E-commerce and traffic congestion: An economic and policy analysis

Transportation Research Part B 83 (2016) 91–103

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

E-commerce and traffic congestion: An economic and policy analysis Jing Shao, Hangjun Yang∗, Xiaoqiang Xing, Liu Yang University of International Business and Economics, Beijing, China

a r t i c l e

i n f o

Article history: Received 10 August 2014 Revised 31 October 2015 Accepted 2 November 2015 Available online 11 December 2015 Keywords: E-commerce Traffic congestion Distribution strategy Social welfare Public policy

a b s t r a c t E-commerce, due to its ability to re-direct consumers from physical stores to online, can potentially alleviate traffic congestion. In this paper, we set up a theoretic model to analyze interactions between a firm’s distribution strategy and traffic congestion. In an unregulated economy, we first characterize the private firm’s optimal strategy concerning e-commerce under the influence of traffic congestion. We then examine a centralized economy where the firm is publicly owned and derive the distribution strategy that maximizes social welfare. Comparing the two cases, we show that the private firm’s incentives may deviate from the socially optimal decisions, which leads to inefficiency. We identify two effects, i.e., monopoly effect and congestion externality effect, which drive the private firm to deviate from the social optimum. Based on our analysis, we propose a differentiated tolls/rebates policy to achieve maximum social welfare. Under such a policy, the firm will not only adopt the socially optimal distribution strategy but offer the socially optimal quantities. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction In order to resolve the traffic congestion conundrum, regulators resort to various approaches to reduce demand for road capacities. Demand management mechanisms such as congestion pricing have been extensively studied and highly advocated in the literature (Lindsey and Verhoef, 2001; de Palma and Lindsey, 2011; Pigou, 1912; Vickrey, 1963). However, it is noteworthy that alternative demand management approaches such as promotion of telecommuting and public transport can also be effective in alleviating traffic congestion, because they can potentially shift the entire traffic demand curve inwards (Verhoef et al., 1996b). E-commerce, due to its ability to re-direct consumers from physical stores to online, can be a potential alternative demand management mechanism that alleviates traffic congestion. Since consumers who purchase online do not need to drive to physical stores, online shopping incurs less traffic than shopping at the traditional channel. Although delivery to online customers also incurs road usage, it typically takes less road capacities due to economy of scale in delivery. A case study using simulation based on empirical data in Finland indicates that replacement of traditional retailing by electronic retailing can potentially lead to 54–93% reduction in traffic depending on delivery methods (Punakivi, 2003; Siikavirta et al., 2003). Therefore, from a social point of view, e-commerce should be broadly adopted to reduce traffic congestion. However, when private firms choose between e-commerce and traditional distribution, their objectives are to maximize their own profits. As a result, conflicts may arise between private firms’ incentives for distribution strategies and social objectives. In particular, in order to maximize social welfare, a social planner considers both the welfare in the product market and congestion costs of all road ∗

Corresponding author. Tel.: +86 10 6449 3638 . E-mail address: [email protected] (H. Yang).

http://dx.doi.org/10.1016/j.trb.2015.11.003 0191-2615/© 2015 Elsevier Ltd. All rights reserved.

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users. However, although a private firm also considers influence of traffic congestion on its demand and profit, the firm ignores the congestion externality incurred by its decisions. Hence, a private firm’s marginal benefit and cost of adopting e-commerce generally differ from the marginal social benefit and cost. In order to achieve higher social welfare, a social planner should understand private firms’ incentives for e-commerce and address the following questions: First, what distribution strategy leads to maximum social welfare? Second, under a specific distribution strategy, what is the socially optimal quantity to be offered to consumers? Third, how would a private firm deviate from the socially optimal decisions? Finally, what policies should be used to induce a firm to choose the socially optimal decisions? To analyze these issues, we set up a theoretic model where a monopolist firm produces and sells a single product to consumers. Consumers who drive to the physical store to purchase the product suffer a delay cost due to traffic congestion; whereas consumers who purchase online can avoid this cost. However, consumers have lower valuation for the firm’s product sold online than that at a physical store due to lack of service, delayed satisfaction, and difficulty to return at the online store. The firm may choose from three distribution strategies: (1) a traditional strategy where it distributes products through a physical store, (2) an electronic strategy where it distributes through an online store, and (3) a mixed strategy where it distributes through both stores. Under this model, we first consider an unregulated economy where the private firm makes decisions to maximize its own profit. We characterize the firm’s optimal distribution strategy, taking into account influence of traffic congestion on consumer demands for the product. We show that the firm’s optimal distribution strategy depends on consumers’ acceptance of e-commerce as well as road users’ congestion costs. We then examine a centralized economy where the firm is publicly owned; and the social planner makes decisions to maximize social welfare. We derive the socially optimal distribution strategy and quantities. Comparing the unregulated and centralized cases, we show that the private firm’s incentives may deviate from the socially optimal decisions. We identify two effects that drive the firm’s quantity decisions to deviate from the socially optimal ones in opposite directions. In particular, the monopoly effect causes the firm to choose a too low quantity compared with the social optimum, while the congestion externality effect leads to a too large quantity under the unregulated equilibrium. The net effect determines the direction of the private firm’s incentive distortion. Finally, we propose a differentiated tolls/rebates policy to achieve maximum social welfare. When the congestion externality effect outweighs the monopoly effect, the social planner should charge a congestion toll to fix the too large quantity. On the other hand, when the monopoly effect outweighs the congestion externality effect, the social planner should offer a rebate to increase the quantity to reach the socially optimal level. We show that the differentiated tolls/rebates policy will not only induce the firm to choose the socially optimal quantities, but ensure the firm to adopt the socially optimal distribution strategy. We highlight the main contributions of our paper as follows: •

•

•

We construct a theoretic model to investigate interactions between a firm’s distribution strategy concerning e-commerce and traffic congestion. We show that the private firm’s incentive may deviate from the social objective and identify the underlying effects that cause the private firm’s incentive distortion. To achieve maximum social welfare, we propose a differentiated tolls/rebates policy that is able to induce the firm to adopt the socially optimal distribution strategy and quantities.

The rest of the paper is organized as follows: We first review the related literature in Section 2. We then set up the model in Section 3. In Section 4, we examine the firm’s optimal distribution strategy in an unregulated economy. In Section 5, we derive the socially optimal distribution strategy and quantities. In Section 6.2, we discuss the private firm’s incentive distortions and propose public policies that elicit the social optimum. Finally, in Section 7 we conclude the paper and suggest future research directions. 2. Related literature While a few papers examine the effects of e-commerce on traffic congestion and environment through case studies (Edwards et al., 2010; Matthews et al., 2001; Punakivi, 2003; Weber et al., 2009), we use an analytical approach to investigate interactions between firms’ distribution strategy involving e-commerce and traffic congestion. Employing analytical approaches, a good number of works in the Transportation literature investigate traffic congestion and its solutions. Congestion pricing, in particular, has been intensively studied due to its effectiveness in managing traffic congestion and achieving social optimum (Brueckner, 2002, 2009; Lindsey and Verhoef, 2001; de Palma and Lindsey, 2011; Pigou, 1912; Vickrey, 1963; Walters, 1961; Zhang and Czerny, 2012). Researchers examine various factors that may influence optimal congestion pricing policies such as time of day, road link, usage of road, information provision, demand uncertainty, and user characteristics (Chung et al., 2012; Daganzo and Lehe, 2015; Lou et al., 2010; Verhoef et al., 1996a; Wie and Tobin, 1998; Yang and Huang, 2004; Zhang and Yang, 2004). However, the above papers do not investigate the impact of firms’ distribution strategies on traffic congestion and welfare. On the other hand, a rich literature in Marketing, Economics, and Operations uses analytical models to study a firm’s optimal distribution decisions (Bernstein et al., 2009; Chiang et al., 2003; Dumrongsiri et al., 2008; Tsay and Agrawal, 2004; Yoo and Lee, 2011). However, this literature does not consider the influence of traffic congestion on firms’ decisions. What is more, our work is also related to research on telecommuting, which is another alternative demand management approach. Using empirical or case studies, several papers investigate factors that affect employees’ choice and frequency of

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telecommuting as well as telecommuting’s impact on traffic and emissions (Mokhtarian and Salomon, 1997; Nurul Habib et al., 2012; Singh et al., 2013; Wells et al., 2001; Wilton et al., 2011). Walls and Safirova (2004) provide a survey of this literature. Setting up an economic model and using numerical approaches, Safirova (2002) shows how telecommuting affects city population and social welfare. There are two major differences between Safirova (2002)’s model and ours. First, in Safirova (2002), firms’ adoption of telecommuting changes the structure of labor supply; but it does not affect consumer demand. In contrast, in our model, congestion reduction due to e-commerce changes consumer demands at different channels, which consequently impacts the firm’s decision and social welfare. Moreover, in Safirova (2002), whether employees telecommute is determined by firms rather than employees themselves. However, in our model, consumers make their personal choices of distribution channels, resulting in a game between the firm and consumers. Finally, our model is broadly related to papers that consider competing, congested facilities or routes. Van Dender (2005) considers two firms that offer a perfect substitute; consumers may choose either firm’s product and will take different routes to the outlet of the selected firm. Under a similar setting, De Borger and Van Dender (2006) derive the socially optimal capacity of a road connecting two outlets. In contrast, we consider two vertically differentiated channels rather than perfect substitutes. More important, we focus on interactions between consumers’ channel choice under the influence of traffic congestion and a firm’s optimal strategy, while the above two papers focus on firms’ optimal decisions for given demand functions. Verhoef et al. (1996a) consider a scenario where road users can choose between a tolled route and an untolled one, which resembles our dualchannel setting. However, they abstract away road users’ purposes for travelling and take road users’ utility as given. In contrast, we explicitly model consumers’ purchasing choice and utility and derive public policies that achieve maximum social welfare in both the product market and transportation sector. 3. Model setup Consider a city where a representative firm sells a product to consumers. The firm chooses from three potential distribution strategies: (1) a traditional strategy under which the firm sells exclusively through a physical store (also referred to as “the traditional channel” hereafter), (2) an electronic strategy under which it sells exclusively through an online store (also referred to as “the electronic channel” hereafter), and (3) a mixed strategy under which it sells through both the physical and online stores. We refer to the three strategies as “T”, “E”, and “M”, respectively. Denote by pXt the retail price that the firm sets at the traditional channel under strategy X, and pXe the retail price at the electronic channel, where X = T, E, M,if applicable. Moreover, denote by DtX (DXe ) the demand at the traditional (electronic) channel under strategy X. And denote by ct (ce ) the variable cost at the traditional (electronic) channel. Assume that ct > ce , which reflects the fact that the traditional channel incurs a higher variable cost than the electronic channel since the traditional channel provides extra services and sales support for customers. In order to purchase the firm’s product at the physical store (if the firm opens one), consumers have to drive through a transport network with capacity K.1 Assume that each consumer purchases at most one unit of the product; and we normalize the total number of consumers in the city to one. If a consumer drives to the physical store, he/she will suffer a delay cost C(Q, K) due to traffic congestion, where Q is the total number of road users. For analytical tractability, we adopt the linear delay function C (Q, K ) = Kθ · Q(θ ≥ 0) that has been used in several theoretical papers such as De Borger and Van Dender (2006), Basso and Zhang (2007), and Yang and Zhang (2011, 2012). For convenience, let β ≡ θ /K ≥ 0, which represents consumers’ congestion cost “sensitivity” to the total number of road users. We denote by V a consumer’s valuation for the product sold at the traditional channel, which has a uniform distribution on [0, 1]. Let vbe the valuation for the product at the traditional channel of a particular consumer. A consumer’s valuation for the product sold at the electronic channel is aV, where 0 < a < 1. This reflects consumers’ lower willingness-to-pay for goods sold online due to lack of service, delayed satisfaction, and difficulty to return at the online store than at a physical store.2 Assume that consumers who purchase online place orders at home and receive delivery from the firm. The firm delivers the product to online consumers from a warehouse close to the physical store. So the delivery vehicles use the same transport network as the traditional consumers. Assume that the capacity of the delivery vehicles is fixed, and the firm dispatches one delivery vehicle for every m online customers. In other words, each unit of product delivered occupies 1/m units of a delivery vehicle. Let h ≡ 1/m; then 0 < h ≤ 1 represents the road capacity that each unit of product takes in transportation. In addition to consumers who drive to the physical store and delivery vehicles that deliver to online consumers, there are also “other road users” whose purposes are not purchasing or delivering the firm’s product, e.g., people who commute to work, drive kids to school, run errands, etc. Denote by n the total number of other road users. In order to focus on congestion incurred by the product market, we assume that n is independent of the total number of road users and possible congestion tolls. One interpretation is that these other road users’ demand for the road is extremely inelastic. For simplicity, assume that the congestion cost

1 Assume that all consumers drive private vehicles to the store. We may also assume that a fraction of consumers take public transit, which does not provide additional insight to our research problem while complicating our analysis. 2 Our consumer choice model is based on the Mussa–Rosen model for vertically differentiated products (Mussa and Rosen, 1978). Due to its simplicity and ability to capture heterogeneous consumers as well as differentiated consumer valuation across channels, the Mussa–Rosen model is widely adopted in theoretical studies on dual-channel issues (Chiang et al., 2003; Feng et al., 2009; Khouja et al., 2010; Mantin et al., 2014; Shao et al., 2015). The Mussa–Rosen model has limitations such as uniform distribution of consumer valuation. However, the uniform distribution of consumer valuation leads to linear demand functions, which guarantees tractability of our problem and leads to closed-form solutions for our further analysis.

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sensitivities of delivery vehicles and other road users are also β .3 We assume that 1 − ct − β n > 0and a − ce − β hn > 0to avoid the trivial outcome that one of the strategies is never optimal. Suppose that a social planner wishes to maximize social welfare, which consists of both the firm profit and consumer surplus, using public policies. We propose a differentiated tolls/rebates policy to induce the firm to choose the socially optimal decisions. The sequence of events is as follows: Stage 1: Stage 2: Stage 3: Stage 4:

The social planner determines and announces the differentiated tolls/rebates policy. The firm chooses a distribution strategy. The firm sets the corresponding prices under the selected strategy. Consumers make purchasing decisions.

4. Firm’s distribution strategy under no regulation In order to understand the firm’s incentive in choosing distribution strategies, we first consider an unregulated economy where the social planner does not apply any public policy. We derive the firm’s optimal distribution strategy by backward induction. Specifically, we first derive the firm’s optimal prices and profits under each strategy. We then compare the firm’s profit under the three strategies and determine the firm’s optimal distribution strategy. 4.1. Firm’s pricing decisions under each strategy Suppose that the firm adopts strategy T; then the firm sells exclusively through a physical store. A consumer may choose to purchase the product at the store or not to purchase. If a consumer with valuation vpurchases the product, then the consumer obtains utility vsubtracted by the retail price at the physical store pTt and the congestion cost β(DtT + n),where DtT + nis the total number of users of the transport network under strategy T. If this net utility is greater than 0, then the consumer will purchase the product. In other words, the marginal consumer’s valuation, denoted by vT ,equals pTt + β(DtT + n). Therefore, the set of consumers who purchase the product is DtT = Prob{V > vT }. Since Vhas a uniform distribution, we have that DtT = 1 − pTt − β(DtT + n). Solving this equation, we obtain the demand function at the traditional channel under strategy T, which is DtT = (1 − pTt − β n)/(1 + β). With the above demand function, the firm chooses the retail price at the traditional channel to maximize its profit π T = ( pTt − ct )DtT . We can solve the first order condition of π T with respect to pTt and obtain the firm’s optimal price. We present T†

T†

the firm’s optimal price pt and demand Dt under strategy T in Appendix A. (The superscript “†” represents the firm’s optimal decisions under no regulation.) It is easy to see that as the cost ct increases, the firm’s profit under strategy T decreases. Note that the firm’s profit also decreases in β and n. This is because as β increases, traditional consumers become more sensitive to congestion; as a result, the firm will obtain less demand. Similarly, as n increases, the road becomes more congested, which also leads to a reduction in demand at the traditional channel. Under strategy E, the firm sells exclusively through an online store. A consumer either purchases at the online store or does not purchase the firm’s product. The marginal consumer who is indifferent between purchasing online and not purchasing satisfies av − pEe = 0. We obtain the marginal consumer’s valuation v = pEe /a. The demand function under strategy E is therefore DEe = 1 − pEe /a. The firm chooses the price at the electronic channel to maximize its profit, π E = ( pEe − ce )DEe − β(hDEe + n)hDEe ,where β(hDEe + n)is the congestion cost of each delivery vehicle and hDEe is the total number of delivery vehicles. We can solve for the firm’s optimal price and demand under strategy E, which are given in Appendix A. Note that the firm’s profit under strategy E is increasing in a. This is because parameter a indicates consumers’ acceptance of the electronic channel; as a increases, the firm can earn more profits from the electronic channel. On the other hand, the firm’s profit under strategy E monotonically decreases in both β and h. This is because as β increases, the firm incurs a higher congestion cost when delivering products to online consumers. Furthermore, the number of delivery vehicles dispatched depends on the economy of scale in delivery, which is reflected by parameter h. As h increases, the firm dispatches more vehicles for the same number of online consumers. For example, computers occupy more space than books during delivery; so h is higher for computers than for books. Therefore, everything else being equal, as h increases, online sales will incur more congestion cost to the firm, which results in a lower firm profit. If the firm adopts strategy M, then it sells the product through both the physical and online stores. Each consumer will purchase the product at the channel where he/she obtains a higher, non-negative utility. The marginal consumer who is indifferent M M M between purchasing at the physical store and online satisfies v − pM t − β(Dt + hDe + n) = av − pe . Solve the equation and get M M M M M v = [pt − pe + β(Dt + hDe + n)]/(1 − a) ≡ v1 . The demand at the traditional channel is therefore:

DtM = 1 − vM 1 .

(1)

Furthermore, the marginal consumer who is indifferent between purchasing online and not purchasing the product satisfies M M av − pM e = 0,which yields v = pe /a ≡ v2 . The demand at the electronic channel is hence those consumers whose valuations for 3 We relax this assumption and consider a case where the firm and individuals have different congestion cost sensitivities in Appendix C. We show that the main results still hold under the extended model.

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the online store are lower than their valuations for the physical store and yet greater than zero. That is, M M M M M DM e = Prob{aV − pe < V − pt − β(Dt + hDe + n), aV − pe > 0} M M M = Prob{vM 2 < V < v1 } = v1 − v2 .

(2)

We solve Eqs. (1) and (2) simultaneously and obtain the demand functions at the traditional and electronic channels under strategy M as follows:

DtM =

M a(1 − a − β h − β n) − apM t + (a + β h) pe , a[1 − a + β(1 − h)]

(3)

DM e =

M aβ(1 + n) − (1 + β) pM e + apt . a[1 − a + β(1 − h)]

(4)

M M M Under strategy M, the firm maximizes its total profit from the two channels, that is, π M = ( pM t − ct )Dt + ( pe − ce )De − M . We solve the firm’s first order conditions with respect to pM and pM simultaneously and obtain the firm’s β(DtM + hDM + n ) hD e e e t

optimal prices and demands (given in Appendix A). When the firm uses a mixed distribution strategy, it price-discriminates among consumers who have heterogenous valuations for the product. In particular, the firm sells to high-valuation consumers at a higher price through the physical store and to low-valuation consumers at a lower price through the online store. M† M† Note that the optimal solution under strategy M must satisfy the non-negative demand constraints, i.e., Dt ≥ 0and De ≥ 0,which leads to aM ≤ a ≤ a¯ M (a¯ M and a M are given in Appendix A). When aM ≤ a ≤ a¯ M ,we can show that the second order condition of the maximization problem under strategy M is also satisfied, which guarantees the internal solution. If a > a¯ M ,then M† M† E† we hit a corner solution where Dt = 0and De = De ,which implies that strategy M collapses to strategy E. This is because for a > a¯ M ,the relative profitability of the electronic channel is high compared with the traditional channel. Therefore, the firm has an incentive to sell only through the electronic channel. On the other hand, for a < a M , the relative profitability of the electronic channel is low. So the firm will sell only through the traditional channel; and strategy M collapses to strategy T. 4.2. Firm’s optimal strategy We now compare the firm’s profit under the three strategies, T, E, and M, and determine the optimal strategy that maximizes the firm’s profit under no regulation. We find that strategy M always dominates strategies T and E in the region where strategy M is feasible. The reason is that strategy M is feasible in a region where a is moderate, which implies that the relative profitability of the traditional and electronic channels is rather balanced. Therefore, the firm can make more profits by selling through both channels than through a single channel. Furthermore, recall that in the regions where a is sufficiently low or high, strategy M will reduce to strategy T or E. For sufficiently low a, i.e., consumers’ acceptance of e-commerce is low, it is most profitable for the firm to sell only through the traditional channel. On the other hand, when a is sufficiently high, the firm will sell only through the electronic channel. We summarize the firm’s optimal strategy in the following proposition. Proposition 1. The firm’s optimal strategy is T for 0 < a < a M , M for aM ≤ a ≤ a¯ M ,and E for a¯ M < a < 1. (See all the proofs in Appendix B.) Fig. 1 illustrates the firm’s profit under the three strategies. The left graph in Fig. 1 shows that as consumers’ acceptance for e-commerce, a, increases, it is optimal for the firm to switch from strategy T to M, and then to E. On the other hand, in the right graph in Fig. 1, as β increases, demand at the traditional channel reduces while the firm’s congestion cost at the electronic channel increases. Therefore, the firm’s profits under strategies T, M, and E all decrease in β . (In this particular case in Fig. 1, M dominates T for all β since the value of a is sufficiently large.) Furthermore, when β is sufficiently large, traditional demand becomes so low due to traffic congestion that it is optimal not to sell at the traditional channel; the firm adopts strategy E as a result. When using our result in Proposition 1 to determine its optimal strategy, the firm needs to know the parameter values. Empirical work in Transportation, Economics, and Marketing provides some estimates for these parameters. To estimate consumers’ acceptance of online goods, a, Liang and Huang (1998) conduct a survey in Taiwan on consumers’ likelihood of buying goods from online stores. In a scale of 7, the estimated consumer acceptance of e-commerce is 3.797 for five categories of products (in terms of our model, a is about 0.54). Kacen et al. (2013) set up a multi-attribute attitude model; using survey data with 224 Midwestern US adults, they report that the average value of a in five product categories is 0.83. Furthermore, recall that in Section 3 we define h ≡ 1/m, where m is the number of products loaded in each delivery vehicle. We can estimate m based on the average volume or weight of each Business Stock-keeping Unit (SKU) of the product and capacity of the delivery vehicles. In addition, cost parameters ct and ce can be estimated from the overheads of physical and online stores. The other two parameters, β , and n, are associated with traffic congestion. Based on a survey at major US metropolitan areas, Calfee and Winston (1998) report that the average willingness-to-pay of commuters is $3.88 per hour. In a recent study, Fezzi et al. (2014) use survey data from Italy to report that the estimated value of travel time is about € 8.6 per hour. We can use these data as estimations of β . Finally, estimation of traffic volume is based on technology such as loop detectors and video monitoring systems (Beymer et al., 1997). Algorithms are designed to extract traffic information from detectors and videos

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Fig. 1. Firm’s profit under the three strategies.

(Kwon et al., 2003; Porikli and Li, 2004). We can then obtain an estimation of n by subtracting the total traffic volume by the numbers of traditional consumers and delivery vehicles acquired from the firm’s sales data.

5. Social optimum Under no regulation, the firm’s decisions may not lead to social optimum. In this section, we consider a centralized economy where the firm is publicly owned; the social planner chooses the distribution strategy and quantities to maximize social welfare. We first derive the optimal quantities under each distribution strategy. Under each strategy, the total social benefit comes from consumers’ utility of consumption of the product. If the firm adopts strategy T, suppose that there are DtT consumers who purchase the firm’s product at the traditional channel. Since the consumers’ valuations are uniformly distributed, the utilities of the “first” and “last” consumers who purchase the product are 1 and 1 − DtT ,respectively. We aggregate all consumers’ surplus and obtain the total social benefit, which equals T SBT = (2 − DtT )DtT /2. The total social cost is composed of the firm’s operating cost at the traditional channel, and the congestion costs of both traditional consumers and other road users. That is, T SC T = ct DtT + β(DtT + n)2 . We can then calculate the marginal social benefit MSBT = ∂ T SBT /∂ DtT = 1 − DtT ,and marginal social cost MSC T = ∂ T SC T /∂ DtT = ct + 2β(DtT + n). The social optimum is at the intersection of the marginal social benefit and cost curves; that is, MSBT = MSC T . Solve and obtain DtT ∗ = (1 − ct − 2β n)/(1 + 2β),which is the socially optimal quantity. (The superscript “∗” represents the social optimum.) Therefore, the quantity DtT ∗ maximizes the net social benefit from the product market less the total social congestion cost. Next, suppose that the firm adopts strategy E; and there are DEe consumers who purchase the firm’s product at the electronic channel. The firm will dispatch hDEe vehicles to deliver products to the online consumers. The total social benefit equals T SBT = (a + a(1 − DEe ))DEe /2. The total social cost consists of the firm’s operating cost at the electronic channel, and congestion costs of both the firm and other road users, i.e., T SC E = ce DEe + β(hDEe + n)2 . We then obtain the marginal social benefit MSBE = a(1 − DEe ),and marginal social cost MSC T = ce + 2β h(hDEe + n). Let MSBT = MSC T and solve for the socially optimal quan2 tity under strategy E, which equals DE∗ e = (a − ce − 2β hn)/(a + 2β h ). Finally, under strategy M, the total social benefit consists of consumers’ utility from both channels, which equals T SBM = M M M M M M 2 (2 − DtM )DtM /2 + (a + a(1 − DM e ))De /2. The total social cost equals T SC = ct Dt + ce De + β(Dt + hDe + n) . The social welfare M M M under strategy M is thus SW = T SB − T SC . Since the firm sells through both channels under strategy M, the social planner should determine the socially optimal quantities at both the traditional and electronic channels. We calculate the first derivatives M∗ M∗ of SWM with respect to DtM and DM e . Solving the two first order conditions simultaneously, we obtain Dt and De ,which are given M∗ M∗ in Appendix A. Furthermore, the two non-negative demand constraints lead to condition, a ≤ a ≤ a¯ ,for strategy M to be feasible (a¯ M∗ and a M∗ are given in Appendix A). We next compare social welfare under the three distribution strategies and obtain the socially optimal strategy: Proposition 2. The socially optimal strategy is T for 0 < a < a M∗ , M for aM∗ ≤ a ≤ a¯ M∗ ,and E for a¯ M∗ < a < 1. Similar to the unregulated case, as consumers’ acceptance for e-commerce a increases, the socially optimal strategy switches from T to M, and then to E. Furthermore, social welfare under strategies T, M, and E all decrease as β increases. When β becomes sufficiently large, strategy E will dominate strategies T and M, since the impact of congestion on social welfare under strategy E is weaker relative to that under the other two strategies.

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6. Incentive distortions and policy analysis In this section, we first compare the private firm’s and social decisions and discuss the private firm’s incentive distortions, that is, how the firm’s decisions deviate from the socially optimal decisions. We then propose public policies that align the private firm’s incentives with the social planner’s decisions to achieve maximum social welfare. 6.1. Private firm’s incentive distortions From Propositions 1 and 2, we find that conflicts arise between the private firm’s incentives and socially optimal decisions. We illustrate the firm’s incentive distortions through a numerical example. Suppose ct = 0.1, ce = 0.05, h = 0.2, β = 0.5, n = 0.4,and a = 0.25. We find that the socially optimal strategy is M; and the socially optimal quantities are 0.241 at the traditional channel and 0.040 at the electronic channel. Whereas, the private firm, under no regulation, will choose strategy T with quantities 0.233 at the traditional channel and zero at the electronic channel. Therefore, there are two incentive distortions of the private firm, i.e., the quantities at the two channels. In order to fix the firm’s incentive distortions, the social planner in general needs two instruments in a public policy to achieve the social optimum. In the following, we propose a differentiated tolls/rebates policy that elicits the socially optimal distribution strategy and quantities. 6.2. Policy analysis We examine three cases where the socially optimal strategy is T, M, and E, respectively. In each case, we derive parameters in the differentiated tolls/rebates policy that achieve maximum social welfare. Finally, we summarize the three cases and present the general differentiated tolls/rebates policy. 6.2.1. Case 1: strategy T is socially optimal From Proposition 2, strategy T is socially optimal when consumers’ acceptance of e-commerce is low (a < a M∗ ). As analyzed above, in order to elicit the social optimum, the social planner needs to induce the firm to adopt strategy T and choose the socially optimal quantity at the traditional channel. The social planner will need two instruments in the public policy. We first derive the policy parameter that induces the firm to choose the socially optimal quantity at the traditional channel. We then discuss how to ensure that the firm only sells through the traditional channel. In order to achieve the socially optimal quantity DtT ∗ ,suppose that the social planner charges traditional consumers a congestion toll τtT . (The other road users may or may not be charged the toll, which will not affect our result.) The congestion toll will affect the number of consumers who use the road, which is also the demand at the physical store. The utility of each consumer who drives through the road and purchases at the physical store equals v − pTt − β(DtT + n) − τtT . Therefore, the utility of the marginal consumer who is indifferent from purchasing and not purchasing the product equals pTt + β(DtT + n) + τtT . The demand hence satisfies DtT = 1 − ( pTt + β(DtT + n) + τtT ). Solve the equation and obtain the demand function, DtT = (1 − pTt − β n − τtT )/(1 + β). With this demand function, the firm chooses the retail price at the traditional channel, pTt ,to maximize its profit. We solve the firm’s problem and obtain the firm’s optimal price. We can also obtain the firm’s optimal quantity, which equals Dt (τtT ) = (1 − ct − β n − τtT )/(2(1 + β)). (We use superscript “‡”to represent the firm’s optimal decision for a given toll.) Note that the firm’s optimal quantity is a function of the congestion toll τtT . The social planner’s objective is to determine a toll τtT such that the T‡

quantity that the firm chooses exactly equals the socially optimal quantity. Therefore, we equalize Dt (τtT ) = DtT ∗ ,and obtain the optimal toll, τtT ∗ (given in Appendix A). Note that τtT ∗ is not necessarily positive for all parameter values. If τtT ∗ is negative, it is in fact a subsidy. This is because in a monopoly market, the quantity that the firm chooses may turn out to be too small compared with the socially optimal quantity. We refer to this as the “monopoly effect”. To fix the too small quantity resulting from the monopoly effect, the social planner should offer consumers a subsidy to shift the demand curve upwards so as to increase the equilibrium quantity to the social optimum. In practice, the subsidy can be distributed to consumers through a rebate or tax credit. We hereafter refer to the subsidy as a “rebate”. In addition to the monopoly effect, there also exists an opposite effect that potentially drives the firm to choose a greater quantity than the social optimum. We refer to this as the “congestion externality effect”. Specifically, on a congested road, each traditional consumer, who is also a road user, ignores the externality incurred by his/her travel on the road, i.e., an increased congestion cost of all other travellers on the road. As a result, an individual consumer may choose to travel and purchase the product, while from the social point of view he/she should not. Therefore, the congestion externality effect results in a too large quantity under the unregulated equilibrium. To eliminate the congestion externality effect, the social planner needs to charge each consumer a positive congestion toll, the purpose of which is to increase each traveller’s cost for using the road until it reaches the marginal social cost. Therefore, the social planner should evaluate the relative strengths of the monopoly effect and congestion externality effect and determine how the firm’s quantity deviates from the social optimum. Under strategy T, we can get the optimal toll/rebate under which the firm chooses exactly the socially optimal quantity at the traditional channel. T‡

Lemma 1. In the case where strategy T is socially optimal, in order to elicit the socially optimal quantity at the traditional channel, the social planner should charge each consumer a congestion toll τtT ∗ if n > nT , while offering each consumer a rebate |τtT ∗ |otherwise.

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(Threshold nT and all other thresholds in the following are given in Appendix A.) Lemma 1 indicates that under strategy T, the social planner may charge a toll or offer a rebate to fix the private firm’s quantity, depending on parameter values. In particular, when n is sufficiently large, the total number of road users is so large that the congestion externality effect outweighs the monopoly effect. As a result, under an unregulated economy, the firm would choose a too large quantity, which requires a congestion toll. On the other hand, when n is sufficiently small, the monopoly effect outweighs the congestion externality effect, which results in a too small quantity. The social planner should therefore increase the quantity by offering consumers a rebate to maximize social welfare. Similarly, the toll/rebate also depends on parameter β . A large β implies a strong congestion externality effect, calling for a toll, while a small β requires a rebate. Note that when the social planner applies the toll/rebate in Lemma 1, the firm does not necessarily adopt strategy T. Rather, the firm may sell through either both channels or the electronic channel only. In order to deter the firm from selling through an electronic channel, the social planner can simply charge online delivery vehicles a sufficiently large toll. If the firm suffers a loss selling at the electronic channel, then it will not launch the electronic channel, i.e., adopt strategy T. But the toll on delivery vehicles is not necessarily equal to the toll on consumers who go to the traditional channel. In practice, the social planner may charge differentiated tolls by vehicle types, e.g., consumers’ private vehicles and the delivery trucks, at the toll station.4

6.2.2. Case 2: strategy E is socially optimal From Proposition 2, strategy E is socially optimal when consumers’ acceptance of e-commerce is high (a > a¯ M∗ ). To achieve E∗ De ,suppose that the social planner charges the firm a congestion toll τeE ,or offers the firm a rebate |τeE∗ |for each unit of the product sold online.5 The firm’s profit is then π E = ( pEe − ce )DEe − β(hDEe + n) − τeE DEe ,where the demand function DEe remains the same as in Section 4.1. The firm maximizes its profit and obtains an optimal quantity De (τeE ). We let Dt (τeE ) = DtT ∗ to calculate the optimal toll under strategy E and get τeE∗ (given in Appendix A). The toll/rebate under strategy E is as follows. E‡

T‡

Lemma 2. In the case where strategy E is socially optimal, in order to elicit the socially optimal quantity at the electronic channel, the social planner should charge a congestion toll τeE∗ if n > nE , while offering a rebate |τeE∗ |otherwise. Note that under Case 2, τeE∗ is monotonically increasing in h. Therefore, τeE∗ is positive (a toll) if h is large, and negative (a rebate) otherwise. This is because as h increases, the firm will dispatch more delivery vehicles for the same amount of sales. This exacerbates the congestion externality effect, which requires a toll rather than a rebate. Similar to Case 1, in Case 2, to ensure the firm not to sell at the traditional channel, the social planner can charge traditional consumers a sufficiently large toll. Under such a toll, traditional consumers’ net utility becomes low. So the firm has to set a low price to attract consumers, which may cause the firm to suffer a loss to sell at the traditional channel. As a result, the firm will only sell through the electronic channel.

6.2.3. Case 3: strategy M is socially optimal Strategy M is socially optimal when consumers’ acceptance of e-commerce is moderate (aM∗ ≤ a ≤ a¯ M∗ ). Under strategy M, let τtM be the congestion toll for each traditional consumer, and τeM be the congestion toll charged the delivery vehicles for each online consumer. Under certain conditions, the social planner may have to offer rebates, i.e., |τtM∗ |and |τeM∗ |,rather than charging tolls. Under the tolls/rebates at the two channels, each consumer who purchases at the traditional channel obtains utility v − M M M M pM t − β(Dt + hDe + n) − τt ; and each online consumer obtains av − pe . Following a similar procedure in Section 4, we can M M M M M derive the demand functions at the two channels, Dt (τt , τe )and De (τt , τeM ). M M M M M M M M The firm maximizes its profit (arguments suppressed), π M = ( pM t − ct )Dt + ( pe − ce )De − β(Dt + hDe + n)hDe − τe De . We can calculate the firm’s optimal quantities Dt (τtM , τeM )and De (τtM , τeM )for given τtM and τeM . From the equalities M‡

M‡

M∗ M∗ De (τtM , τeM ) = DtM∗ and Dt (τtM , τeM ) = DM∗ e ,we derive the optimal tolls τt and τe (given in Appendix A). The tolls/rebates under strategy M are as follows: M‡

M‡

Lemma 3. In the case where strategy M is socially optimal, in order to elicit the socially optimal quantities, the social planner should charge each traditional consumer a congestion toll τtM∗ if n > ntM ,while offering each consumer a rebate |τtM∗ |otherwise. In addition, the social planner should charge the firm a congestion toll τeM∗ for each online consumer if n > nM e ,while offering the firm a rebate |τeM∗ |for each online consumer otherwise. Similar to Lemmas 1 and 2, under strategy M, the social planner may charge tolls or offer rebates depending on the relative strengths of the monopoly effect and congestion externality effect. Furthermore, under strategy M, the social planner also needs to balance the net social benefits between the two channels by adjusting the tolls/rebates. As a result, the differentiated tolls/rebates in Lemma 3 induce the firm to choose the socially optimal quantities at both channels.

4 In some cases, the social planner may charge a uniform toll rather than differentiated tolls for ease of implementation. However, our focus is on finding the first-best policy, which as analyzed above, is achieved through differentiated tolls rather than a uniform toll. 5 Alternatively, the social planner can charge the congestion toll for each delivery vehicle, which simply equals τeE /h. Similarly, the rebate can be offered to online consumers directly, which affects neither tractability of the problem nor our intuitions and insights.

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6.2.4. Differentiated tolls/rebates policy We can see that in all the three cases in Sections 6.2.1, 6.2.2, and 6.2.3, there always exist differentiated tolls/rebates such that the firm adopts the socially optimal distribution strategy and quantities. We summarizes the differentiated tolls/rebates policy in the following proposition. Proposition 3. There always exists a differentiated tolls/rebates policy that induces the firm to choose the socially optimal distribution strategy and quantities. We use a numerical example to illustrate the differentiated tolls/rebates policy in Proposition 3. Suppose ct = 0.1, ce = 0.05, h = 0.2, β = 0.5,and n = 0.6. We first calculate the two thresholds in Proposition 2, aM∗ = 0.235and a¯ M∗ = 0.388. Therefore, the socially optimal strategy is T for a< 0.235, E for a > 0.388, and M for 0.235 ≤ a ≤ 0.388. We first consider a case where a = 0.22and strategy T is socially optimal. Calculate and get τtT ∗ = 0.15; that is, the social planner should charge traditional consumers a congestion toll equal to 0.15 to elicit the socially optimal quantity at the traditional channel. Furthermore, to prevent the firm from choosing strategy M or E, the social planner should charge the firm’s delivery vehicles a sufficiently large congestion toll. From our calculation, the minimum toll equals 0.014. That is, if the social planner charges the firm’s delivery vehicles a toll greater than or equal to 0.014 for each unit of product carried in the vehicle, the firm will not launch an electronic channel. To summarize, for a = 0.22,the optimal policy is to charge traditional consumers a congestion toll equal to 0.15 and charge the online goods a toll equal to 0.014. Under this policy, the firm will adopt the socially optimal strategy T and offer the socially optimal quantity at the traditional channel. Consider another case where a = 0.3and the socially optimal strategy is M. We calculate and obtain that τtM∗ = 0.137and τeM∗ = −0.043. Therefore, if the social planner charges a congestion toll 0.137 at the traditional channel and offers a rebate 0.043 at the electronic channel, then the firm will choose strategy M and the socially optimal quantities at both channels. 7. Conclusion In this research, we investigate the interactions between a firm’s distribution strategies concerning e-commerce and traffic congestion. Compared with traditional distribution, e-commerce can reduce consumers’ shopping cost since consumers avoid hassle of driving to physical stores. However, due to lack of service, delayed satisfaction, and difficulty to return, consumers’ valuation for the electronic channel is lower than that for the traditional channel. Therefore, in an unregulated economy, the firm trades-off the benefits and costs of launching e-commerce and chooses a distribution strategy to maximize its own profit. We show that the firm may adopt a traditional, mixed, or electronic distribution strategy, as consumers’ acceptance of e-commerce increases. Furthermore, when road users become more sensitive to traffic congestion, the firm has a stronger incentive to adopt the electronic distribution strategy. If the firm is publicly owned, a social planner makes decisions to maximize social welfare. However, the private firm may deviate from the socially optimal strategy as well as the socially optimal quantity at each channel, incurring incentive distortions. We identify two effects that drive the firm to deviate from the socially optimal quantities. One is the monopoly effect that causes the firm to choose a too small quantity; the other is the congestion externality effect that drives the quantity too large. The two forces are in opposite directions; and the net effect, depending on parameter values, determines whether the firm chooses a larger or smaller quantity than the social optimum. To fix the firm’s quantity distortions in both channels, we propose a differentiated tolls/rebates policy. We show that under this policy, the firm will not only choose the socially optimal quantities but also the socially optimal distribution strategy. Our work aims to provide an analytical framework to study the interaction between firms distribution strategy and traffic congestion. Some of our assumptions can be relaxed in order to obtain more general results. First, as consumers may live at different distances from the physical store, they may have heterogenous congestion costs while driving to the store. Similarly, consumers may suffer from different levels of disutility due to congestion delay. It is worthwhile to consider various consumer heterogeneity while exploring the impact of e-commerce on congestion. Furthermore, e-commerce enables inhabitants to live in suburbs with lower housing price and better traffic condition and air quality. Similar to telecommuting, e-commerce may cause urban expansion, which potentially leads to more serious traffic congestion due to longer travel distances of commuters. It would be interesting and important to consider the impact of urban expansion caused by e-commerce on social welfare and its solution. Finally, future research may evaluate the impact of e-commerce in more complex settings such as a supply chain where the firm distributes through independent retailers and a city with competing firms. In a competitive market, e.g., we expect that the congestion effect is more likely to outweigh the monopoly effect, which results in a congestion toll rather than a rebate. Acknowledgments We would like to thank the three anonymous referees, Hai Yang (the Editor-in-Chief), Anming Zhang, and Harish Krishnan for their helpful comments. We also gratefully acknowledge financial support from the Fundamental Research Funds for the Central Universities in UIBE (15JQ03), the National Natural Science Foundation of China (71301025, 71201028, 71401035, 71571043), and the National Social Science Foundation of China (14BGL178).

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Appendix A. Solutions and thresholds Let A1 = 1 − ct + ce and A2 = h + n − hn; the following are thresholds and quantities in Sections 4–6:

ce (1 + β) + β h(1 + n) − ct β h , ct + β + β n

aM ≡

A1 − β A2 +

M

a¯ ≡



(5)

A21 + β(β A22 − 2A1 A2 + 4h(ce + h − ct h)) 2

,

(6)

β¯ M ≡

act − ce h(1 + n − ct ) − a − an + ce

(7)

aM∗ ≡

ce + 2β(h(1 + n − ct ) + ce ) , 2β + 2β n + ct

(8)

M∗

a¯

≡

τtT ∗ = nT =



4β(A2 (1 + ct + ce + β A2 ) + 2h2 (1 − ct ) − 2ce n(1 − h)) + 2A21 2

− β A2 ,

ct + 3β n + 2β 2 n − 1 , 1 + 2β 1 − ct

β(2β + 3)

τeE∗ = nE =

A1 +

(10)

,

(11)

ace + 3aβ hn + 2β 2 h3 n − a2 , a + 2β h2

(12)

a(a − ce ) , β h(3a + 2β h2 )

τtM∗ =

(9)

(13)

(1 − 3β n − 2β − ct )a2 + aT1 + 2β h(β hn + ct h − ce − h) , a(1 − a + 2β − 4β h) + 2β h2

(14)

where˜T1 = 2β ce + 4β h + 3β n + ct + 2β 2 n − 4β 2 hn − 2β ct h − 1,

τeM∗ =

a3 − (1 + 2β + ce + 3β hn − 2β h)a2 + aT2 + 2β 2 h3 n , a(1 − a + 2β − 4β h) + 2β h2 Table 1 The firm’s optimal prices and demands under the three strategies (superscript “†” represents the private firm’s optimality under a specific strategy). T

E

M

pX† t

1+ct −β n 2

–

1+ct −β n 2

DtX†

1−ct −β n 2(1+β)

–

a(1−a−ct +ce −β h−β n+β hn)+β h(ce +h−ct h) 2(a(1−a+β −2β h)+β h2 )

–

a(a+ce +β h(2h+n)) 2(a+β h2 )

a(a(1−a−ce +β −3β h−β hn)+β(ce +h+h2 −ce h−ct h+ct h2 )+ce ) 2(a(1−a+β −2β h)+β h2 )

–

a−ce −β hn 2(a+β h2 )

a(β +ct +β n)−β(ce +h+hn−ct h)−ce 2(a(1−a+β −2β h)+β h2 )

pX† e DX† e

Table 2 The socially optimal quantities under the three strategies (superscript “∗” represents social optimum under a specific strategy). T

E

M

DtX∗

1−ct −2β n 1+2β

–

a(1−a−ct +ce −2β h−2β n+2β hn)+2β h(ce +h−ct h) a(1−a+2β −4β h)+2β h2

DX∗ e

–

a−ce −2β hn a+2β h2

a(ct +2β +2β n)−2β(h+hn+ce −ct h)−ce a(1−a+2β −4β h)+2β h2

(15)

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where˜T2 = 3β hn + 2β ce + 2β h + ce − 4β 2 h2 n + 2β 2 hn + 2β ct h2 − 2β ce h − 2β ct h − 2β h2 , ntM =

(1 + 2β ct h − 2β ce − 4β h − ct )a − (1 − ct − 2β)a2 − 2β ct h2 + 2β ce h + 2β h2 , β(3a − 4aβ h + 2β h2 − 3a2 + 2aβ)

(16)

nM e =

a(a2 − (1 − 2β h + 2β + ce )a + 2β ct h2 − 2β ce h − 2β ct h − 2β h2 + 2β ce + 2β h + ce ) . β h(3a − 4aβ h + 2β h2 − 3a2 + 2aβ)

(17)

Appendix B. Proofs Proof of Proposition 1. Let DEN denote the denominator of pt and pe . First, we calculate π M† − π E† . The denominator equals 4DEN(a + β h2 ); and the numerator is a quadratic term. Therefore, we have that π M† − π E† ≥ 0. So for aM ≤ a ≤ a¯ M ,π M† ≥ π E† . Similarly, we calculate π M† − π T † . The denominator equals 4DEN(1 + β); and numerator is a quadratic term. So for aM ≤ a ≤ a¯ M ,π M† ≥ π T† . Hence, for aM ≤ a ≤ a¯ M ,strategy M dominates both strategies T and E. Furthermore, we assume a − ce − 2β hn > 0in Section 3. Under this condition, condition a − ce − β hn > 0also holds, which E† guarantees De > 0. We can calculate ∂π E† /∂ a, which is positive under the condition a − ce − β hn > 0. Therefore, π E† is monotonically increasing in a, while π T† is independent of a. Therefore, there exists a threshold a† such that π T† > π E† if a < a†; and π T† < π E† otherwise. So for a < a M strategy T dominates strategies M and E; and for a > a¯ M strategy E dominates. Combine and the desired result follows.  M†

M†

Proofs of Lemmas 1, 2 and 3. Note that τtT ∗ ,τeE∗ ,τtM∗ ,and τeM∗ are all linear and increasing in n. Therefore, we can solve for a threshold for each toll/rebate; and the desired threshold results follow.  M∗ − SW E∗ and get a fraction. The denominator is Proof of Proposition 2. Let DEN∗ be the denominator of pM∗ t ; calculate SW 2DEN∗ (a + 2β h2 ); and the numerator is a quadratic term. Therefore, for aM∗ < a < a¯ M∗ ,SWM∗ > SWE∗ . Similarly, the denominator of SW M∗ − SW T ∗ equals 2DEN∗ (1 + 2β); and the numerator is also a quadratic term. So we have that SWM∗ > SWT∗ for aM∗ < a < a¯ M∗ . Furthermore, we assume a − ce − 2β hn > 0in Section 3. Under this condition, ∂ SWE∗ /∂ a > 0. Therefore, SWE∗ is monotonically increasing in a, while SWT∗ is independent of a. Therefore, there exists a threshold a∗ such that SWT∗ > SWE∗ if a < a∗ ; and SWT∗ < SWE∗ otherwise. So for a < a M∗ strategy T dominates strategies M and E; and for a > a¯ M∗ strategy E dominates. Combine and the desired result follows. 

Proof of Proposition 3. Follows directly from Lemmas 1 to 3.



Appendix C. Differentiated congestion cost sensitivities In this section, we consider an extended model where the firm and individuals have different congestion cost sensitivities. Specifically, we denote by t the firm’s congestion cost sensitivity, while the congestion cost sensitivity of consumers and other road users is still β . Under this extended model, using a numerical study, we can show that Proposition 1 continues to hold. What is more, we can show that both thresholds a M and a¯ M increase in t. This implies that as the firm becomes more cost sensitive to traffic congestion, the firm will be less likely to prefer electronic distribution. This is intuitive because one of the benefits of e-commerce as a replacement of traditional distribution is the decreased total congestion cost transferred from consumers to the firm due to economy of scale in economy in online delivery. Although the firm directly bears the congestion cost under electronic distribution, it still benefits from congestion reduction since demand is not affected by traffic congestion. However, as t increases, the firm’s congestion cost increases, which weakens the firm’s incentive to replace traditional distribution with e-commerce. Similarly, we can also show that Proposition 2 still holds. Also, the thresholds a M∗ and a¯ M∗ increase in t. This indicates that as t increases, the social planner is also more likely to prefer traditional distribution to electronic distribution. Appendix D. Chained trips In this section, we examine an extension where consumers may make chained trips. Ghaly (1990) reports that 40% of trips that people make involve more than one stop. In particular, O’Kelly (1981) finds that 63% of grocery and 74% of non-grocery shopping trips are multi-purpose. In the case of traditional distribution, consumers’ chained trips can reduce congestion since total distance traveled by each consumer is shorter. In this extension, we consider effects of traditional consumers’ chained trips on e-commerce and congestion. Specifically, we normalize the distance of each traditional consumer’s shopping trip to 1. Suppose that each traditional consumer will travel an average of κ distance for other purposes if these trips are not chained to his/her shopping trip. Then the total distance travelled by each consumer is 1 + κ . When the consumer chains these trips to his/her shopping trip, the total distance traveled will decrease. Let λ∈ (0, 1) be the average percentage of saving in each consumer’s travelling distance of other trips due to trip chaining; then each traditional consumer’s total distance traveled is 1 + κ(1 − λ).

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We numerically show that Proposition 1 continues to hold. Furthermore, we find that both thresholds a M and a¯ M increase in λ. The intuition is that in the traditional channel, as trip chaining saves more distances traveled, i.e., λ increases, congestion is reduced, which increases the firm’s demand. As a result, the firm’s profit increases as λ increases. Therefore, as λ increases, it is more likely that the firm’s profit is higher under strategy T than under strategy M, since the congestion reduction effect is stronger under strategy T than under M. Similarly, as λ increases, strategy M is more likely to be preferred to strategy E. Similarly, in Proposition 2, the thresholds a M∗ and a¯ M∗ also increase in λ, which implies that as λ increases, the social planner is also more likely to prefer traditional distribution to e-commerce.

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