與密度卻相對有所變化,就如同成本所呈現的方式有所不同。有時候成本可以單純的話為金錢作為計算,但有些成為卻是外部性或是不可計量,然而這些成本都不會因擁擠收費而憑空消失,只是轉換為其他型態(ex,負面情緒)等。
H2:選擇最低成本,通勤者在眾多選擇下,將選擇總成本最小的方式通勤。
H3:其他時間成本不計算,通勤者在非瓶頸路段時的通勤時間不列入模式中。
七、瓶頸路段之擁擠模式
一般而言,通勤者抵達工作場所之時刻可以分成三種型態:(1)提早抵達、(2)準時抵達、(3)延遲抵達。假設車輛進入瓶頸路段的時刻為,而車輛在瓶頸路段上排隊等候的時間長度為,通勤者抵達工作場所的準時時刻為,在此即可將三種型態分別表示如下:
提早 (式7-1)
準時 (式7-2)
延遲 (式7-3) 透過(式7-1)與(式7-3),將可能夠達成準時抵達的時刻設為,提早抵達的時間長度設為,以及延遲抵達的時間長度設為。則(式7-1)、(式7-2)與(式7-3)可改寫如下: 提早 (式7-4) 準時 (式7-5)
延遲 (式7-6)
接著考慮整個瓶頸路段之均衡狀態及均衡成本。首先將每小時排隊等候之成本設為,每小時提早抵達之成本設為及每小時延遲抵達之成本設為。再根據H1與H2,可將總均衡成本表示如下:
, (式7-7) 在此將(式7-4)、(式7-5)及(式7-6)帶入(式7-7),可表示如下: , (式7-8) , (式7-9) , (式7-10) (式7-8)、(式7-10)及(式7-9)分別代表提早、準時及延遲三種不同型態之成本。由於根據H2,故每輛車在內之成本皆相同時方能達成均衡,在此之均衡條件為。 如此,(式7-8)與(式7-10)達成均衡的條件如下: , (式7-11) , (式7-12)
進入瓶頸路段時刻(t)
圖1均衡狀態下之排隊等候時間長度
進入瓶頸路段時刻(t)
圖1均衡狀態下之排隊等候時間長度

八、時間成本與價值探討 1. 遲到模式:在處於上班遲到的情況下,開車通勤者會因休閒時間、工作時間、淨收入(net income)、遲到時間以及瓶頸路口前等候時間等因素,產生對其整體效用的增減,故本研究之目標效用函數(U)的形式如下所示:
Max U=U(Te ,Tw, I,TL, To)
Te:休閒時段
Tw:工作時段
I:淨收入(net income)
TL:開車通勤者之遲到時段
TQ:瓶頸路段入口前車輛之排隊等候時段
本遲到模式之時間以及所得限制式如下:
時間限制: T=T+(TQ-T)+T
所得限制: I = wTw– Ω wTL –εTQ – φ
T:一天24小時
w:平均每位開車通勤者之單位時間工資率。
Q:每單位遲到時間之懲罰比率。
ε:通勤車輛每單位排隊等候時間之行車成 如燃油消耗、運具折損、維修保養與保險等。 φ:所有休閒時間之消費金額。 在遲到模式中,我們假設遲到之懲罰金額即為通勤者因遲到而減少正常工作時間之懲罰,然而此一懲罰變數依各公司規定之不同視各公司情況而定,一般而言可分為有形與無形兩種情況,有形之規定較為明確且可加以量化,如依遲到之時間多寡扣除部分比率之所得以明訂懲罰標準;而無形之情況較難加以量化,且遲到之懲罰效果不會立即呈現出來,但並不表示其不存在,公司或許會以另一種方式加以懲罰,如升遷管道受阻或考績評比不佳等方式,不論以何種方式皆是為了達到懲罰遲到通勤者之目的。 2.早到模式:在處於提早到達工作場所的情況下,開車通勤者經由休閒時間、工作時間、淨收入、早到時間以及等候時間等因素,產生對其整體效用的增減。因此本文之目標效用函數(U)的形式如下所示:
Max U=U(Tρ,TW, I,TE, To)
TE:通勤者之早到時段。
一般而言,開車通勤者受到時間、所得限制的假設如下:
時間限制: T=Tρ+TQ+TE + T
所得限制 I= wТw-εTо-φ

早到工作場所之通勤者,其並不會因早到時段之長短而對其淨所得產生增減之效果,因為在一般現實生活中通勤者對早到時間之利用不外乎看報、喝茶、聊天等此類休閒行為,對於通勤者之所得不會產生影響, 故在此並不考慮早到時間此一懲罰變數。
八、零等候收費模型
為使路段效用最大,即無擁擠狀況之產生,且進行擁擠收費後不增加通勤者的均衡運輸成本,因此必須對通勤者徵收零等候最佳通行費,且收費後仍然不改變其收費前之均衡成本。故在該擁擠收費體制下會使得(式7-10)、(式7-9)及(式7-8)中之,且。根據此一結果,可求得零等候最佳收費如下
(1)提早開始服務:
, , (式8-1)

(2)準時開始服務: , , (式8-2)
(3)延遲開始服務:
, , (式8-3) 根據上述結果,可得到(圖8-1)之零等候最佳收費結構圖。藉此可得知,零等候最佳收費之模式,是透過不斷變動收費金額,以消散排隊之情形

圖8-1 零等候最佳收費
圖8-1 零等候最佳收費
進入等候系統時刻(t)
進入等候系統時刻(t)

九、階梯式收費模型 其設計原理乃是在無擁擠最佳收費之三角形內截取一個或數個不同時段來收取單一或階段式之擁擠收費。因爲該擁擠收費結構是內接於無擁擠最佳收費三角形中之矩形或多邊形(由多個內接矩形往上堆積而成),故在單階段或多階段之收費方式中皆可產生最多之擁擠費收入(即最大之矩形或多邊形面積)與其他可能之擁擠費收入組合(即其他可能之矩形或多邊形面積組合),以彈性地減少瓶頸入口前車輛排隊擁擠的時間。又因為最佳單階段等候收費結構最多僅能消除等候收費前全體通勤者等候時間之50%,故有需要發展兩階段以及兩階段以上之階梯式等候收費結構,以補強單階段等候收費方式在等候減少效果上之不足。從最佳單階段、兩階段等的收費結構特徵與等候減少效果,以預測最佳n階段等候收費之結構特徵與等候減少效果。最佳n階段等候收費結構之n個收費金額必將均衡通勤成本(或最高之齡等候最佳收費)等分成(n+1)等分;各階段之收費時間長度接等於瓶頸入口前車輛排隊等候起訖時間長度之1/(n+1);最佳n階段等候收費結構可達到消除等候收費前全體通勤者總排隊等候時間之n/(n+1)之效果。
十、高速公路實施閘到電子收費實施之應用

首先考慮擁擠收費前高速公路與替代道路之均衡狀態。由於每一通勤者行駛之通勤路徑,皆是以總通勤成本最小之原則下來決定其出發時刻,故可得兩通勤路徑之目標函數:

(2)式中,由於高速公路上該瓶頸路段的流量等於容量,所以行駛時間為一固定值。
(3)式中,因假設(7)當連接高速公路瓶頸路段的匣道呈現排隊擁擠現象時,替代道路則無此情形發生之故,該式中並沒有排隊擁擠時間的成本函數。
為了求出單階段費率p,以及其收費開始(t+)、結束(t-)時刻,吾人可繪出下列三個圖形:即圖2、圖3以及圖4,以方便列出相關等式來求解。由於替代路徑並沒有排隊擁擠現象發生,吾人將根據兩條道路特徵的不同,探討對通勤者使用不同路徑下之通勤時間。由於高速公路瓶頸路段之車流量等於設計容量之故,所以車輛在該路段始終以某一速度行進,故車輛之行駛時間為一定值。而在匣道A處(即瓶頸入口前) 排隊擁擠車輛則以停等之方式行進,所以車輛在匣道A處之排隊擁擠時間會隨著延滯車輛之增減呈現近線性方式之穩定增減(如圖2)。然而替代路徑則因車流量小於設計容量之關係,本身並無排隊擁擠現象發生,其車輛的增加,會使行駛速度呈現較劇烈之變化,相對地在固定距離下行駛時間必定也呈現劇烈變化,故以非線性方式來表示(如 3)。依據圖2、圖3以及圖4,吾人可列出(4)-(12)等九個等式,等式中符號眾多, 讀者可參考附錄1以便快速尋找出其定義。

(4).(5) 表示擁擠費率
(6) 表是通勤者於t+時出發,經閘道A進入高速公路抵達工作場所知早到時間成本。
(7) 表是通勤者於t-時出發,經閘道A進入高速公路抵達工作場所支持到時間成本。
(8) 表示t#~t##時段內行駛替代道路之車輛數。
(9) 收費後於t"~t-時段內行駛高速公路或於t"~t"時段內行駛替代道路之 每一位通勤者的均衡通勤成本。
(10) 表示實施擁擠收費後,於收費時段內有付費通行之通勤者人數。
(11 )式為實施擁擠收費後因部分通勤者改行替代道路導致高速公路匣道A上所減 少之排隊擁擠時間成本。
(12) 式中,等號左邊表示政府或相關單位對於擁擠收費前之總排隊擁擠時間成本所欲消除的百分比(1/"E" ),(12)式等號右邊代表擁擠收費後所消除的排隊時間成本,而該成本除了包含 擁擠收費之收入(ρ,Ω)外,尚包括因部分通勤者改走替代路徑而形成匣道A處排隊擁 擠時間成本之減少(ψ)。 本文將利用Mathematica數學軟體解(4)至(12)之聯立方程式後,計算出單階 段擁擠費率ρ值,以及擁擠收費開始(t-)和結束(t+)時刻之值,至於多階段之擁擠費率,則可依循本節求解單階段之步驟求得。 數值列:表1中給定總排隊擁擠時間成本消除百分比為67%,68%,65%,60%之前提下,求得之費率(ρ)若愈低,則進入高速公路之車輛(Ω)將愈多。其中最佳解(68%)乃是發生於費率(p)為NT$54,且進入高速公路之車輛(Ω)為2720輛之情況。表1中由上而下 之四個例子中所減少之總排隊擁擠時間成本(=ρxΩ+ψ)分別為 NT$288766; NTS291615;NT$239385;NT$259869,故可知在最佳解之情況下,總排隊擁擠時間成本之減少是最多的。

有無平行替代路徑假設下之擁擠費率比較:若不存在替代道路之前提下,則將會出現不同於表1之費率結構,此處列出表2以資比較。表1可獲知最佳的擁擠費率結構。但若不存在替代路徑之前提下,則將會出現不同於表1之費率結構,此處列出表2以資比較。表2中之是代表實施最佳單階段擁擠收費後之總排隊擁擠時間成本消除百分比,從表2可知存在替代路徑前提下之排隊擁擠減少效果(68%)明顯優於不存在替代路徑 前提下之排隊擁擠減少效果(50%)。

十一、限制探討與未來發展 在本文前段所歸納個一些假說,均對於擁擠定價此議題上有所受限。H1:總成本不變,其因以通勤者行為之觀點而看,因而對於交通道路、環境評估無法給予政府或相關部門較好之建議。H3,其他時間成本不計入模型,然而扣除擁擠的排隊等候時間,其他真正的通勤時間對於通勤者而言占比將當大,且變異數也非常大,因此難以精準評估。此外,此系列之相關文獻,在通勤者時間價值的探討與成本的考量上都屬於列舉法,一一列舉可能產生之成本再納入計算,然而每個通勤者之所感知的延滯成本將有相當大的差異,例如,同樣遲到20分鐘抵達公司,但不同的人而言,其所面臨的延遲成本都將有所不同,因此若是以此成本作為後續模型推導之基礎,將不能有效精準評估。 對於未來之研究建議,若是未來相關文獻,可利用”道路擁擠時間長度”為基礎進行模型推導,因為每個人在某一瓶頸路口所排隊等候之時間的變異數會小於通勤者延滯成本之變異數,進而可改善模型,使其達成較精準且具有彈性之模型。

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Traffic Congestion Levels Are Rising in Major Cities Around the World.

...medical risks. The second part will offer several feasible solutions to the traffic congestion issue, which are carpooling, establishing an intelligent traffic control system and raise taxes. In the first place, it can be argued that a series of problems can be incurred by high traffic congestion levels. To begin with, traffic jams, arguably, will give rise to increased travel time. Taking China for example, Yang et al. (2011) indicated that traffic congestion, in China, was a serious “urban illness” problem, which had resulted in delays in travel time. Accordingly, the economic efficiency of the whole city is understood to be affected to some extent. Secondly, traffic congestion is responsible for bringing about a large number of economic losses for individuals as well as the waste of oil resources. Generally speaking, the continuous stop and start driving in traffic jams will burn more fuel than smooth driving on an open highway. As a result, extra money will be spent on fuels. Just as Du and Zheng (2012) pointed out that traffic jams could result in tremendous economic losses and waste of fuel resources. In addition, another issue is that high traffic congestion levels may cause significant medical risks. Encountering traffic jams will probably be a severe problem during transferring or picking up a patient to an emergency medical procedure. Carnall (1996) argued that traffic congestion, around the hospital sites, would delay...

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