Transportation gas emissions with online retailing: a spatial model

ABSTRACT We analyse the impact of online retailing on transportation gas emissions in a spatial duopoly with upstream suppliers. We consider: (1) pure offline competition with two physical retailers; and (2) online/offline competition, where an online retailer competes against an offline retailer. When the upstream suppliers are located in the city centre, transportation gas emissions are lower under online/offline competition. However, when the upstream suppliers are at the endpoints, online retailing might increase transportation gas emissions. This happens when: (1) in the online/offline competition case, the physical retailer does not locate at the endpoint; (2) the transportation costs of the suppliers’ commercial trucks are sufficiently larger than those of the consumers’ private cars; and (3) the competitiveness of the offline retailer is high enough.


INTRODUCTION
Transportation gas emissions are a big concern nowadays due to their negative impact in terms of greenhouse gases. 1 According to Dilek et al. (2018), transportation has been the second biggest source of greenhouse gas emissions in the United States and Europe in 2015. In particular, about 65% of transportation emissions is due to the consumption of gasoline by personal vehicle use (Cachon, 2014). Similarly, 23% of transportation-related emissions is generated by commercial trucks, and 70% of European transport emissions in 2014 is generated by total road transport (Dilek et al., 2018).
As argued by van Loon et al. (2015), consumers' trips play a relevant role on overall transportation gas emissions. Similarly, trucks' journeys for inventory replenishments generate transportation gas emissions. Motivated by these observations, some studies attempt to analyse the environmental impact of transportation gas emissions for retailing purposes. Indeed, the distance between the retailers and the consumers, and the distance between the suppliers and the retailers determine the level of transportation gas emissions by affecting the overall road transport. Cachon (2014) develops a monopolistic retail supply chain model which includes a cost for environmental externalities, and investigates the effectiveness of a carbon tax in reducing transportation gas emissions. Park et al. (2015) extend the analysis of Cachon (2014) to the case of monopolistic competition. Dilek et al. (2018) focus on a spatial duopolistic competitive setting à la Hotelling (1929) with endogenous locations and fixed prices, and find that when competition is more intense, the overall transportation gas emissions tend to increase.
The above-mentioned studies focus on transportation gas emissions by assuming that the retailers are physically located in the space. However, nowadays e-commerce provides an alternative way for consumers to shop. Since Amazon emerged in the United States in 1995, online retailing has become increasingly important. In 2014, more than 46% of European shoppers chose online retailing (EcommerceEurope, 2015), while online retailing accounted for 14.9% of China retail sales in 2016 (China e-Business Research Center (CECRC), 2016). 2 The aim of this paper is to investigate the impact of online retailing on the level of transportation gas emissions. In particular, we study how the appearance of online retailing affects transportation gas emissions by changing the equilibrium distance between consumers, retailers and suppliers. We focus on the following questions: Might online retailing give rise to an environmental deterioration by increasing the overall transportation gas emissions? And if so, when? In other words, we aim to characterize the conditions at which online retailing, where the goods are delivered to the consumer's home, is more likely to increase the transportation gas emissions with respect to physical retailing, where the consumers need to travel to the retailer's store.
Using the Hotelling linear city model, we consider two cases: (1) pure offline competition, where two physical retailers compete each other; and (2) online/offline competition, where an online retailer competes with a physical retailer. We also assume that there are two upstream suppliers, one for each downstream retailer. When the upstream suppliers are close each other (namely, they are both located at the midpoint of the city), online retailing benefits the environment by reducing the transportation gas emissions with respect to physical retailing. However, when the upstream suppliers are located at the endpoints of the city, online retailing might generate greater transportation gas emissions, thus being detrimental for the environment. This happens when the following conditions are simultaneously satisfied: (1) in the online/offline competition case, the physical retailer does not locate at the endpoint of the city in equilibrium; (2) the transportation cost of the commercial trucks used by the suppliers is sufficiently larger than the transportation cost of the private cars used by the consumers; and (3) the competitiveness of the offline retailer with respect to the online retailer is high enough.
Our results contribute to the ongoing debate about the environmental impact of e-commerce. As noted by Palsson et al. (2017), the environmental efficiency of online retailing with respect to offline retailing can be determined by a series of factors, namely: product waste and product returns, buildings, packaging, and the overall consumers' trips and the freight transportation costs. Carrillo et al. (2014) argue that 'the main factors driving [the different environmental impact of physical and online retailing] are the distance that the customer has to drive to buy the item via a traditional retailer' (p.744), and Tehrani et al. (2009) claim that 'e-shopping is an effective method in the reduction of air pollution … resulting from substitution of delivery vans for personal trips for supermarket goods' (p. 898). According to Allen et al. (2018) and Bergmann et al. (2020), the most costly and challenging phase of the e-commerce logistic is represented by the delivery of the goods to the consumer's home. It also represents a crucial factor when comparing transportation gas emissions under traditional retailing and under online retailing (Wiese et al., 2012).
Case study and empirical literature about the impact of online retailing on transportation gas emissions provides ambiguous results. Siikavirta et al. (2002) consider home delivery grocery services and argue that online retailing can reduce transportation gas emissions by 87%. The environmental benefits of online shopping have been also highlighted by Mokhatarian (2004), Cairns (2005) and Wiese et al. (2012). However, Matthews et al. (2001Matthews et al. ( , 2002 and Williams and Tagami (2003) provide opposite evidence by showing that online retailing has augmented transportation gas emissions in the Japanese book industry. Van Loon et al. (2015) and Jaller and Pahwa (2020) also point out that online shopping might generate more greenhouses gases than offline retailing. In this paper, we complement this literature by proposing a theoretical analysis based on a simple game-theoretic duopolistic spatial model. 3 The rest of this paper proceeds as follows. In the second section we introduce the model. In the third section we solve the model for both pure offline competition and online/offline competition when the upstream suppliers are located at the midpoint of the city, derive the transportation gas emissions in the two situations, and compare them. In the fourth section, we consider a situation where the upstream suppliers are located at the endpoints of the city. The fifth section concludes. The proofs are in the Appendix in the supplemental data online. Following Hotelling (1929), we suppose that consumers are uniformly distributed on a segment of length one. We denote by x [ [0, 1] the location of a consumer. There are two downstream retailers, say firm RA and firm RB, selling an identical good. Firm RA is a physical retailer located at x RA [ [0, 1]. Firm RB can be either a physical retailer or an online retailer. If firm RB is a physical retailer, it locates at x RB [ [0, 1]. Without loss of generality, we assume that firm RA locates at the left of firm RB, x RA ≤ x RB . If firm RB is an online retailer, it has no 'physical location' in a conventional sense (e.g., Balasubramanian, 1998;Bouckaert, 2000;Colombo & Matsushima, 2020), as it works as an online digital platform such as Amazon Marketplace or Alibaba that 'efficiently and effectively let large numbers of sellers and buyers interact' (Reinartz et al., 2019, p. 351).

THE MODEL
Each consumer buys 1 or 0 units of the good. We assume that the reservation price is so high that the market is always covered in equilibrium. 4 If the consumer buys from a physical retailer, he travels by car from his location to the firm's store and picks up the good. 5 We assume quadratic transportation costs to avoid the non-existence of equilibria in pure strategies (D'Aspremont et al., 1979). Therefore, the utility function of a consumer located at x and buying from the physical store of firm Ri, with i = A, B, is: where v is the reservation price; p Ri is the retail price of firm Ri; c c is the consumers' transportation cost per unit of distance travelled by car per unit of product purchased; and (x − x Ri ) 2 captures the quadratic nature of the transportation costs. If firm RB is an online retailer and the consumer buys from it, the consumer sustains no transportation costs. However, as in Balasubramanian (1998), the consumer suffers a disutility cost equal to z . 0, which is due for example to the delay in receiving products, the inability of consumers to inspect the product beforehand and the returning products. 6 In this case, the utility function of the consumer is: In addition, there is an upstream supplier for each downstream retailer. Let Si denote the upstream supplier of firm Ri. Supplier Si supplies the good to the downstream retailer Ri (or to Ri's consumers in the case of online retailingsee below) by receiving the wholesale price w Si . As in Dilek et al. (2018), we assume that the upstream suppliers sustain the transportation costs. Suppose that supplier Si is located at x Si . 7 In the case of an offline purchase, the supplier delivers the good to the retailer's store, whereas in the case of an online purchase the supplier delivers the good directly to the consumer on the behalf of the retailer. When supplying a d distant downstream retailer or consumer, an upstream supplier incurs a transportation cost c t d 2 , where c t is the suppliers transportation cost per unit of distance travelled by truck per unit of product delivered. 8 There is a direct relationship between the transportation cost c c and c t , and the level of gas emissions: in particular, as in Cachon (2014), Park et al. (2015) and Dilek et al. (2018), we assume that the overall transportation costs are a direct measure of the level of transportation gas emissions. Therefore, we assume that emissions are also quadratic in distance. 9 We impose the following parameter restrictions. First, we assume z/c c ≤K 0 ; [19 − c t /c c ]/4. Note that z/c c is a measure of the competitiveness of the physical retailer with respect to the online retailer: when z/c c is high (low), the physical retailer is highly (scarcely) competitive with respect to the online retailer. By assuming that z/c c is not too high, we guarantee that the online retailer is not dropped out from the market. Second, we assume c t /c c ≤ 1. By assuming that the transportation cost of the supplier is not too high relative to the transportation cost of the consumers, we guarantee that in equilibrium the profits of the suppliers are positive. Furthermore, the assumption that the transportation costs of the supplier are lower than the transportation costs of the consumers is supported by empirical observations. For example, Cachon (2014Cachon ( , pp. 1915Cachon ( -1916, based on the estimates of Barnes and Langworthy (2004) and McKinnon and Woodburn (1994), show that 'a truck has a variable operating cost per kilometre that is less than five times that of a car, but carries at least 500 times more product', so that c t ≤ c c . Similarly, Dilek et al. (2018, p. 148) assume that 'the economies of scale effect between the truck-load and the passenger-car-load often dominates the transportation costs coefficients'. 10 We consider the following three-stage game. In stage 1, the two upstream suppliers set the wholesale prices. In stage 2, if downstream firm RB is a physical retailer, the two retailers choose simultaneously the locations; if firm RB is an online retailer, only firm RA chooses the location. In stage 3, the two downstream retailers choose simultaneously the price. We solve the game by backward induction.

MINIMAL DISTANCE BETWEEN SUPPLIERS
In this section we assume that x SA = x SB = 1/2, that is, the two suppliers are located in the middle of the city.

Pure offline competition
First, we consider the case where firm RB is a physical retailer. By solving with respect to x, we get the indifferent consumer between RA and RB: Therefore, the profit functions of firm RA and firm RB are , respectively. In stage 3, by solving the first-order conditions ∂p RA /∂p RA = 0 and ∂p RB /∂p RB = 0, we obtain: In stage 2, the downstream physical retailers choose their locations by anticipating the thirdstage equilibrium prices (4). As shown by Ziss (1993) and Matsumura and Matsushima (2009), in the case of marginal cost differentials, the equilibrium location is characterized by maximal differentiation in pure strategies if the cost asymmetry is low. Otherwise, if the marginal cost asymmetry is large, it is possible to show that a mixed strategy equilibrium exists where the firms choose the two endpoints of the segment with equal probability (Matsumura & Matsushima, 2009, proposition 1). 11 When moving to stage 1, the upstream suppliers set the wholesale prices by maximizing their profits functions, namely . By invoking symmetry when solving the first-order conditions, we obtain w * SA = w * SB = (12c c + c t )/4. Note that this implies that in stage 2, the retailers maximally differentiate in equilibrium, that is, x RA * = 0 and x RB * = 1.
Therefore, when the warehouses of the suppliers are located in the middle of the markets, the maximum differentiation principle (D'Aspremont et al., 1979) holds. Indeed, two opposite forces affect the equilibrium location decision of the retailers: the demand effect and the strategic effect. The demand effect works as a centripetal force (each firm wants to move toward the centre in order to enlarge its demand), whereas the strategic effect works as a centrifugal force (each firm wants to separate from the rival in order to mitigate price competition). In the case of quadratic transportation costs, the strategic effect dominates (D'Aspremont et al., 1979). With competing upstream suppliers, there is a third force at work: the wholesale price effect. Indeed, consider firm RA. When it moves to the right, the distance between RA and its supplier decreases. As the transportation costs of SA decrease, the wholesale price decreases as well. In other words, the wholesale price effect works as a centripetal force. However, in the case of two physical retailers, the strategic effect dominates both the demand effect and the wholesale price effect, so that the principle of maximum differentiation still holds.
In equilibrium, the market is equally shared between the two downstream physical retailers. Therefore, the consumers located at the left (right) of 0.5 buy from firm RA (RB).
Given the equilibrium locations of the retailers locate, the total transportation gas emissions, E * , follow: In (5), the first and second terms capture the overall transportation costs of the consumers when going to firms RA and RB, respectively, in order to pick up the good; instead, the third and fourth terms capture the inventory replenishment costs of the upstream suppliers carrying the good to firms RA and RB, respectively. Not surprisingly, the transportation gas emissions are strictly increasing in c c and c t .

3.2.
Online/offline competition Now we introduce online retailing. In particular, we assume that firm RB is an online retailer. Therefore, in the downstream market, there is competition between a physical retailer (firm RA) located at x RA and an online retailer (firm RB) with no physical location. Correspondingly, supplier SA serves the physical retailer by carrying the good to firm RA's store (so that a consumer needs to move to firm RA's store to pick up the good), whereas supplier SB serves the online retailer by carrying the goods directly to firm RB's consumers.
By equating u RA = v − p RA − c c (x − x RA ) 2 and u RB = v − z − p RB , we get the left and right indifferent consumer, respectively: Before proceeding, it should be noted that depending on the location of firm RA, two types of market structure could exist: a fringe market structure (Figure 1, on the left) and an interior market structure (Figure 1, on the right). In the fringe market structure, all the consumers located at the left (right) of x R RA buy from firm RA (RB); in the interior market structure, all the consumers located between (outside) x L RA and x R RA buy from firm RA(RB). 12 The analysis of the third-stage equilibrium retail priceswhich depend on the market structureis shown in the Appendix in the supplemental data online.
The following lemma characterizes the location equilibrium in the online/offline competition case when the suppliers' warehouses are located at 0.5. 13 Lemma 1: Only the fringe market structure emerges in equilibrium. In particular, when max [K 2 , 0] , z/c c , K 1 , the physical retailer locates at x F RA,1 = 0, whereas when For proof, see the Appendix in the supplemental data online. Figure 2 illustrates Lemma 1. Lemma 1 shows that only the fringe market structure can arise in equilibrium. In the fringe market structure, similarly to the case of pure online competition, the demand effect, the wholesale price effect and the strategic effect are at work. When firm RA moves toward the right, it increases its own demand (demand effect), while the wholesale price decreases (wholesale price effect). However, by moving to the right, firm RA induces the downstream online retailer to react by reducing its price (strategic effect), similarly to the case of pure offline competition (Colombo & Hou, 2021). Therefore, the demand effect and the wholesale price effect work as two centripetal forces, whereas the strategic effect works as a centrifugal force.
The strength of these three effects depends on z/c c . When z/c c is high (K 3 , z/c c , K 0 ) the competitive advantage of the online retailer over the physical retailer is low, and the strategic effect is low: the physical retailer chooses x F RA,2 , which is strictly greater than zero. When z/c c is quite low (max [K 2 , 0] , z/c c , K 1 ), the competitive advantage of the online retailer over the physical retailer is quite high, thus yielding a high strategic effect which dominates the wholesale price effect and the demand effect. In this case, the physical retailer locates at zero. 14 Therefore, online retailing alters the location equilibrium in the downstream market. In particular, under pure offline competition, the two offline retailers locate at the endpoints, whereas under online/offline competition, the physical retailer might locate within the city. Now we solve the first stage of the game. The profits functions of the suppliers in the fringe market structure are By maximizing with respect to the wholesale prices, we get the equilibrium wholesale prices. 15 The total transportation gas emissions are therefore: 16 Note that the first term in (7) indicates the overall transportation costs of the consumers when going to firm RA to pick up the good; the second term indicates the transportation costs of supplier SB; finally, the third term captures the inventory replenishment costs of supplier SA carrying the good from its warehouse to firm RA's store.
3.3. Environmental impact of online retailing when x SA = x SB = 1/2 In this section we compare the equilibrium transportation gas emissions in the pure offline competition case and in the online/offline competition case when the suppliers are located in the middle of the city. By comparing (5) and (7), we can state the following proposition.
Proposition 1: Under minimal distance between the suppliers, the transportation gas emissions in the online/offline competition case are lower than those in the pure offline competition case.
Proposition 1 shows that the participation of an online retailer is beneficial for the environment by reducing the amount of transportation gas emissions. 17 This is final result of three different effects. First, since the consumers purchasing from the online retailer now do not need to travel to the shop, the total transportation gas emissions of the consumers decrease. Of course, supplier SB sustains the transportation costs when it carries the good from its warehouse to the consumers buying from the online retailer, and this is detrimental for the environment. In other words, the transportation costs of the consumers are replaced by those of the trucks, so that the final impact is ambiguous and depends on the relative environmental efficiency of cars and truck. Second, in those cases where the offline retailer does not locate at the endpoint, the overall transportation costs sustained by the consumers buying from the physical retailer decrease. Indeed, the arise of an online retailer might induce the retailer to locate closer to the centre of the city (see the discussion about Lemma 1). This is beneficial for the environment, because the physical retailer is now closer to the centre of its own market, thus reducing the transportation costs of the consumers patronizing the offline shop. 18 Third, when considering the transportation costs of the suppliers, it can be observed that supplier SA and retailer RA become closer when an online retailer competes against a physical retailer. Indeed, as the suppliers are located in the middle of the market, when retailer RA moves toward the centre as a consequence of the online competition, the transportation costs of supplier SA to replenish the physical retailer diminish.
The second and third pro-environmental effects of online competition outlined above dominate the first effect (whose sign is ambiguous), thus implying that the transportation gas emissions are reduced when an online retailer competes against an offline retailer.

MAXIMAL DISTANCE BETWEEN SUPPLIERS
We now consider an alternative case in which the two upstream suppliers are located at the endpoints of the city, that is, x SA = 0 and x SB = 1.

Pure offline competition
When considering competition between two offline retailers, the analysis of stages 2 and 3 runs as in the case of minimal distance between suppliers (equations 3 and 4). In stage 1, the upstream suppliers set the wholesale prices by maximizing where now x SA = 0 and x SB = 1. By using symmetry and solving the first-order conditions, we getŵ * SA =ŵ * SB = 3c c , which implies x RA * = 0 and x RB * = 1. Therefore, even in the case of maximal distance between suppliers, the two retailers maximally differentiate in equilibrium.
The total transportation gas emissions,Ê * , are: It can be observed that the total transportation gas emissions decrease when x SA = 0 and x SB = 1, with respect to the case where x SA = x SB = 1/2, as the third and fourth terms are zero. Indeed, there are no replenishment costs of the upstream suppliers, as the upstream suppliers are located at the same point of the downstream physical retailers.

Online/offline competition
In this section we calculate the equilibrium outcome when an online retailer competes against a physical retailer. The analysis is similar to the earlier section 'Online/offline competition'. We state the following lemma.
Lemma 2: Only the fringe market structure emerges in equilibrium. In particular, when 0 , z/c c ,K 1 , the physical retailer locates atx F RA,1 = 0; when 0.25 , c t /c c , 1 and K 1 , z/c c , min [K 2 ,K 3 ], it locates at . 19 For proof, see the Appendix in the supplemental data online. Figure 3 illustrates the equilibrium location of the physical retailer as a function of z/c c . As the intuition is similar to the case of minimal distance between suppliers, we refer to the discussion about Figure 2.
Moving to the first stage of the game, by maximizing the profits functions we get the equilibrium wholesale prices. 20 Now, we can derive the total transportation gas emissions,Ê, in the online/offline competition case under maximal distance between suppliers. They are: 21 In this section we compare the equilibrium transportation gas emissions in the pure offline and the online/offline competition cases when there is maximal distance between the suppliers. By comparing (8) and (9), we can state the following proposition. Proposition 2 shows that, differently from the case of minimal distance between suppliers, online retailing might increase the total transportation gas emissions when there is maximal distance between suppliers. 22 The explanation is the following. The first effect outlined in the third section is still ambiguous: the transportation costs of the consumers moving to the shops are substituted by the transportation costs of the trucks carrying the goods to the consumers' houses. The second effect is still positive: when moving to the right as a consequence of online competition, the physical retailer is better positioned (it is now in the middle of its own market areas), thus lowering the transportation costs of its own consumers. However, the third effect, relative to the transportation costs for replenishing the physical retailer, is now negative (recall it was positive in the framework discussed in the third section). Indeed, when moving toward the centre, the physical retailer increases the distance between itself and its supplier, thus negatively affecting the total environmental performance in the offline/online competition case. When this last effect dominates, the environmental performance of online retailing is negative. Furthermore, Proposition 2 characterizes the factors that make online retailing more likely to be detrimental for the environment by means of an increase of the transportation gas emissions. Consider condition (a) first. When firm RA locates at the endpoint, the distance between firm RA and its supplier is zero, both under pure offline competition and online/offline competition, so that the negative environmental effect of online retailing vanishes. Therefore, a necessary condition for online retailing to increase the transportation gas emissions is that firm RA does not locate at the endpoint in equilibrium. Condition (b) is quite obvious. It requires that the transportation efficiency of the trucks is sufficiently low relative to the transportation efficiency of the private cars. Under online/offline competition, the supplier serves the consumers of the online retailer. Therefore, if the transportation costs of the trucks are sufficiently large relative to the transportation costs of the consumers' private cars, it is more likely that the transportation gas emissions are greater in the online/offline competition case than in the pure offline competition case. The empirical evidence in Cachon (2014), Barnes and Langworthy (2004) and McKinnon and Woodburn (1994) seems to suggest that even if trucks are likely to be more efficient than cars due to the economies of scale in transportation, still several factor might affect the value of the ratio between c t and c c . For example, the improvement of car fuel efficiency as required of US car manufacturers (Vlasic, 2011) might push up the ratio c t /c c . Similarly, the expansion of eco-friendly cities has reduced the transportation costs of the consumers by means of efficient public transportations (Balasubramanian et al., 2017), thus lowering the parameter c c .
Finally, we consider condition (c), which requires that the competitive advantage of the physical retailer relative to the online retailer is high enough. As noted above, the participation of the online retailer might induce firm RA to move closer to the midpoint of the linear city, thus increasing the distance between firm RA and its supplier. When z/c c is high, the equilibrium market share of the physical retailer is large. As a consequence, all else being equal, the transportation costs of supplier SA increase, thus increasing the overall transportation gas emissions in the online/offline competition case. Note that while online retailing has increased significantly worldwide, traditional retailing is still the preferred option for several consumers (e.g., Liu et al., 2017; and see the empirical evidence mentioned in the first section). This implies that z/c c is high enough. 23

CONCLUSIONS
In this paper we investigate the impact of online retailing on total transportation gas emissions in a Hotelling model with upstream suppliers. We consider two alternative versions of the model: (1) pure offline competition, where there are two physical retailers; and (2) online/offline competition, where an online retailer competes against an offline retailer. Furthermore, we consider both the case where the upstream suppliers are located in the middle of the city and the case where they are located at the endpoints. We aim to characterize in a simple stylized model the factors that make online retailing more likely to increase the transportation gas emissions under the two alternative localizations of the suppliers. 24 After showing that the appearance of the online retailer modifies the location choice of the physical retailer, we compare the transportation gas emissions under pure offline and online/offline competitions. We show that when the upstream suppliers are located in the middle of the city, the transportation gas emissions are lower in the online/offline competition mode. Thus, online retailing benefits the environment. However, when the upstream suppliers are located at the endpoints of the city, online retailing might increase the total transportation gas emissions. In particular, this happens when: (1) under online/offline competition, the physical retailer does not locate at the endpoint in equilibrium; (2) the transportation cost of the commercial trucks used by the supplier serving the consumers that purchase from the online retailer is sufficiently larger than the transportation costs of the private cars; and (3) the competitiveness of the physical retailer with respect to the online retailer is high. 25 Our results have the following implications. First, online retailing may not be an effective mode to ameliorate the environment by reducing the transportation gas emissions. This might be the case when the upstream suppliers are spatially separated. As the location of the suppliers' warehouses plays a key role in affecting the transportation gas emissions, zoning the warehouse locations might improve the environmental performance of online retailing. Second, one might consider imposing zoning restrictions on the physical retailers. Indeed, a necessary condition for online retailing to be detrimental for the environment is that the physical retailer locates significantly far apart from its warehouse. Thus, preventing such spatial separation between the physical retailer and its warehouse by means of zoning regulation might help reducing the impact of online retailing on transportation gas emissions. 26 Our model can be extended in several directions. First, it can be used to analyse the case in which more than two physical retailers choose their locations endogenously. The density and the location of the physical retailers is likely to influence the consumers' transportation costs, and thus the environmental performance of online retailing. Second, the model could include the cost of using and maintaining the transaction platform by the online retailer, which also generates carbon emissions (Jones, 2018;Sivaraman et al., 2007;Weber et al., 2010). Third, the model could be modified to introduce carbon penalty. Taxing differently private cars and commercial trucks is likely to induce different market structures, and, consequently, different levels of transportation gas emissions. Therefore, an appropriate tax structure could reduce the environmental impact of online retailing (Ding & Jin, 2019). Fourth, we assumed throughout the paper that both the traditional and the online retailer set a uniform price. While the spatial interpretation of the Hotelling segment in our model makes it reasonable to assume that the traditional retailer cannot price discriminate between those consumers that go to the shop to pick up the good, the online retailer, by carrying the good directly to the consumers' houses, might have the possibility (and the convenience) to set different prices at different locations (i.e., spatially price discriminate). Such an extension of our model would be related to the traditional literature about spatial price discrimination (e.g., see the seminal contributions of Lederer & Hurter, 1986;Norman & Thisse, 1999;and Thisse & Vives, 1988), which has been developed in a pure offline competition framework, but not in an online/offline competition set-up. Lastly, the model does not capture the implications of a 'dual-channel' structure, that is, a situation where the same manufacturer owns both a physical store and an online store (Carrillo et al., 2014). Introducing a dual channel would require adding at least an additional manufacturer to the present set-up in order to maintain the competitive nature of the framework.
In this paper, we have assumed that the suppliers are exogenously located (either at the endpoints or in the middle of the city). Alternatively, one might consider the case of endogenous locations. A complete analysis seems to be very hard to manage due to the difficulties emerging in the case of online/offline competition. As a preliminary step, we perform the following exercise. Suppose there is a unique supplier serving both retailers (or one retailer and the consumers of the other retailer in the case of online/offline competition) and whose location is endogenous. The wholesale prices instead are exogenously given. Therefore, the timing of the game is the following. In stage 1, the upstream supplier sets the location. In stage 2, if firm RB is a physical retailer, the two retailers choose simultaneously the locations; if firm RB is an online retailer, only firm RA chooses the location. In stage 3, the two downstream retailers choose simultaneously the price. The complete analysis is reported in the Appendix in the supplemental data online. In this case, it can be observed that online retailing increases the emissions when the competitive advantage of the physical retailer relative to the online retailer is high enough, similar to condition (c) in Proposition 2. However, further research is needed to generalize the analysis to endogenous location of the supplier(s).

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors .

NOTES
1 The increasing amount of greenhouse gases is one of the main factors responsible for global warming (Zand et al., 2019). 2 The appearance of online retailing has reshaped the retailing market. Not only are the equilibrium prices of physical retailers expected to change after the entrance of online competitors, but also the equilibrium locations of physical retailers are likely to modify. Indeed, offline (or physical) retailers often relocate due the emerging of online competitors. For example, Guo and Lai (2017) argue that 'numerous physical retailers have moved into urban areas, close to highly dense populations' (p. 439) due to online competition. Kotkin (2001), Dixon and Marston (2002) and Li (2010) claim that online competition would induce traditional retailers to locate mainly to suburban areas. Hou (2019, 2021) characterize the effect of online retailing on the equilibrium locations of traditional retailers in a Hotelling duopoly model. Furthermore, as noted by Abukhader (2008), consumer behaviour is likely to change when online retailing is possible. 3 Our paper also builds on other strands of research. First, it builds on the theoretical literature on transportation gas emissions (Cachon, 2014;Dilek et al., 2018;Park et al., 2015) by incorporating online competition within a theoretical framework. Second, it builds on the literature on online/offline competition (Balasubramanian, 1998;Bouckaert, 2000;Colombo & Matsushima, 2020;Guo & Lai, 2017;Nakayama, 2009) by explicitly addressing the environmental impact of online versus offline retailing. 4 While this is a common assumption in Hotelling-type models (e.g., D'Aspremont et al., 1979) to make the analysis feasible, it should be observed that online shopping has probably led to an expansion of retail spending. In this case, all else being equal, online retailing would imply greater transportation costs. We thank an anonymous reviewer for this comment. However, modelling online/offline competition in an uncovered market goes behind the scope of this paper. 5 Clearly, the consumer also returns to home. Therefore, every journey is a roundtrip. However, since this is true for every consumer, we can consider the trip from home to the store only. 6 We exclude the possibility that z is negative, which is explored by Colombo and Matsushima (2020). 7 We shall consider two alternative locations of the suppliers: x SA = x SB = 1/2 in the third section, and x SA = 0 and x SB = 1 in the fourth section. 8 Following Dilek et al. (2018), the transportation costs could include: the non-fuel variable cost to transport the vehicle per unit of distance, the amount of fuel used to transport the vehicle per unit of distance, the per unit cost of fuel, the amount of carbon emission released by consumption of one unit of fuel, the price of carbon or cost of emissions per unit released, and load carried by vehicle. (p. 148) In order to avoid the obvious pro-environmental effects of online retailing, we abstract from the possibility that the supplier could organize the delivery to the consumers in such a way to reduce the number of trips. 9 However, in the Appendix in the supplemental data online we also discuss the case where emissions linear in distance, and show that the results are qualitatively the same. 10 Of course, as pointed out by a referee, it might be that, under some circumstances, especially in urban areas, consumers might visit the shops by walking, cycling, taking public transport, etc. In this case, it might be that the unit transportation costs of the consumers are lower than that of the trucks. 11 In the present set-up, the marginal costs of the downstream retailers are represented by the wholesale prices. 12 There is another case where all consumers located at the right (left) of x L RA buy from firm RA (RB). This case is symmetric to the fringe-market structure illustrated in Figure 1, and it happens when x RA ≥ 1/2. Therefore, we limit our analysis to x RA ≤ 1/2. 13 The relevant thresholds in Lemma 1 are indicated in the Appendix in the supplemental data online. 14 There is a parameter space where no equilibrium exists. 15 The full derivation of the wholesale prices is relegated in the Appendix in the supplemental data online. It can be observed that the wholesale price of the supplier that serves the online retailer can be lower than that of the supplier that serves the physical retailer. In particular, this happens when the ratio z/c c is sufficiently high, that is, the competitiveness of the online retailer is low. Details are available from the authors upon request. 16 The equilibrium equations of the transportation gas emissions are reported in the Appendix in the supplemental data online. 17 Proposition 1 holds even when emissions are linear in distance. See the Appendix in the supplemental data online. 18 The equilibrium-indifferent consumer in the case of pure offline competition is 0.5, whereas it is: 16c c − c t + 56c 2 c − 24c c c t + c 2 c + 100zc c − 4zc t 2(25c c − c t ) in the case of online/offline competition, when the physical retailer locates at the endpoint and where x R RA < 0.5. Therefore, online competition reduces the market area of the physical retailer when the location is the same under both competitive environments. However, when the physical retailer does not locate at the endpoint, the indifferent consumer also moves to the right, thus enlarging the demand area of the physical retailer and determining an improvement in terms of the transportation costs. A similar analysis holds for the case of maximal distance between suppliers. 19 The relevant thresholds in Lemma 2 are indicated in the Appendix in the supplemental data online. 20 The full derivation of the wholesale prices is shown in the Appendix in the supplemental data online. 21 The complete expressions in (9) are reported in the Appendix in the supplemental data online. 22 When the emissions are supposed to be linear rather than quadratic, the results are qualitatively the same, as discussed in the Appendix in the supplemental data online. 23 As shown by Colombo and Hou (2021), when z/c c is sufficiently low, the traditional retailer would be driven out from the market. 24 We do not take into account the implications of online retailing for traffic congestions. For a theoretical analysis of e-commerce and traffic congestions, see Shao et al. (2016). 25 As already mentioned, we do not take into consideration the possibility for the upstream supplier that serves the consumers to organize the journey in such a way to reduce the overall transportation costs. This has an obvious pro-environmental effect of online retailing that might reduce the number of cases where online retailing is detrimental for the environment. However, this would not qualitatively change the main conclusions of our analysis, which highlights which factors make online retailing more likely to increase the transportation gas emissions. 26 For a general analysis of zoning in a duopolistic model with pure offline competition, see Bárcena-Ruiz et al. (2014). More generally, as argued by Zhao et al. (2017), 'the challenges of reduce pollution and realize more environment-friendly product distribution have drawn greater attention from the government, and policies should be formulated to address these concerns associated with the development of online shopping' (p. 1155).