Transaction costs and tradable mobility credits

Transportation Research Part B 46 (2012) 189–203

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Transportation Research Part B journal homepage: www.elsevier.com/locate/trb

Transaction costs and tradable mobility credits Yu (Marco) Nie ⇑ Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, United States

a r t i c l e

i n f o

Article history: Received 1 July 2011 Received in revised form 30 September 2011 Accepted 1 October 2011

Keywords: Transaction cost Tradable mobility credits Congestion pricing Auction market Negotiated market

a b s t r a c t Artificial markets for mobility credits have been proposed as an alternative to conventional congestion pricing schemes. This paper examines the effects of transaction costs on two types of markets: an auction market and a negotiated market. In an auction market, users purchase all of the needed mobility credits through a competitive bidding process. In a negotiated market, the users initially receive certain amount of mobility credits from the government and trade with each other through negotiation to fulfill their needs. We assume that a brokerage service is built in both markets to facilitate transactions and accordingly, the users have to pay a commission fee proportional to the value of trade. The users are also given the option to purchase credits from the government if for some reasons they cannot use or wish to avoid the markets. Our analyses suggest that the auction market can achieve the desired equilibrium allocation of mobility credits as long as the government sets its price properly and the unit transaction cost is lower than the price that the market would reach in absence of transaction costs. However, in the negotiated market, transaction costs could divert the system from the desired equilibrium regardless of their magnitude. More importantly, the initial allocation of mobility credits may affect the final equilibrium even when marginal transaction costs are constant.  2011 Elsevier Ltd. All rights reserved.

1. Introduction Economic instruments are powerful tools for managing traffic congestion. Among these instruments pricing probably has received the most attention thanks to the influential work of Pigou (1920). In order to maximize social welfare, Pigou and his numerous followers argued, travelers would have to pay a congestion tax to make up for the discrepancy between their average and marginal travel costs. Although congestion pricing is beautifully simple and appealing in theory, getting the notion accepted and implemented in practice is not. For one thing, it is difficult to determine where and how much the travelers have to be tolled so that the system efficiency would be improved as predicted by the theory. More difficult to tackle than these technical nuances is the public outcry that unavoidably leads to political opposition. It is hardly a surprise that congestion tolls can be easily perceived and rejected as yet another tax by those who simply do not understand Pigouvian tax, or those who are sensitive to the size and role of the government. Nevertheless, the opposers do have legitimate, well-grounded arguments. Among other issues, congestion pricing does tend to make travel more expensive for some travelers, and even worse, it imposes an unequal redistribution effect that favors rich over poor (Evans, 1992; Arnott et al., 1994; Hau, 1998). Many ideas have been explored to overcome the opposition to congestion pricing. One line of thinking focuses on achieving Pareto-improving, i.e., improving the system efficiency at nobody’s cost. Pareto-improving may be accomplished by properly designed pricing strategies (Lawphongpanich and Yin, 2010; Wu et al., 2011), or through compensation schemes

⇑ Tel.: +1 847 467 0502; fax: +1 847 491 4011. E-mail address: [email protected] 0191-2615/$ - see front matter  2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2011.10.002

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Y. Nie / Transportation Research Part B 46 (2012) 189–203

that allow all or part of the toll revenues to be refunded to travelers (Liu et al., 2009; Nie and Liu, 2010; Guo and Yang, 2010). Another line of thinking centers around a market-based solution, borrowing the concept from various tradable permit schemes for environmental protection (e.g. Dales, 1968; Tietenberg, 1985, 2003). It is well known that an appropriately designed tradable permit system can minimize the total cost of reaching a pre-determined pollution standard regardless of the initial allocation of permits (Montgomery, 1972). Verhoef et al. (1997) examine several applications of tradable permits in managing road transport externality. Of particular interest is the so-called ‘‘tradable road-pricing smart card’’, which allows users to trade among themselves the ‘‘units’’ stored in smart cards that can be used to pay tolls. Viegas (2001) discusses a similar scheme which allocates ‘‘mobility credits’’ to all taxpayers, who can freely trade these rights and use them to pay tolls and/or transit fares. More recently, Yang and Wang (2011) propose a mathematical model that formalizes the analysis of tradable mobility credits. In this model, the government sets a predetermined congestion reduction goal and tries to achieve it by creating a market for mobility credits. The government plays two roles in this market: it issues mobility credits to all eligible travelers, and it determines how many credits are to be charged on each road. Yang and Wang (2011) shows that, if the government makes right decisions about credit provisions and spatial charges, the competitive market will determine the optimal credit price and allocation that meet the initial control goal. A market for mobility credits is an appealing alternative to traditional pricing schemes mainly because it addresses the aforementioned implementation obstacles. First, it gives travelers the freedom to choose how to use their initial endowment of credits based on their value of time and mobility needs, which ensures everybody benefit from the improvement of system efficiency (Yang and Wang, 2011). Second, the initial allocation of credits may be used by the government to alleviate the unequal redistributive impacts. Finally, as the government neither dictates the actual amount of tolls1 nor directly collects them, the payment for mobility is less likely to be perceived as a tax. This paper aims to investigate one aspect that has hitherto received little attention, namely the impacts of transaction costs on the performance of markets for mobility credits. Yang and Wang (2011) presume that transaction costs are ‘‘low enough’’ in their model, citing the fact that transaction may be made using affordable electronic technologies at low costs. The transaction cost considered in this paper involves the transfer of property right in a market. As Coase (1960) put it, in order to carry out a market transaction it is necessary to discover who it is that one wishes to deal with, to inform people that one wishes to deal and on what terms, to conduct negotiations leading up to a bargain, to draw up the contract, to undertake the inspection needed to make sure that the terms of the contract are being observed, and so on. There is no doubt that technology can help reduce many of the above costs. Some, however, may not be reduced to a negligible level even with an ideal, fully computerized system. It would still take time to find and negotiate with potential buyes/ sellers within such a system. Also, the rules of the market have to be enforced. Finally, the cost of building and operating such a system may be substantial. In modern stock exchange markets, the average transaction costs2 range between 0.2% and 0.8% of trade value (Berkowitz et al., 1988; Jones and Lipson, 2001). It seems reasonable to expect that the rate of transaction cost to trade value would be higher in a mobility market, because of its relatively low market capitalization. Stavins (1995) shows that transaction costs can reduce the trading of pollution permits from the optimal level and thereby increasing the total control costs. More interestingly, he shows that the theorem of Montgomery (1972), i.e, the equilibrium allocation of permits is independent of the initial allocation, only holds when transaction costs are an affine function of the volume of trade. Nagurney and Dhanda (2000) study oligopolistic markets for pollution permits that explicitly consider transaction costs. Their focus is to propose a general formulation and an algorithm based on the variational inequality theory, rather than analyzing the impacts of transaction costs. However, their numerical example show that the increases in transaction costs resulted in decreased trade volume, which agrees with the analysis by Stavins (1995). To account for the effects of transaction costs, this paper assumes that a brokerage service will be created, along with the market, to facilitate the transaction of mobility credits. Accordingly, a buyer or seller has to pay for a brokerage fee proportional to trade value. Two different types of markets are considered. In the first, which is mainly employed as a benchmark for comparison, (tradable) mobility credits are auctioned off.3 Compared to traditional pricing scheme, the main differences are that the credit price is determined by the bidding process, and that each buyer has to pay for transactions in addition to the bid price. The second market arrangement is the same as discussed in Yang and Wang (2011). Users will receive a certain amount of credits from the government and trade them with each other through the brokerage facility. Because they do not buy all of the needed credits from the market, the users may incur lower transaction costs in such a market. Hereafter we shall refer to the first type as the auction market, and the second as the negotiated market.4 Creating an artificial commodity and forcing people to trade it in a market just to fulfil daily transportation needs may be even more controversial than congestion pricing itself. A person who badly needs to use a toll road may not be able to find 1 This is only partially true, because in an ideal situation the final price would be determined by credit provisions and spatial charges, both controlled by the government. 2 In a stock market, these costs typically include both commission fee and institutional execution cost, i.e., the difference between the actual price and the prevailing price at the time the order was placed to the trading desk. 3 See Teodorovic et al. (2008) for an example of auction-based congestion pricing. 4 This term was initially chosen for no good reason. Yet, as a reviewer pointed out, Investopedia (http://www.investopedia.com/terms/n/negotiatedmarket.asp#axzz1VORA2MLc) defines a ‘‘negotiated market’’ as the ‘‘type of secondary market exchange in which the prices of each security are bargained out between buyers and sellers’’. Thus, describing Yang and Wang’s market as a ‘‘negotiated market’’ seems to be consistent with the general terminology.

Y. Nie / Transportation Research Part B 46 (2012) 189–203

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someone who is willing to sell him/her the credits at an affordable price. The market could create speculators who seek to game the system for profits. Above all, such a policy may be considered as an infringement of personal freedom in some countries. One resolution to this issue is to have the government step in and offer to sell credits5 to individual who wish to avoid the market all together. Inevitably, this remedy drags the government back to the pricing business that it wishes to avoid. Among other things the government now has to set a price for credits, which presents both a challenge and an opportunity. It is a challenge because an inappropriately chosen government price could destroy the market; it is an opportunity because the government price can be used to guide the market, to fulfill emergency needs, and to provide a check on speculations. Clearly, the goal of the government is to find a price that will simultaneously keep the market active and achieve the desired congestion reduction target. One of the primary questions that this paper attempts to answer is whether and how the government can set its price to meet this goal in different markets and in presence of non-trivial transaction costs. In the following, Section 2 introduces notations and reviews Yang and Wang’s model. Section 3 proposes and analyzes the models for both auction and negotiated markets. The case of elastic demand is briefly discussed in Section 4. Section 5 presents a numerical example that is focused on examining how the unit transaction cost and the government price affect the performance of the markets. Section 6 concludes the paper. 2. Preliminaries Consider a transportation network G(N, A), where N represents a set of nodes and A represents a set of links. Let xa and ta(xa) be the total link flow and travel time on link a 2 A, where ta() is a non-negative, strictly increasing and convex function. Let R and S denote the sets of origin and destination nodes, respectively. The travel demand between O–D pair r–s is assumed to be fixed at qrs (This assumption will be relaxed in Section 5.). The set of paths that connect an O–D pair rs is denoted by Krs, and the flow on path k, "k 2 Krs is represented by fkrs . Assume now that an artificial market for mobility credits is introduced by the government to reduce traffic congestion. The government will first determine how many units of mobility credits a traveler has to pay, denoted as ja, to use link a. Then, the government will issue a certain amount of credits, denoted as P, and distribute them among eligible travelers depending on the type of the market. In a market such as considered in Yang and Wang (2011), every traveler will receive an initial endowment of credits and trade them with each other in the market. Yang and Wang (2011) suggest that the equilibrium flow pattern in such a negotiated market can be found from the following traffic assignment model with a side constraint:

min

zðxÞ ¼

XZ

X

ta ðwÞdw

ð1Þ

0

a

s:t: :

xa

fkrs ¼ qrs

8r 2 R; s 2 S

ð2Þ

k

XXX r

X a fkrs

s

fkrs drs a;k ¼ xa

8a 2 A

ð3Þ

k

ja xa 6 P

ð4Þ

P 0 8k 2 K rs ; r 2 R; s 2 S

ð5Þ

where drs a;k ¼ 1 if link a is on path krs, and 0 otherwise. Compared to the classic user-equilibrium (UE) traffic assignment model (Beckmann et al., 1956; Sheffi, 1985), the only difference is the credit feasibility constraint (4), which requires that the total demand for credits should not exceed the total supply. Thus, the above problem is still a non-linear program defined on a non-empty6 polyhedron, with an objective function that is strictly convex with respect to the vector of link flows x = {xa}. The Karush–Kuhn–Tucker (KKT) conditions of the above optimization problem include the following complementarity conditions:

Xh

i ðt a ðxa Þ þ pja Þdrs a;k P lrs 8r; s; k

a

Xh

fkrs X

! ¼ 0; 8r; s; k

ð7Þ

a

ja xa 6 P

a

p

i ðt a ðxa Þ þ pja Þdrs a;k  lrs

ð6Þ

X

ð8Þ !

ja xa  P ¼ 0

ð9Þ

a

where lrs and p, the multipliers associated with Constraints (2) and (4), can be interpreted as the minimum travel cost between the O–D pair r–s and the market clearance price for credits, respectively. Conditions (6) and (7) are similar to the clas5 6

Any credits sold by the government in this way will increase the total supply of credits in the market. For simplicity, the feasible set is always assumed to be non-empty in this paper.

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sic UE conditions except that link travel cost becomes the sum of travel time and the cost of the required credits. The market equilibrium conditions (6) and (7) states that the price of the credit is positive only when all credits issued by the government are consumed. In other words, mobility credits have no market value if there is a surplus. The market price p is not necessarily unique. However, Yang and Wang (2011) shows that if any O–D pair has more than one used path with different credit charges at the equilibrium, the credit price is uniquely determined. Suppose now that the government wishes to reduce congestion to the lowest possible level using the above market mech  anism. In other words, the goal is to achieve a system optimum (SO) flow pattern, denoted as x ¼ xa , which minimizes    total travel time. According to Hearn and Ramana (1998), an SO link toll s ¼ sa , which ensures that x⁄ solves the corresponding tolled user equilibrium, must satisfy the following linear constraints:

Xh

i   ðt a xa þ sa Þdrs a;k P lrs ; 8k; r; s

a X     XX ðt a xa þ sa Þxa ¼ qrs lrs a

r

ð10Þ ð11Þ

s

An SO toll may or may not be a marginal cost toll. However, for any given SO toll, the government can initialize the credit market by setting

ja ¼ rsa ; 8a; P ¼

X

r ja xa ;

ð12Þ

a

where r is a positive scalar. Yang and Wang (2011) showed that, for a credit market set up in this way, x is always the solution to Problems (1)–(5), and that the credit price is always equal to 1/r if the SO flow pattern is such that this price can be uniquely determined. In other words, for any r > 0 and SO toll s, j and P determined from (12) always ensure an SO flow pattern is a tolled user equilibrium, i.e.,

Xh

i   ðt a xa þ ja Þdrs a;k P lrs ; 8k; r; s

a X     XX ðt a xa þ ja Þxa ¼ qrs lrs a

X ðja xa Þ ¼ P

r

ð13Þ ð14Þ

s

ð15Þ

a

Without loss of generality, we shall assume r = 1 hereafter, which sets the market clearance price p = 1. If s is the mar dt ðx Þ ginal cost toll, the value of link toll can be interpreted as the marginal travel time xa dxaa . Accordingly, p = 1 implies that the value of one unit of credit equals one unit of marginal travel time (cf. (12)). 3. Markets with transaction costs and the government option Since the model presented in the previous section does not have any parameters regarding trading, it can also be used to describe other market arrangements, such as an auction market in which the government sells all credits to users through competitive bidding. Certainly, this is true only if the cost of transaction is not considered, because transaction costs depend on trade value and hence also depend on the initial allocation of credits. Without transaction costs, the credit price is always determined by P (supply) and j = {ja} (demand). If the demand is fixed, the initial allocation would only affect individual welfare, but not the final equilibrium flow pattern and the credit price. In this section, we will discuss how transaction costs would affect the behavior of a market for mobility credits, and how such impacts change in different markets. Our analyses are based on the following two assumptions: Assumption 1. Anyone who buy or sell credits in the market will have to use a brokerage service and hence must pay a commission fee pt/r for each credit traded, where r is defined in Eq. (12). As explained before, r measures the time value of each unit of credit: the larger r is, the lower value each credit contains. Thus, the transaction cost can also be defined as pt per each unit of trade value. In the following, r is always assumed to be 1. Assumption 2. The government will sell credits, in addition to those already in the market, to any travelers at price pg. Note that this price includes all administrative costs such as transaction and operation. 3.1. Auction market In this market, travelers do not receive any credits for free and have to purchase all needed credits. For each credit purchased through the competitive bidding process, they pay a bid price p plus the transaction cost pt. They can also purchase

Y. Nie / Transportation Research Part B 46 (2012) 189–203

193

credits from the government at the price pg. Let ya be the number of travelers on link a who purchase credits from the market. The equilibrium problem with an auction market can be formulated as follows:

min

zðxÞ ¼

X Z

xa

0

a

t a ðwÞdw þ ðxa  ya Þja pg þ ya ja pt

ð16Þ

s:t: : X

fkrs ¼ qrs

8r 2 R; s 2 S

ð17Þ

k

XXX r

X

s

fkrs drs a;k ¼ xa

8a 2 A

ð18Þ

k

ja ya 6 P

ð19Þ

a

ya 6 xa ; 8a

ð20Þ

fkrs

ð21Þ

P 0 8k 2 K rs ; r 2 R; s 2 S; ya P 0

Constraint (19) is the new credit feasibility condition, which states that the total credits purchased by all buyers must not exceed the total supply. Note that when pg ? 1 and pt = 0, (16)–(21) is reduced to the model presented in the previous section. Note that for the given assumptions, the objective function (16) is strictly convex with respect to x = {xa} but not strictly convex with respect to y = {ya}. Thus, the above problem may not have a unique optimal solution for y. Introducing p as the multiplier for the Constraint (19) and ka for the constraint (20), the KKT conditions can be written as follows:

Xh

i ðt a ðxa Þ þ pg ja  ka Þdrs a;k P lrs ; 8r; s; k

a

fkrs

Xh

ðt a ðxa Þ þ pg ja 

ka Þdrs a;k

i

ð22Þ

!  lrs

¼ 0; 8r; s; k

ð23Þ

a

ja ðpt  pg þ pÞ þ ka P 0 8a

ð24Þ

ya ðja ðpt  pg þ pÞ þ ka Þ ¼ 0 8a

ð25Þ

ka ðya  xa Þ ¼ 0; ya 6 xa 8a ! X X ja ya  P ¼ 0; ja ya 6 P p

ð26Þ

a

ð27Þ

a

We say the auction market is inactive if nobody purchases credits from it, i.e., ya = 0, "a. Proposition 1. The auction market is inactive if pt > pg. Proof. If pt > pg, then ja(pt  pg + p) > 0 ? ja(pt  pg + p) + ka > 0 (note that p P 0 and ka P 0 by definition). Hence ya = 0, "a follows from Condition (25). h The above result has an intuitive interpretation: if the unit transaction cost is even higher than the price offered by the government, everyone will buy from the government even if the nominal price of the credit is zero. Consequently, the market will be abandoned. The next result shows under what condition the market will work properly to achieve the desired equilibrium. Proposition 2. Let x be the SO flow pattern, and j and P be determined by (12) with r = 1. Also assume at SO, the credit price can be uniquely determined. 1. If 0 6 pt < 1 and pg P 1, credit price p = 1  pt and x is the solution to the equilibrium problem with the auction market (16)– (21); 2. If 0 6 pt < pg < 1, credit price p = pg  pt and x is not the solution to (16)–(21); 3. If 1 < pt < pg, p = 0 and x is not the solution to (16)–(21). Proof. To prove 1, we only need to show that one can always find a valid set of multipliers ka, "a and p such that the KKT conditions (22)–(27) holds for xa ; 8a. Because pt < 1 and pg P 1, we can always find a p > 0 such that p + pt < pg. Two obserP P vations are in order: (a) p > 0 implies a ja ya ¼ P ¼ a xa ka ; (b) p + pt < pg implies that for any a such that ja > 0, ka > 0,  which implies ya ¼ xa > 0. From (b) we have ka = ja(pg  pt  p), which, once plugged in (22) and (23), leads to

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Y. Nie / Transportation Research Part B 46 (2012) 189–203

Xh a

Xh

i   ðt a xa þ ðpt þ pÞja Þdrs a;k P lrs ; 8r; s; k

ð28Þ

i XX    ðt a xa þ ðpt þ pÞja Þdrs qrs lrs a;k xa ¼

ð29Þ

a

r

s

The above is equivalent to (13)–(15) as long as one can find a p > 0 such that pt + p = 1. This is guaranteed by the condition pt < 1. To prove 2, note that the market price must not exceed the government price, or the market will be inactive. Thus, p 6 pg < 1. As the credit price is reduced from the level at system optimum (i.e. 1), the traveler will shift to the paths with P higher credit charge to reach a new equilibrium. Thus, at the new tolled equilibrium, we must have a xa ja > P. For any P vector y = {    ,ya,    } such that a ya ¼ P, there must exist at least one ya < xa and ja > 0. This implies that ka = 0, and accordingly (pt + p  pg)ja = 0 ? p = pg  pt. Because the new flow pattern differs from SO, it must not be SO as per the uniqueness of SO link flows. Statement 3 can be proven similarly as 2. Since now the total price of the credit p + pt must exceed 1 (note pP0), the traveler will have to shift to the paths with lower credit charge compared to the SO flow pattern. Thus, at the new tolled P P equilibrium (which is clearly not SO), a ya ja 6 a xa ja < P, which means the credit is oversupplied and consequently, its price will become 0. h The above results are summarized using Fig. 1. First, note that in the area under the 45 degree line (Area IV), the market becomes inactive as stated in Proposition 1. The left-upper area in Fig. 1 (Area I) corresponds to relative low transaction costs (<1), which the auction market can absorb by adjusting the credit price while maintaining the optimal efficiency. In Area III, where pt > 1, the cost of operating the market is too high to maintain the optimal system efficiency. The market price for credits will be reduced to zero. Yet, the trading will continue as long as there is no better alternative (either there is no government option or the government charges even higher). In Area II, where pt < pg < 1, the government price is too low to sustain the SO flow pattern. Interestingly, the government option may seem to be a perfect alternative to the market in this case, because Proposition 2 shows that the market will always adjust its price such that p + pt = pg. The question is: would everyone purchase credits from the government instead of the market, which might eventually lead to an inactive market? The answer is no. To see this, note that if the market does become inactive, the credit price p will become zero, and hence Condition (24) implies ka > 0 ? ya = xa "a, which contradicts with the assumption of an inactive market. To summarize, in an auction market, the best pricing strategy for the government is to start with a price slightly higher than the optimal price, and to increase it only when the market is not active. If the government has to offer a price significantly higher than 1 (the optimal price) to just keep the market alive, it indicates that the unit transaction cost is well above 1, and hence the market is likely too expensive to operate. In general, operating the market is worthwhile only if the total transaction costs do not exceed the total benefits from the congestion relief it promises to produce. The following analysis shows that this condition may not be satisfied even when pt is well below 1. Consider the BPR-type travel time function ta ðxa Þ ¼ t 0a ð1 þ aðxa =C a Þb Þ. Let xa ;  xa be the volume on link a at system optimum and user equilibrium respectively. According to the price of anarchy (Roughgarden, 2005), we have

X a

t a ðxa Þxa 6

ðb þ 1Þ1þ1=b ðb þ 1Þ1þ1=b  b

X   t a xa xa a

Fig. 1. Credit price as a function of the government price (pg) and the unit transaction cost (pt). SO is ensured only in the shaded area.

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Y. Nie / Transportation Research Part B 46 (2012) 189–203

In other words, the total travel time saving from any pricing strategy P, denoted as SP, is bounded by

SP 6

b ðb þ 1Þ

1þ1=b

b

X   ta xa xa

ð30Þ

a

 b If the marginal cost toll is adopted, i.e., sa ¼ t 0a ab xa =C a , and assuming that at SO the total free flow travel time equals 1  c times of the total travel time (0 < c < 1). We then have

0P   P a  1 t a xa xa t 0 xa Ba   a   C P a     ¼ b@P P  A ¼ bc t a xa xa t a xa xa t a xa xa P

sa xa

a

a

ð31Þ

a

According to Proposition 2, when pt < 1 and pg P 1, the total transaction costs C T ¼ pt

X   C T ¼ pt bc t a xa xa :

P

s

 a a xa .

It follows from Eq. (31) that

a

The market is too expensive to operate if CT is larger than the upper bound for travel time saving SP, i.e.,

pt bc

X   t a xa xa P a

b ðb þ 1Þ1þ1=b  b

X   t a xa xa ! pt P

1



c ðb þ 1Þ1þ1=b  b

a

ð32Þ

When c = 0.5 (i.e., congestion doubles the total travel time) and b = 4, the lower bound for pt given by the above formula is about 0.57. It should be noted that the lower bound given in (32) is not tight in the sense that the total transaction costs may exceed the travel time savings at a pt well below the lower bound. Moreover, the lower bound becomes larger for lighter congestion (i.e. smaller c), because the total time saving is always estimated from the price of anarchy, which is independent of the congestion level. However, it is enough for our purpose to show that the market solution may generate negative net benefits when transaction costs are accounted for, even when the market seems to work properly (pt < 1 < pg).7 3.2. Negotiated market In this section, a different market arrangement is considered, where each traveler receives an initial endowment of credits from the government and then trades them with each other through negotiations. The buyers and sellers are assumed to share the commission fee for the trading, and for simplicity, it is assumed that for each unit of credit traded, both the buyer and the seller would pay pt for the brokerage service (r = 1). Similarly, the travelers have the option to buy credit from the government at the price pg to fulfill their unmet needs. We also assume that everyone from the same O–D pair initially receives the same amount of credits /rs from the government.8 Mathematically, this can be written as

XX r

/rs qrs ¼ P

ð33Þ

s

P rs rs Let g rs a da;k ja denote the required credits on k denotes the travelers on path krs who purchase credits from the market, mk ¼ rs rs path krs, and qk ¼ mk  /rs denote the extra credits one has to purchase, either from the market or the government, when traveling on path krs. The equilibrium problem with a negotiated market is formulated as follows:

min

zðxÞ ¼

XZ

X

ta ðwÞdw þ

0

a

s:t: :

xa

fkrs ¼ qrs

X X X

  rs  rs rs pg ðfkrs  g rs k Þ qk þ þ g k qk pt r

s

ð34Þ

k

8r 2 R; s 2 S

ð35Þ

k

XXX r

s

r

s

XXX rs g rs k 6 fk ;

fkrs

P 0;

fkrs drs a;k ¼ xa

8a 2 A

ð36Þ

rs g rs 8k 2 K rs ; r 2 R; s 2 S k qk 6 0

ð37Þ

k

k

8k 2 K rs ; r 2 R; s 2 S g rs 8k 2 K rs ; r 2 R; s 2 S k P 0

ð38Þ ð39Þ

7 The above analysis assumes the marginal cost toll. It is well known that, in the case of fixed demand, the SO flow pattern may be decentralized by different toll schemes that yield different amounts of revenue (e.g. Hearn and Ramana, 1998; Dial, 2000). Therefore, an SO toll with a smaller revenue footprint may reduce the impacts of transaction costs in the above analysis. Whether such a scheme exists and how much it can reduce transaction costs, of course, depends on specific problem settings. 8 This assumption allows the government to differentiate the initial allocation based on geographical locations. Be promising that may sound, such a differentiation is difficult to implement because, among other issues, O–D pairs in reality are not as well defined as in the model. Alternatively, one can assume that everyone receives the same amount of credits regardless of their O–D pair. We note that the analyses that follow are applicable regardless of the allocation scheme.

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Y. Nie / Transportation Research Part B 46 (2012) 189–203

where [a]+ = a if a P 0, and 0 otherwise. As indicated in the second term of the objective function, the travelers who abandons the market would purchase credits from the government only when his/her initial endowment /rs is not enough to cover all credit charges. The third term of the objective function ensures that both buyers and sellers in the market pay for transactions in proportion to the amount of trading. Also worth noting is the market clearance constraint in the negotiated market (Constraint (37)), which is formulated differently from that in an auction one. Here, the requirement is that the credits needed by all those who opt to use the market should not exceed the sum of their own initial endowments. In other words, either the market is cleared (i.e. credits sold exactly balances credits purchased), or no trading should take place at all. The KKT conditions of the negotiated market problem are:

 X

 rs  rs t a ðxa Þdrs a;k þ pg qk þ  kk P lrs 8r; s; k a

fkrs

X

a

  rs  rs ta ðxa Þdrs a;k þ pg qk þ  kk  lrs

ð40Þ

! ¼ 0; 8r; s; k

ð41Þ

rs rs rs pqrs 8r; s; k k  pg ½qk þ þ pt qk þ kk P 0   rs rs rs rs rs g k pqk  pg ½qk þ þ pt qk þ kk ¼ 0 8r; s; k  rs  rs rs 8r; s; k ¼ 0; g rs krs k g k  fk k 6 fk ! XXX XXX rs rs p g rs g rs ¼ 0; k qk k qk 6 0 r

s

r

k

s

ð42Þ ð43Þ ð44Þ ð45Þ

k

where p and krs k are the multipliers associated with the Constraints (37) and (38), respectively. Proposition 3. Let x⁄ be the SO flow pattern, and j and P be determined by (12) with r = 1. Also assume (I) at SO, the credit price can be uniquely determined, and (II) pt = 0; 1. If pg > 1, the credit price p = 1 and x⁄ is the solution to the equilibrium problem with the negotiated market (34)–(39); 2. If pg < 1, the credit price p = pg whenever the market is active, and x⁄ is not the solution to (34)–(39). Proof. We first assume p = 1 and proceed to show that the optimal solution to (34)–(39) will be SO under this assumption. rs With pt = 0, and pg > 1, all users will choose market, i.e., g rs k ¼ fk . It follows from Conditions (44) and (43) that  rs  rs rs pqk  pg qk þ þ kk ¼ 0. Accordingly, Conditions (40) and (41) become

X    X   rs     t a xa da;k þ pqrs t a xa þ pja drs a;k P lrs 8r; s; k k P lrs ! a

fkrs

X   rs  ta xa da;k þ pqrs k  lrs

!

a

¼ 0; ! fkrs

a

 X    ðt a xa þ pja Þdrs a;k  lrs

ð46Þ ! ¼ 08r; s; k

ð47Þ

a

 rs ¼ lrs þ /rs . Comparing the above with (13)–(15), we can see that the SO flow pattern is attained when p = 1. Hithwhere l erto we show that SO is one solution of Problem (34)–(39). Since (34)–(39) must have the unique link flow solution, it is impossible to find a non-SO flow pattern as an alternative solution. This proves 1. rs To prove 2, we first show that, when pg < 1, p cannot be smaller than pg. Suppose p < pg, we will have g rs k ¼ fk , which in turn leads to Conditions (46) and (47) as shown above. However, since p < 1, the flows will shift to paths with higher credit charges compared to the SO pattern. Thus, at the new flow pattern,

XXX r

s

k

fkrs qrs k ¼

XXX r

s

fkrs





mrsk  /rs > 0

k

rs It follows that at least for some path g rs k < fk , or Constraint (37) will be violated. This contradicts with the assumption p < pg. rs Next, we show that p > pg is also impossible whenever the market is active. Suppose p > pg, we have g rs k ¼ 0 ! kk ¼ 0 for any rs used path. Since the market is active, there must exist at least one used path whose q < 0. For this path, Condition (42) k rs rs rs rs rs implies that krs P p q  p q ¼ p q > 0 ! g ¼ f , a contradiction. Hence, p = p . As explained above, since the users g g k k þ k k k k now pay lower credit price than they do at SO, they can afford using paths with higher credit charge, and hence depart from the SO flow pattern. h

Comparing Proposition 3 to Proposition 2 reveals that the behavior of the negotiated and auction markets is similar when pt = 0. When pt > 0, however, the auction and negotiated markets behave very differently. To reveal this difference, consider a case where pt  1, pg  1 and j and P are determined by (12) with r = 1. Because the government price is very high and the market has a very low transaction cost, everyone would use the credit market, i.e. rs g rs p > 0. With this assumption and from Condition (44) we know that for any used path at SO, k ¼ fk , and the credit rs price rs rs pqk  pg qrs k þ þ pt qk þ kk ¼ 0. Suppose now that all O–D pairs in the network except r–s uses only one path at SO. Further,

Y. Nie / Transportation Research Part B 46 (2012) 189–203

197

rs rs rs suppose that the O–D pair r–s uses two paths, k and l, at SO and mrs k –ml ! qk –ql . In order that the credit market admits SO, we must have

X   rs rs X    rs rs t a xa dk;a þ pqrs ta xa dl;a þ pqrs k þ pt qk ¼ l þ pt ql a

ð48Þ

a

Clearly, if the market price is set to

 rs rs  P   P    rs t a xa dk;a  ta xa drs l;a þ pt qk  ql p¼

a

a

¼ 1 þ pt

qrsl  qrsk

rs rs q  q k

l

qrsl  qrsk

ð49Þ

Eq. (48) would be balanced without making any changes to the underlying SO flow pattern. Note that the second equality in Eq. (49) holds because according to the equilibrium condition at SO

X   rs X   rs X   rs X   rs rs rs rs t a xa dk;a þ mrs ta xa dl;a þ mrs ta xa dk;a  t a xa dl;a ¼ mrs k ¼ l ! l  mk ¼ ql  qk a

a

a

a

Unlike in an auction market, however, the relationship between p and pt cannot be described simply using p + pt = 1, even 9 rs in this very restrictive case. For example, if qrs the creditis k < 0; ql < 0 , then p = 1 + pt. This provides an interesting case where  rs rs rs priced higher than 1 by the market, and yet the flow pattern remains at SO. Furthermore, if qrs k > 0; ql < 0; p ¼ 1 þ pt qk þ ql =  rs      ql  qrsk ¼ 1 þ pt mrsk þ mrsl  2/rs = mrsl  mrsk , which clearly indicates that the optimal credit price may depend on the initial allocation and the credit charges on the used paths. rs rs If O–D pair rs has the third used path h, and mrs h – ml – mk , then balancing the following equations,

X   rs rs X    rs rs X    rs rs ¼ t a xa dk;a þ pqrs ta xa dl;a þ pqrs t a xa dh;a þ pqrs k þ pt qk ¼ l þ pt ql h þ pt qh ; a

a

a

  would require more than just choosing an appropriate p. In general, the flow pattern xa will be forced to deviate from SO to settle at a new tolled equilibrium. The same argument applies to the case where more than one O–D pair has two used paths or more at SO. If the initial allocation can be differentiated based on O–D pairs, it may provide extra freedoms to balance the above equation without having to deviate from the SO flow pattern. However, as long as the link tolls are fixed, the maximum number of added freedoms through O–D differentiation is w  1, where w is the number of O–D pairs. It is easy to see that this may still be far smaller than the number of equations needed for equilibrating costs on all used paths at SO. In a nutshell, even a small transaction cost can cause efficiency loss in a negotiated mobility market. The magnitude of this impact is affected by the initial credit allocation and other problem-specific parameters such as network topology and the level of congestion. Moreover, the loss of efficiency is independent of government price, i.e., it cannot be mitigated by the government by choosing a ‘‘right’’ price.

4. Case of elastic demand The analyses given in the previous section can be extended to the case of elastic demand. For the auction credit market model, the objective function (16) becomes

min zðxÞ ¼

X Z a

0

xa

t a ðwÞdw þ ðxa  ya Þja pg þ ya ja pt



Z 0

qrs

D1 rs ðwÞdw

ð50Þ

where D1 rs is the inverse demand function for the O–D pair rs. As is well known (see e.g. Sheffi, 1985), the elastic demand problem can be converted to a fixed demand one by adding an exclusive link to connect each O–D pair. These dummy links   should (1) have link performance functions set as W rs ðv Þ ¼ D1 rs ðqrs  v Þ (where qrs is the upper bound of the demand between rs), (2) not be used by travelers of any other O–D pairs, and (3) forbid tolls. As long as this transformation is properly conducted, the elastic demand problem can be analyzed as a fixed demand one for our purpose, which we shall not repeat to be brief. One issue that arises in the elastic demand negotiated market model warrants some discussion here. Note that by our assumption, everyone from the same O–D pair will receive the same amount of initial credits. Thus, those who are assigned to the dummy link (they choose either to forgo the trip or to use other modes) will bear the highest possible transaction cost because they have to sell all their credits. This may be undesirable especially when the purpose of credit-based congestion pricing is to shift demands to alternative modes such as transit. One possibility is to waive or subsidize the transaction costs paid by transit users, which might be implemented by linking certain transit fare reduction voucher to each credit transaction. 9

The market can be cleared even when the users of both paths have surplus of credits, because the users from other O–D pairs can purchase them.

198

Y. Nie / Transportation Research Part B 46 (2012) 189–203

5. Numerical results Consider the network assignment problem shown in Fig. 2, whose topology mimics the well-known Braess network (Braess, 2005). An additional link with constant travel time is added to connect the O–D pair 1–4. Thus, the model considered herein can be viewed as an elastic demand model with a constant inverse demand function, although the parameters are set such that the dummy link (link 6) will not be used in most cases. As a benchmark, Table 1 reports the UE and SO solutions for this problem. Note that the total travel time at UE and SO, denoted as T and T⁄, are 373.7143 and 337.4167, respectively. Also, according to the SO solution, the government should issue K = 136.5833 credits. A traveler will either buy all needed credits from an auction market, or make up for the discrepancy, through a negotiated market, between the initial endowment of credit (136.5833/6 = 22.7639 in this case) and the needed credit. Our focus is to examine how the models with the two different markets behave under different combinations of the unit transaction cost (pt) and the government price (pg). To measure the performance of the market we use four indexes: the credit price (p); the total travel time (T); the total credit bought or sold in the market (Pm); the total credit consumed by all travelers (Pc). 5.1. Auction market We check all possible combinations of pg and pt, each ranges between 0 and 2 and is discretized with a uniform 0.05 interval. In total, there are 41  41 = 1681 combinations. For each combination, an auction market problem is solved using MATLAB’s fmincon function, and the four aforementioned evaluation indexes are recorded. The resulting two-dimensional contour diagrams, in which the color is used to represent the value of an index corresponding to a pg–pt combination, are plotted in Fig. 3. To overcome the inability of the coloring scheme to capture small changes, Fig. 4 plots cross-sections for each contour map at four discrete values of pt (0, 0.5, 1.5 and 2). Figs. 3a and 4a show that the credit price changes with pt and pg in a pattern that exactly agrees with the prediction of Proposition 2 (also cf. Fig. 1). Namely, the credit price can be adjusted to accommodate the transaction cost when pt < pg and pt < 1, but will drop to zero whenever pt P 1. As analyzed before, this indicates that the government has the ability, at least in theory, to maximize the efficiency of the auction market as long as the unit transaction cost is reasonably low. Figs. 3b and 4b reveal that the total system travel time remains at the level of SO when pg > 1 > pt > 0, and yet it begins to increase once pg is below 1 and/or pt exceeds 1. Not surprisingly, the pattern revealed in Fig. 3d is highly correlated with that in Fig. 3b. Note that SO can be achieved only when the credits initially supplied by the government exactly balances the demands. On the one hand, when pg < 1, the government effectively under-prices credits, and hence has to inject extra credits into the system to keep up with the elevated demand. On the other hand, when credits become too expensive thanks to high transaction costs, some users will shift to routes that charge less credits, and as a result, not all the initially issued credits will be consumed. In both cases, the deviation from SO is directly associated with imbalance between the supply of and demand for credits.

Fig. 2. The revised Braess network.

Table 1 UE and SO solutions for the Braess network. UE solution

SO solution

Path

Flow

Time

Toll

Flow

Time

Toll

1 2 3 4

0 3.7143 2.2857 0

68.5714 62.2857 62.2857 80

0 0 0 0

1.7917 0.75 3.4583 0

64.5 44.5 54.5 80

14.5 34.5 24.5 0

Total

6

373.7143

0

6

337.4167

136.5833

Note: Tolls given in the last column are first-best marginal tolls. The last row reports the total travel time and tolls of all users.

199

Y. Nie / Transportation Research Part B 46 (2012) 189–203 * Travel time increase (T − T )

Market clearance price (p) 2

2

120

0.9 1.8

1.8 0.8

1.6 1.4

1.4 1.2 0.5

1

pg

g

p

80

0.6

1.2

0.4

0.8 0.6

0.3

0.4

0.2

0.2

0.1

0

100

1.6 0.7

0.5

1

1.5

60

0.8 40

0.6 0.4

20

0.2

0 0

1

0

2

0

0.5

p

t

pt

(a)

(b)

Credits traded through market (Π m )

1.5

2

0

Extra credits (Π c − Π)

2

2 120

1.8 1.6

1.8

20

1.6

100

1.4

0

1.4 −20

80

1

60

0.8 40

0.6 0.4

20 0.2

1.2

pg

1.2

pg

1

−40

1 0.8

−60

0.6

−80

0.4

−100

0.2 −120

0

0 0

0.5

1

p

1.5

2

0

0

0.5

1

t

pt

(c)

(d)

1.5

2

Fig. 3. Behavior of the auction market under different combinations of pt and pg.

Figs. 3c and 4c confirm that the market becomes inactive when pt > pg (Proposition 1). Also, all initially issued credits are consumed and sold through the auction market when pt < pg and pt < 1. As discussed before, this is true even when the market and the government prices are identical; that is, when pt < pg < 1 ? p = pg  pt (cf. Proposition 2). Finally, the units of credits purchased from the market decrease linearly as pt increases beyond 1, indicating that the price of credits is too high to be consumed at the optimal level. We note that this linear relationship is likely due to the linear form of the link performance functions.

5.2. Negotiated market The 1681 different combinations of pg and pt are now used as inputs in the negotiated market model. Fig. 5 plots the contour diagrams of the four evaluation indexes in all 1681 cases, and Fig. 6 plots four cross-sections at different values of pt. Fig. 6a and b show that, when pt = 0, the market price p = min(1, pg) and the system deviates from SO when pg < 1. This verifies the results of Proposition 3. Note that the cross-section lines associated with pt = 0 in Fig. 6a, b and d is very similar to their counterparts in Fig. 4a, b, and d, respectively. Therefore, when transaction costs are negligible the auction and negotiated markets seem to behave similarly. The noticeable differences have to do with the credits traded through the market (cf. Fig. 6c): first, the amount of the total traded credits is much smaller in a negotiated market; second, a negotiated market can become inactive when pg is sufficiently small (<0.3 in this example). Both are resulted from the initial distribution of credits in a negotiated market. When pt > 0, the changes of the credit price in a negotiated market demonstrate a pattern very different from that in an auction market. When pt = 0.5 (cf. Fig. 6a), the credit price is first kept at 0.5 until pg reaches 1. Then it gradually increases to a

200

Y. Nie / Transportation Research Part B 46 (2012) 189–203 140 p =0

1.2

Travel time increase (T − T * )

Market clearance price (p)

1.4

t

p = 0.5 t

1

pt = 1.5 p =2 t

0.8 0.6 0.4 0.2

120 pt = 0 p = 0.5

100

t

pt = 1.5

80

pt = 2

60 40 20 0 −20

0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

2

0.2

0.4

0.6

0.8

1

pg

(a)

(b)

g

2

1.8

1.6

60 40

120

Extra credits (Π c − Π )

Credits traded through market ( Π m )

140

1.4

1.2

p

100 p =0 t

p = 0.5

80

t

p = 1.5 t

60

p =2 t

40

20 0 −20

pt = 0

−40

pt = 0.5 p = 1.5 t

−60

p =2 t

−80 −100

20 −120 0 0

0.2

0.4

0.6

0.8

1

p

1.2

1.4

1.6

1.8

2

−140 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

pg

g

(c)

(d) Fig. 4. Four cross-sections of contour plots in Fig. 3.

higher level (still less than 1) and remains at that level after pg reaches roughly 1.3. This pattern applies to all pt < 1, although the details vary with pt. For example, the highest credit price appears to first decrease with pt and then increase after pt roughly exceeds 0.8. When pt > 1 and/or pt > pg, the market price always equals pt, regardless of the government price. At the first glimpse, this may appear counter-intuitive because no trading takes place in these cases according to Figs. 5c and 6c. Note that when the market is inactive (i.e., all g rs k ¼ 0), Constraint (37) is actually binding, leading to non-zero multipliers that are interpreted as the credit price. This non-zero price turns out to be the unit transaction cost that prohibits the trading in the market in the first place. This suggests that the credit price in the negotiated market model already includes the unit transaction cost, whereas in the auction market model, the transaction cost are paid for separately from the credit price. Fig. 5b and Fig. 6b reveal that a negotiated market may not be able to achieve SO in the presence of transaction costs. More importantly, this inability seems to be an inherent property independent of the government price and the magnitude of transaction costs. When pt = 0.5, for example, the system travel time reaches its lowest level and remains unchanged once pg approximately exceeds 1.3. It is clear from Fig. 6b that there is a noticeable discrepancy between this lowest system travel time and the travel time at SO. A close look at the results indicate that such discrepancies exist for any pt > 0, although they may be rather small when pt is close to zero.10 As expected, the credit price affects the trading of credits in a negotiated market. For pt = 0.5, the increase of the credit price from 0.5 to its maximum value is evidently synchronized with the increase in trading from zero to its maximum (cf. Figs. 6a and c). Correspondingly, the extra credits issued by the government decrease from about 20 to 0. Clearly, as pg increases, the demand for the credits in the marketplace increases, and so does the price. In fact, any pg < 1.3 seems to under-price the credit, and consequently, encourage its excessive consumption. Although the government can eliminate 10 Indeed, the values of T  T⁄ within the seemingly white region in Fig. 5b are actually not zero. They simply cannot be visualized in the contour plots because they are too close to zero.

201

Y. Nie / Transportation Research Part B 46 (2012) 189–203 *

Market clearance price (p)

Travel time increase (T − T )

2

2 1.8

1.8

1.8

30

1.6 1.6

1.6 1.4

1.4

1

1.2 g

1

p

g

1.2

p

25

1.4 1.2

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0 0

0.5

1

1.5

2

20

1 15

0.8

10

5

0

0

0 0

0.5

1

pt

p

(a)

(b)

1.5

2

t

Credits traded through market (Πm ) 2

Extra credits (Πc− Π)

2

14

1.8

45

1.8

40

1.6

35

1.4

30

1.2

25

1

20

0.8

15

0.6

10

0.4

5

12 1.6 10

1.4

8

pg

pg

1.2 1

6

0.8 0.6

4

0.4 2 0.2

0

0.2

0

0 0

0.5

1

1.5

2

−5

0 0

0.5

1

pt

p

(c)

(d)

1.5

2

t

Fig. 5. Behavior of the negotiated market under different combinations of pt and pg.

the excessive demand for credits by raising the price, it cannot achieve SO this way. Fig. 6d shows that the supply of the credits perfectly balances the demand for pt = 0.5 and pg > 1.3, and yet the system is still not at SO. We close this section by noting that most solution patterns observed above are likely to be problem specific and hence their details are of limited general interests. These results, however, do consistently demonstrate that transaction costs may significantly impact the credit price and prevent a negotiated market from achieving maximum efficiency. Also, unlike in an auction market, these impacts are more complicated and cannot be easily mitigated, even when transaction costs are low.

6. Conclusion The success of tradable-permit systems for environment protection has stimulated interests in using the similar schemes to manage road transport externality. This paper demonstrates that transaction costs, if not negligible, have important consequences on the analysis of markets for mobility credits. Above all, the consideration of transaction costs makes the outcomes of the system depend on the market arrangement, particularly the initial allocation of mobility credits. If everyone has to acquire all needed credits from an auction market, we show that the system is relatively robust in that it will not deviate from the desired equilibrium, provided that the unit transaction cost is lower than the price that the market would reach in absence of transaction costs. In a negotiated market, in which users have to trade their initially endowed mobility credits with each other, transaction costs could divert the system from the desired equilibrium regardless of its magnitude. This result agrees with the finding of Stavins (1995) except for one point. Stavins (1995) showed that when the marginal

202

Y. Nie / Transportation Research Part B 46 (2012) 189–203 40

2.5

p =0

pt = 0

Travel time increase (T − T*)

Market clearance price (p)

2

t

35

pt = 0.5 pt = 1.5 pt = 2

1.5

1

0.5

p = 0.5 t

p = 1.5

30

t

pt = 2

25 20 15 10 5 0

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

−5 0

2

0.2

0.4

0.6

0.8

pg

1

(a)

1.4

1.8

1.6

2

(b) 50

15

pt = 0

pt = 0

p = 1.5 t

p = 1.5 t

10

pt = 0.5

40

pt = 0.5

Extra credits ( Πc −Π)

Credits traded through market (Πm )

1.2

pg

pt = 2

5

pt = 2

30

20

10

0

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

−10 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

p

p

g

g

(c)

(d) Fig. 6. Four cross-sections of contour plots in Fig. 5.

transaction cost are constant (i.e., transaction costs are an affine function of the volume of trading), the final equilibrium is independent of initial allocation of permits. Our analysis suggests that the initial allocation of credits in a negotiated mobility credit market may affect the final equilibrium even when marginal transaction costs are constant. An interesting direction for future research is to find an initial allocation scheme such that the deviation from the desirable equilibrium is minimized. Another possibility is to examine how the functional form of the transaction cost would affect the analyses. Interesting scenarios may include but are not limited to: the case where only the sellers need to pay for the commission fee, or the transaction function with a constant independent of trade value; non-linear transaction function such as discussed in Stavins (1995). The analogy between markets for mobility credits and for emission permits may lead to the impression that these markets would be similarly effective. However, we caution that important differences exist between these markets and the benefits they promise. A company can determine on its own what to do and how much it would cost if certain emissions have to be reduced by a given amount. Had the government had that information, it is possible to formulate an emission pricing scheme that minimizes the total control cost for an overall emission reduction target. However, collecting this information is difficult and expensive (Stavins, 1995). A market for emission permits can help the government avoid this great hurdle. With such a market, the government only needs to set the emission target and to issue permits accordingly. The companies can determine, based on control technologies available and other operational constraints, how much permits they need to acquire in order to minimize their own cost. Ideally, the price of permits will be such determined that every company that carry out positive levels of control has the same marginal control cost, which ensures that the system control cost is minimized. It is clear the road transport system works very differently, because a road user would not know what it takes to reduce their average travel time to certain level - in fact, under the user equilibrium assumption, no traveler could reduce their own travel time unilaterally. Therefore, to achieve the control target (congestion reduction), the behavior of the travelers have to be deliberately coordinated by the government, with or without a market for mobility credits. As explained before, the government has to specify the credit charge link by link in order to ‘‘guide’’ the users. While such an effort

Y. Nie / Transportation Research Part B 46 (2012) 189–203

203

may be facilitated using a trial-and-error scheme such as suggested in Yang et al. (2004), it remains to be a time- and laborintensive process. Suffice it to say here that the information that the government would need to run a mobility credit market is as much as the information required to operate a conventional pricing scheme. Therefore, the mobility credit market does not reduce the administrative burden of the government, unlike in the case of emission control. Finally, as Coase (1960) argued, the market may not solve the pollution problem if the cost of a rearrangement of rights (i.e. the transaction cost) is greater than the increased value of production conditional on the rearrangement. In this case, direct regulation may produce better results because the government has the power to rearrange rights at a lower cost. Likewise, whether direct regulation (i.e. pricing) or a market for permits is a better option for managing road transport externality depends on transaction costs. Despite the many amenities that the market-based solution has to offer, more research is still needed to compare the benefits and costs involved in operating the markets and running a pricing scheme. Acknowledgements I am grateful to Professor Hai Yang at Hong Kong University of Science and Technology and Professor David Boyce at Northwestern University for comments on an earlier version of this paper. Valuable comments from two anonymous referees are greatly appreciated. I accept full responsibility for all the remaining errors and shortcomings. References Arnott, R., de Palma, A., Lindsey, R., 1994. The welfare effects of congestion tolls with heterogeneous commuters. Journal of Transport Economics and Policy 28 (2), 139–161. Beckmann, M., McGuire, C.B., Winsten, C.B., 1956. Studies in the Economics of Transportation. 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