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Impact of Congestion Charge and Minimum Wage on TNCs: A Case Study for San Francisco
{ Transportation network companies (TNCs) like Uber, Lyft and Didi, have dramatically changed urban transportation. While the emergence of TNC significantly benefits passengers and drivers, it also brings negative externalities that have to be addressed by regulatory intervention. In recent years, this concern has prompted several cities to take actions to regulate TNCs NYC2019surcharge, ban2018gan, SFSPUR, seattleregulation2020. Despite numerous works on the operation and management strategies of TNC platforms, only a handful of works have considered the mathematical model for policy analysis on the ride-hailing market. This paper aims to formulate an economic equilibrium model to evaluate the impacts of various regulations on the TNC economy.
{\bf Background and Motivation} \\ TNCs are disrupting the urban transportation systems. On the one hand, they offer on-demand ride services at prices that many riders can afford. On the other hand, they create numerous job opportunities for drivers working as independent contractors. These favorable demand and supply factors led to the TNC's explosive growth.} However, the resulting growth has raised two public concerns in large metropolitan areas. The first is due to increased traffic congestion. In New York City, Uber, Lyft, Juno and Via together dispatch nearly 600,000 rides per day, involving about 80,000 vehicles. Schaller schaller2017empty estimates that from 2013 to 2017 TNC trips in NYC increased by 15%, traffic speed dropped by 15%, VMT increased by 36%, and the number of TNC vehicles increased by 59%. He suggested regulation to reduce TNC vehicles deadhead time (when vehicles are carrying no passengers) in order to limit congestion. Two reports castiglione2016tncs,castiglione2018tncs by the San Francisco County Transportation Authority identified TNC impact on traffic congestion and estimated that TNCs account for approximately 50 percent of the increase in congestion in San Francisco between 2010 and 2016. More recently, Uber and Lyft commissioned Fehr & Peer to estimate the TNC share of VMT in six US Metropolitan Regions, Boston, Chicago, Los Angeles, Seattle, San Francisco and Washington. Their report balding2019 concludes that Uber and Lyft have a nontrivial impact in core urban areas such as San Francisco County, where they account for 12.8% of total VMT.
The second concern is provoked by the very low earnings of TNC drivers. The success of the on-demand ride-hailing business relies on short passenger waiting times that require a large pool of available but idle TNC drivers. This pushes down driver wages. Parrott and Reich parrott2018earning revealed that the majority of for-hire vehicle drivers in NYC work full-time. They found that the median driver earnings declined almost $\$$3 per hour from $\$$25.67 in September 2016 to $\$$22.90 in October 2017, and that 85 percent of drivers made less than the minimum wage after deducting vehicle expenses. A follow-up study parrott2020minimum examined the payments of drivers working for TNCs in Seattle and discovered that their average net earning is \$9.73/hour (after expenses), well below the \$16.39/hour minimum wage. Further, more than four-fifths of full time drivers purchased their vehicle primarily or partly to provide TNC services, and nearly three-fourths rely on TNC driving as their sole source of income. These drivers are hired as independent contractors, who can not unionize to negotiate for labor rights such as minimum wage, overtime compensation, and paid time-off.
These concerns have prompted cities to regulate TNCs. To address congestion, New York City Taxi and Limousine Commission (NYCTLC) introduced a \$2.75 charge on all for-hire vehicle trips that pass through the “congestion zone” of the city NYC2019surcharge. The congestion zone is the area south of 96th Street in Manhattan, and the charge is assessed on each trip that starts from, ends in, or passes through the congestion area. To protect TNC drivers, NYCTLC imposed a minimum per-trip wage for drivers amounting to a wage floor of \$25.76/hour or \$17.22/hour after vehicle expenses ban2018gan. This is equivalent to the \$15/hour minimum wage after deducting a paid-time off supplement of \$2.22/hour. In addition to NYC, similar regulations are being considered by other U.S. cities. In November 2019 Chicago approved a congestion tax on ride-hailing services for weekday single-passenger trips (and lowered the tax on shared trips) in the downtown area to raise \$40 million per year chicago_surcharge. Also in November 2019 San Francisco passed a special 3.25% excise tax on TNC rides to raise \$30-\$35 million per year for congestion mitigation projects SFSPUR. At around the same time, the Seattle City Council unanimously approved the “Fare Share” plan, which provides TNC driver protections including a fair wage after expenses and a first-in-the-nation Driver Resolution Center to offer support services for drivers to fight against unwarranted deactivations seattleregulation2020. In September 2019 California passed bill AB5 vox_gig which classifies hundreds of thousands of independent contractors (gig workers) including TNC drivers as employees to protect them with minimum wage and other employee benefits. These actions imply a changing regulatory environment to address TNC-provoked concerns in large cities.
{ {\bf Research Problem and Contribution} }\\ This paper presents a study calculating the impact on TNCs of the joint imposition of a congestion charge and a driver minimum wage. The impact is formulated within a framework comprised of a queuing theoretic model of the arrivals of passengers and drivers, a general equilibrium model that predicts market prices, passenger demand and driver supply, and a profit maximizing model of the TNC platform decisions. This framework enables the assessment of the impact in terms of changes in ride prices, passenger waiting time, driver wage, numbers of passengers and drivers, vehicle occupancy rate, platform rent, and city tax revenue. The key conclusions of this study are:
There is an extensive literature on app-based ride-hailing platforms. Many studies investigated the platform pricing strategy under various interacting factors. Zha et al zha2016economic developed an aggregate model to capture the interactions among passengers, drivers and the platform, and found that the first-best solution is not sustainable when the matching function exhibits increasing returns to scale and the cost function of the platform is subject to economies of scale. Bai et al Bai2018coordinating considered an on-demand service platform using earning-sensitive independent providers with heterogeneous reservation price, and concluded that it is optimal to charge a higher price when demand increases, and that the platform should offer a higher payout ratio as demand increases, capacity decreases, or customers become more sensitive to waiting time. Taylor taylor2018demand examined how delay sensitivity and agent independence affect the platform's optimal price and wage and identified the complexity caused by uncertainty in customer valuation. Hu and Zhou hu2019price studied the commission setting of the ride-sourcing platform and showed that an optimal fixed-commission contract can achieve at least 75% of the optimal profit when there is no pre-committed relationship between price and wage.
Platform pricing has also been studied with temporal and spatial considerations. From the temporal aspect, Cachon et al cachon2017role showed that surge pricing can significantly increase platform profit relative to contracts that have a fixed price or fixed wage, and that all stakeholders can benefit from the use of surge pricing on a platform with driver self-scheduling capacity. Castillo et al castillo2017surge showed that surge pricing can avoid cases where vehicles are sent on a wild goose chase to pick up distant customers, wasting driver time and reducing earnings. Zha et al zha2017surge investigated the impact of surge pricing using a bi-level programming framework, and showed that compared to static pricing, the platform and drivers are found generally to enjoy higher revenue while customers may be made worse off during highly surged periods. Banerjee et al banerjee2015pricing developed a queuing theoretic model to study the optimal (profit-maximizing) pricing of ride-sharing platforms. They show that the performance of a dynamic price (in terms of revenue and throughput) does not exceed that of a static price, but it is more robust to fluctuations of model parameters. From the spatial aspect, Bimpikis et al bimpikis2019spatial considered the price discrimination of a ride-sourcing platform over a transportation network and established that profits and consumer surplus at the equilibrium corresponding to the platform's optimal pricing are maximized when the demand pattern is “balanced” across the network's locations. Guda and Subramanian guda2019your studied the spatial pricing of a ride-sourcing platform over a transportation network and showed that surge pricing can be useful even in zones where supply exceeds demand. Zha et al zha2018geometric developed a model to investigate the effects of spatial pricing on ride-sourcing markets and found that the platform may resort to relatively higher price to avoid an inefficient supply state if spatial price differentiation is not allowed. In addition to platform pricing, studies also touch upon driver supply Hall_Kreuger, gurvich2019operations, platform operations yang2020optimizing, vazifeh2018addressing, platform competition nikzad2017thickness, bernstein2019competition, and regulations li2019regulating, benjaafar2018labor, yu2019balancing, vignon2020regulating. Please see wang2019ridesourcing for a comprehensive literature review.
Road pricing has attracted substantial research attention for decades. The idea was initially proposed by Pigou pigou2017economics, which inspired several seminal works including Vickery vickrey1955some, Walters walters1961theory and Beckmann beckmann1967optimal. Since then, various taxing schemes have been proposed in the literature, including charge based on cordon-crossing, distance traveled, time spent traveling, or time spent in congestion may2000effects. For instance, Zhang and Yang zhang2004optimal investigate the cordon-based second-best congestion pricing problem on road networks that jointly consider toll levels and toll locations. Yang et al yang2010road study road pricing for effective congestion control without knowing the link travel time and travel demand. Liu and Li liu2017pricing derive a time-varying toll combined with a flat ride-sharing price to nudge morning travelers to depart in off-peak hours. Despite this large literature in transportation economics, the research on congestion charges for TNCs is relatively scarce. A TNC congestion charge is distinctive since it involves decisions of the profit-maximizing platform and the passengers and drivers in the two-sided ride-hailing market. Li et al li2019regulating proposed a market equilibrium model to evaluate the impact of various regulatory policies and analyzed the incidence of a TNC tax on passengers, drivers, and the TNC platform. Schaller schaller2018making conducted an in-depth analysis of how to apply pricing to new mobility services, and recommended that a surcharge on taxi/for-hire trips in central Manhattan be applied as an hourly charge. Recent work of Vignon and Yin vignon2020regulating investigated the performance of various regulation policies on ride-sourcing platforms with congestion externality and product differentiation taken into account. They compared a uniform toll that treats all vehicles identically with a differentiated toll that treats idle vehicles, solo rides and pooled rides differently, and showed that a differentiated toll offers little advantage over a uniform one.
Only a handful of studies considered wage regulation of TNCs. Gurvich gurvich2016operations studied the platform's profit maximizing wage level for self-scheduling drivers, and showed that under a minimum wage, the platform limits agent flexibility by restricting the number of agents that can work during some time intervals. Parrott and Reich parrott2018earning utilized administrative data of New York City and showed by simulation that the proposed minimum wage standard in New York City will increase driver wage by 22.5 percent while hurting passengers by slightly increasing ride fare and waiting time. Li et al. li2019regulating and Benjaafar et al. benjaafar2018labor developed market equilibrium models to show that wage regulations on TNC will benefit both passengers and drivers, because wage regulation curbs TNC labor market power li2019regulating. Zhang and Nie zhang2019pool proposed a market equilibrium model for ride-sourcing platforms that offers a mix of solo and pooled rides. They showed that a wage floor on TNC drivers will force the platform to hire more drivers, which will reduce the appeal of collective modes and the supply efficiency and is likely to worsen traffic congestion.
This paper differs from the aforementioned works in that we explore the {\em joint} impact of congestion charge and driver minimum wage on the TNC market. We are the first to point out that distinct regulatory policies on TNCs do interfere with each other when they are jointly implemented, which may produce surprising market outcomes that deviate from the expectation of the policy maker. We are also the first to establish models that compare the trip-based congestion charge and the time-based congestion charge and identify the superiority of time-based congestion in certain regimes of practical interest. These results will provide valuable insights for city planners who are considering implementing (e.g., San Francisco), or have already implemented (e.g., NYC and Seattle) a congestion charge and a minimum wage to address TNC externalities.
We consider a transportation system comprised of a city council, a TNC platform, and a group of passengers and drivers. The city council approves legislation (e.g., cap on the total number of vehicles, minimum wage for TNC drivers, congestion charge on TNC trips) to regulate the operations of the TNC platform. The platform sets fares and wages and hires drivers to maximize its profit under these regulations. The pricing decisions affect the choices of passengers and drivers, and these choices collectively determine the platform's profit. We will describe a market equilibrium model to capture the decisions of passengers, drivers, and the TNC platform. The model will be used to investigate how TNC market outcomes are affected by regulation.
The TNC platform matches randomly arriving passengers to idle TNC drivers. Upon arrival, each passenger joins a queue and waits until she or he is matched to an idle driver\footnote{For simplicity, we do not consider the case of multiple passengers sharing the same vehicle.}. This matching is modeled as a continuous-time queuing process, in which each passenger defines a “job” and each driver is a “server”. The server is “idle” if the vehicle is not occupied, and it is “busy” if a passenger is on board or if the vehicle is dispatched and on its way to pick up a passenger. Assume that passenger arrivals form a Poisson process with rate $\lambda > 0$, and denote $N$ as the total number of TNC drivers. This matching process forms a M/G/N queue, and the expected number of idle servers (vehicles) is ${N_I} = N - \lambda /\mu $, with $\mu $ being the service rate ($1/\mu$ is the amount of time a passenger occupies a vehicle on average). We assume that $N > \lambda /\mu $. { Given the model parameters, the average waiting time for the M/G/N queue can be derived approximately in an analytical form. We comment that this is the ride confirmation time, which represents the time elapsed after the ride is requested and before the ride is confirmed. It differs from the pickup time (from ride confirmation to pickup), which will be treated below. }
The total travel cost of the TNC passenger consists of the waiting time for pickup, the travel time during the trip, and the monetary payment for the ride service. We refer to this total travel cost as the “generalized cost” and define it as the weighted sum of waiting time, travel time, and trip fare. It may differ for distinct passengers due to the randomness in trip length, trip duration, and the matching process of the TNC platform. Since we primarily focus on aggregate market outcomes, we define the average generalized cost as:
where ${t_w}$ is the average waiting time, $t_0$ is the average trip duration (in minutes), and $p_f $ is the average price of a TNC ride. The parameters $\alpha$ and $\beta$ specify the passenger trade-off between time and money. Note that $\alpha$ is generally larger than $\beta$ since empirical study suggests that the value of time while waiting is larger than the value of time while traveling in the vehicle. It is important to emphasize that we do not need to assume that all passengers have the same travel cost. The heterogeneity in passengers is irrelevant as we focus on the aggregate market outcome, which typically depends on the average cost $c$. A widely-studied example is the logit choice model, where the total number of agents choosing a particular mode only depends on the average cost of each mode. In this spirit, we define a demand function that determines the arrival rate of TNC passengers as a function of the average generalized cost:
where \({\lambda _0}\) is the arrival rate of potential passengers (total travel demand in the city), and \({F_p}( \cdot )\) is the proportion of potential passengers who choose a TNC ride. We assume that \({F_p}( \cdot )\) is a strictly decreasing and continuously differentiable function so that a higher TNC travel cost $c$ will lead to fewer TNC passengers. The logit model is a special case of ((ref)).
The passenger waiting time $t_w$ intimately interacts with other endogenous decision variables $\lambda$ and $N$. To delineate this relation, we divide a TNC ride into three time periods: (1) from ride being requested to the ride being confirmed, (2) from the ride being confirmed to passenger pickup, (3) from passenger pickup to drop-off. Let ${t_m}$, ${t_p}$, and ${t_0}$ represent the length of these three periods, respectively, then we have ${t_w} = {t_m} + {t_p}$, and ${t_0}$ as the average trip distance $L$ divided by traffic speed $v$, i.e., ${t_0} = L/v$. Since the platform immediately matches each newly arrived passenger to the nearest idle vehicle, ${t_m}$ is the average waiting time in the queue, and $t_p$ depends on the traffic speed $v$ and the distance of the passenger to the nearest idle vehicle, which further depends on the number of idle vehicles ${N_I}$. Therefore, we write $t_p$ as a function of $N_I$ and $v$, i.e., $t_p(N_I, v)$. The following assumption is imposed on $t_p(\cdot)$:
Assumption (ref) requires that the pickup time decreases with respect to the number of idle vehicles and the traffic speed. We suppose traffic speed $v(N)$ is a function of the total number $N$ of vehicles and impose the following assumption on $v(\cdot)$:
{ Using data of San Francisco and New York City for the M/G/N queue, we find that the ride confirmation time $t_m$ is very short, i.e., less than 1 seconds. This is negligible compared to the pickup time \({t_p}\), which is typically around 3-5 minutes.} Therefore we ignore \({t_m}\) and express the total waiting time \({t_w}\) as\footnote{The waiting time can be significantly larger in rush hours. In this case, one can add $t_m$ to $t_w$ as the waiting time in the queue. We believe that this will not affect our conclusion, but we neglect this term in this paper for analytic tractability.}
The number of idle vehicles $N_I$ depends on $\lambda$ and $N$, whereas the average traffic speed $v $ depends on $N$.
In the TNC market, drivers can decide whether to remain subscribed to the TNC platform depending on the long-term average earnings offered by the platform. The average hourly wage of drivers depends on the ride fare of the TNC trip, the commission rate set by the platform, and the occupancy rate of the vehicles. It can be described as:
where $p_d$ is the average per-trip payment to drivers. The driver payment \({p_d}\) differs from the passenger trip fare $p_f$. The difference $p_f-p_d$ is kept by the platform as profit. Therefore, the commission rate of the platform (typically 25%-40%) can be written as $(p_f-p_d)/p_f$. The average hourly wage ((ref)) is just the total platform payment to all drivers $\lambda {p_d}$ divided by the total number of drivers $N$. Each driver may have an hourly earning that differs from the earning of others due to the randomness in work schedule, driver location, and repositioning strategy. However, as we primarily focus on the aggregated market outcome, the heteregeneity in driver earnings is irrelevant as far as the aggregate market outcome (e.g.,total number of TNC passengers or drivers) only depends on the average hourly earning over all TNC drivers. Note that this is the case for the well-established logit choice model. More generally, we define a supply function that determines the total number of TNC drivers as a function of the average hourly wage:
where $N_0$ is the number of potential drivers (all drivers seeking a job), and $F_d(w)$ is a strictly increasing and continuously differentiable function that gives the proportion of drivers willing to join TNC. Note that the logit model is a special case of ((ref))
The TNC platform determines the ride prices and the driver payment to gauge passengers and drivers to maximize its profit. In each time period, the platform revenue is the total ride fares received from passengers, i.e., $\lambda p_f$, and the platform cost is the total payment made to the drivers, i.e., $\lambda p_d$. The profit of the platform can be thus written as the difference between the revenue and the cost
where ((ref)) is the demand function and ((ref)) is the supply function. Note that $t_p$ depends on $\lambda$ and $N$, and $t_0$ depends on the traffic speed which is a function of $N$. The overall problem not only involves $p_f$ and $p_d$ as decision variables, but also involves $N$, $\lambda$, $t_p$, $v$ and $t_0$ as endogenous variables. The optimal solution to ((ref)) represents the platform's profit-maximizing pricing decision in absence of the regulatory intervention.
{ The profit maximization problem ((ref)) is a constrained optimization which can be solved by various gradient-based algorithms bertsekas1997nonlinear. However, since the problem is non-concave with respect to $p_d$ and $p_f$, it is difficult to assert whether the obtained solution is globally optimal. To address this concern, we apply a change of variable and treat $\lambda$ and $N$ as the new decision variables. More specifically, given $\lambda$ and $N$, we can use ((ref))-((ref)) to uniquely determine $p_f$ and $p_d$ as follows:
where ((ref)) is derived from ((ref)), and ((ref)) is derived from ((ref)). Note that the right-hand sides of ((ref)) and ((ref)) are both functions of $\lambda$ and $N$. By plugging ((ref)) and ((ref)) into ((ref)), we can transform the profit maximization problem ((ref)) into the following unconstrained optimization:
where $\lambda$ and $N$ are decision variables. Clearly, ((ref)) is equivalent to ((ref)). We note that although ((ref)) is non-concave with respect to $\lambda$ and $N$, under certain mild conditions, it is concave with respect to $\lambda$ for fixed $N$. We formally summarize this result as the following proposition:
The proof can be found in Appendix A. Proposition (ref) suggests that for any fixed $N$, we can efficiently derive the unique optimal $\lambda$ that maximizes the profit by solving a concave program. This result is based on a few mild assumptions: (a) the logit model ((ref)) is used for studying customer discrete choice, (b) the convexity of $t_p(\cdot)$ simply requires that the marginal benefit of adding extra idle vehicles in reducing passenger waiting time decreases with respect to $N_I$, which is consistent with intuition. Based on this result, we can obtain the optimal combination of $(\lambda, N)$ by enumerating over $N$. This provides the globally optimal solution to ((ref)). }
Regulation policies, such as congestion charge and driver minimum wage, modify the incentives of passengers and drivers and affect the pricing decision of the TNC platform. To capture this effect, we formulate the platform pricing problem under the minimum wage, trip-based congestion charge, and time-based congestion charge.
{\bf Minimum wage:} To capture the impact of a driver wage floor $w_0$, we impose the constraint that requires the driver hourly earning to be greater than $w_0$. The optimal pricing problem under minimum wage regulation can be formulated as:
where constraint ((ref)) captures the wage floor on TNC driver earnings. Note that we relax the equality constraint ((ref)) to inequality constraint ((ref)). This permits the TNC platform to hire a subset of drivers who are willing to work for TNC in case the minimum wage is set so high that it is unprofitable for the platform to hire all the willing drivers in the market.
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{\bf Trip-based congestion charge:} Many existing congestion charge schemes are trip-based (e.g., New York City, Seattle, Chicago). The trip-based congestion charge assesses an extra fee of $p_t$ on each TNC trip in the congestion area. When a congestion charge $p_t$ and a minimum wage $w_0$ are imposed concurrently, the optimal pricing problem can be formulated as follows:
where the per-trip congestion charge $p_t$ is incorporated into the passenger travel cost within the demand function ((ref)). Another way to formulate the congestion charge is by adding it to the cost of the platform. This is easier to implement as it only requires the platform to transfer the accumulated congestion charge of all trips within certain period to the city. In this case, the optimal pricing problem can be written as:
where $p_t$ is incorporated into the profit of the platform instead of the travel cost of the passengers. Economists find that whether a tax is levied on the buyer or seller of the good does not matter because they always share the tax burden based on their elasticities varian2014intermediate. This principle also applies here:
Proposition (ref) states that the two formulations of trip-based congestion charge, i.e., ((ref)) and ((ref)), lead to the same market outcome. The proof is omitted since it can be simply derived by a change of variable.
{\bf Time-based congestion charge:} Distinct from the trip-based congestion charge, the time-based charge is levied on TNC vehicles based on vehicle hours instead of trip volumes. The key difference between the two congestion charge schemes is that time-based congestion charge not only penalizes TNC trips, but also penalizes idle TNC hours and thus incentivizes the platform to increase vehicle utilization. When the time-based congestion charge $p_h$ and a minimum wage $w_0$ are concurrently levied on TNC drivers, we have the following formulation:
When the time-based congestion charge is levied on the TNC platform, we have the following formulation:
Similar to the trip-based congestion charge, these two forms of formulations are equivalent.
Proposition (ref) states that the two formulations of time-based congestion charge, i.e., ((ref)) and ((ref)), lead to the same market outcome. The proof is omitted since it is similar to that of Proposition (ref).
This section analyzes the joint impact of a trip-based congestion charge and a minimum wage for TNC drivers. We consider a platform that determines the ride fare $p_f$ and the per-trip driver payment $p_d$ to maximize its profit $\lambda(p_f-p_d)$ under the trip-based congestion charge $p_t$ and a minimum wage $w_0$. The optimal pricing problem can be formulated as ((ref)) or ((ref)). For sake of exposition, we will start with a realistic numerical example for San Francisco. The numerical example will be complemented by a theoretical analysis presented later that shows the insights derived from the numerical example can be generalized.
We investigate the impact of the proposed regulations via a case study for San Francisco (followed by theoretical analysis in the next subsection). Assume that passengers choose their transport mode based on the total travel cost. We use a logit model so the demand function for TNC rides is
where $c$ is the total travel cost of a TNC trip, and $\epsilon>0$ and $c_0$ are parameters. Similarly, drivers choose to work for the TNC depending on its wage. Under a logit model, the supply function is
where $\sigma$ is a parameter. We note that ((ref)) is a special case of the general demand function ((ref)), and ((ref)) is a special case of the general supply function ((ref)).
Passenger pickup time $t_p$ follows the “square root law” established in arnott1996taxi and li2019regulating:
where the constant $M$ depends on the travel times in the city. The square root law establishes that the average pickup time is inversely proportional to the square root of the number of idle vehicles in the city, $(N - \lambda /\mu)$. The intuition behind ((ref)) is straightforward. Suppose all idle vehicles are uniformly distributed throughout the city, then the distance between any two nearby idle vehicles is inversely proportional to the square root of the total number of idle vehicles. This distance is proportional to that between the passenger and the closest idle vehicle, which determines the pickup time. A justification of the square root law can be found in li2019regulating.
The average traffic speed $v$ is a function of the total traffic. Using Greenshield model greenshields1953study gives the linear speed-density relation\footnote{Since TNC vehicles only account for a small percentage of the overall traffic, the Greenshield model can be regarded as a linear approximation in a small neighborhood of a nonlinear speed-density function.},
where $N_b$ is the background traffic\footnote{TNC trips may substitute taxis or private vehicles. This may introduce coupling between the TNC demand and the background traffic $N_b$. For simplicity, we neglect this substitution effect and assume $N_b$ is exogenous. We leave it for future work to investigate how the coupling between $\lambda$ and $N_b$ affect the conclusion of this paper. }, $N$ is the number of TNC vehicles, and $v_0$ and $\kappa$ are model parameters. Assuming that $N_b$ is constant, ((ref)) is equivalent to
In summary, the model parameters are \[{\Theta}=\{\lambda_0, N_0, M, L, v_f, \kappa, \alpha, \epsilon, c_0, \sigma, w_0\}. \] In the numerical study we set the parameters values so that the optimal solution to ((ref)) matches the real data of San Francisco city. The values of these model parameters are summarized below: \[ \lambda_0=1049/\text{min}, \, N_0=10000, \, M = 41.18, \quad L=2.6 \text{ mile}, \quad {v_f} = 15 \text{ mph},\quad \kappa = 0.0003,\] \[\alpha=2.33, \, \epsilon=0.33, \, c_0=31.2, \, \sigma=0.089, \, w_0=\$31.04/\text{hour}.\] For the data source (from San Francisco) and justification of these parameter values, please refer to Appendix B.
We solve the profit maximizing problem ((ref)) for different values of congestion charge $p_t$ under a fixed wage floor $w_0$, and plot all the variables as a function of $p_t$. The minimum wage of TNC drivers in San Francisco is set in a way similar to that in NYC. Under current NYC regulations, the TNC driver minimum wage is $\$25.76$/hour, which is equivalent to the $\$15$/hour minimum wage of NYC after deducting vehicle expenses such as insurance, maintenance and taxes. Since the hourly minimum wage of San Francisco is $\$0.59$ higher than in NYC, we set $w_0=\$25.76+\$0.59=\$26.35$/hour to compensate for this difference.
Figure (ref)- Figure (ref) show the number of drivers, passenger arrival rate, and the occupancy rate of TNC vehicles as a function of the congestion charge $p_t$ when the minimum wage is set at $w_0=\$26.35$/hour. Figure (ref) shows the per-trip ride fare $p_f$ and the driver payment $p_d$. Figure (ref)-Figure (ref) show the passenger pickup time and travel cost. Figure (ref) shows the driver wage (which equals the minimum wage). Figure (ref) and Figure (ref) show the platform profit and city's tax revenue under different values of ${p_t}$, respectively.
Clearly, the optimal solution as a function of $p_t$ has two distinct regimes:
This is a surprising result: the number of drivers is unaffected by the congestion charge $p_t$ when $p_t\leq \$2.1$/trip. It is in contrast with the case when there is only a congestion charge and no minimum wage (see li2019regulating). Therefore, this set of result indicates that the effect of a congestion charge on congestion relief is mitigated by the wage floor on TNC drivers. In certain regimes, the congestion charge cannot directly curb traffic congestion by reducing the number of TNC vehicles.
The reason behind this surprising result is rooted in the platform's power in the labor market. The platform is a monopoly in the labor market and sets driver wages. When there is no regulation (i.e., ${p_t} = 0$ and ${w_0} =0$), the platform hires fewer drivers to maximize its profit compared to a competitive labor market where the TNC faces the competitive driver wage. In a certain regime, the minimum wage squeezes the platform's market power and induces it to hire more drivers li2019regulating. This indicates that the marginal profit of hiring additional drivers under the minimum wage regulation is positive. When the congestion charge is insignificant, this marginal profit reduces but remains positive, and thus the platform still hires all drivers available in the labor market. The number of drivers is upper bounded by $N\leq N_0F_d(w_0)$. Therefore, in the first regime, $N$ remains constant and satisfies $N=N_0F_d(w_0)$. If the congestion charge is further increased, the marginal profit of hiring an additional driver reduces to zero, and the system enters the second regime.
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Figures (ref)-(ref) show that the tax burden primarily falls on the ride-hailing platform as opposed to passengers and drivers. As the trip-based charge increases, the passenger cost increases slightly, the driver wage remains unchanged, while platform profit reduces significantly. In particular, under a trip-based tax of \$2/trip, passenger cost increases by 0.6%, driver wage remains constant, and platform profit declines by 59.5%. This is because drivers are protected by the minimum wage, and the passenger's price elasticity\footnote{The passenger price elasticity is $\dfrac{\partial \lambda}{\partial p_f}\dfrac{p_f}{\lambda}$. We calculate $\dfrac{\partial \lambda}{\partial p_f}$ assuming that the waiting time $t_w$ is fixed under different $p_t$. This is a reasonable approximation since $t_w$ does not change significantly under distinct $p_t$ (Figure (ref)).} is relatively high (Figure (ref)) so that the platform has to refrain from significantly increasing the ride fare.
We show that the result reported in Figure (ref)-Figure (ref) (including number of drivers, number of passengers, platform revenue, and tax revenue) is robust for a large range of model parameters. For notation convenience, let $\tilde w$ be the optimal driver wage set by the platform in the absence of any regulation (i.e., ${p_t} = {w_0} = 0$), and denote by ${N^*_t}({p_t})$ the optimal number of drivers to ((ref)) under a fixed wage floor, which depends on $p_t$. We then have the following result.
The proof of Theorem 1 is can be found in Appendix C. It states that for any wage floor in an appropriate range, there is always a regime in which the congestion charge does not affect the number of TNC vehicles or drivers. In this case, the congestion charge will not directly curb the congestion by reducing the number of TNC vehicle on the city's streets. Instead, it can only indirectly mitigate the traffic congestion by collecting taxes to subsidize public transit to attract passengers. Note that $\tilde{w}$ and $w_1$ can be calculated numerically, and ${\bar p_t}$ depends on the wage floor ${w_0}$. For the case of San Francisco, we calculate that $\tilde{w}=\$21.55$/hour, $w_1=\$29.20$/hour, and $\bar{p}_t=\$2.1$/trip when $w_0=\$26.35$/hour.
This section considers the profit maximization problem under a wage floor and a time-based congestion charge. Under the time-based charge, each vehicle is penalized based on the total time it stays active on the platform (whether there is a passenger on board or not). Let $p_h$ denote the per-vehicle per-unit-time congestion charge. The total charge (per unit time) is $N p_h$, and the profit maximization problem is cast as ((ref)). For sake of exposition, we will first present a numerical example for San Francisco. The insights derived from the numerical study will be examined by theoretical analysis later to demonstrate its independence on model parameters.
In the numerical study, we will solve the profit maximization problem ((ref)) for different time-based congestion charge $p_h$ under a fixed wage floor $w_0=\$26.35$/hour. The model parameters of ((ref)) are the same as those in Section (ref).
Figure (ref) - Figure (ref) display the number of drivers, passenger arrival rates, and vehicle occupancy as a function of the time-based congestion charge. Figure (ref) shows the ride fare and per-trip driver payment. Figure (ref) and Figure (ref) show the passenger pickup time and total travel cost. Figure (ref) shows the driver wage. Figure (ref) and Figure (ref) present the platform profit and tax revenue, respectively. Clearly, the plots in Figure (ref)-(ref) have two distinct regimes:
Simulation results suggest that the time-based congestion charge does not affect the number of TNC vehicles unless the charge is greater than $\$6.2$/hour. In that case the effect of the congestion charge on congestion relief is mitigated by the minimum wage on TNC drivers. This observation is consistent with the results in Section (ref) and for the same reason. However, in contrast with the trip-based charge, the time-based charge does not affect passenger arrivals (Figure (ref)). This indicates that the time-based charge leads to a direct money transfer from the platform to the city in the first regime without affecting the passengers or drivers. This is evidenced by the linear curves in the first regime of Figure (ref)-(ref).
The quantitative results in Figure (ref)-Figure (ref) are robust with respect to the variation of model parameters. Formally, denote by ${N^*_h}({p_h})$ and $\lambda^*_h(p_h)$ the optimal number of drivers and passenger arrival rates to ((ref)) under a fixed wage floor. We have the following result.
The proof of Theorem (ref) can be found in Appendix D. Theorem (ref) states that there exists a regime under which both the number of TNC drivers and the passenger arrival rates are unaffected by the congestion charge. This indicates that the ride fare, driver wage and passenger cost remain constant in this regime and the congestion charge is entirely imposed on the platform through a direct money transfer from the platform to the city. In this scheme, congestion charge will not directly curb the congestion by reducing traffic in the city. Instead, it can only indirectly mitigate traffic congestion by collecting taxes to subsidize public transit.
This section provides a comparison of the trip-based and time-based congestion charges. To ensure a meaningful comparison, we first set a target for the city's tax revenue. This target can be achieved by setting the appropriate charges. For each scheme, we find the charge that exactly attains the targeted tax revenue and we compare the two schemes for the same target. The model parameters are consistent with previous case studies in Section (ref) and Section (ref).
Figures (ref)-(ref) compare the number of drivers, passenger arrival rate and the vehicle occupancy of the two schemes for different targets for the city's tax revenue. Figure (ref) and Figure (ref) compare the ride fare and the pickup time for the two schemes. Figure (ref) compares the platform profit under the trip-based and time-based charges. These results reveal that for the same realized tax revenue, the time-based charge is Pareto superior to the trip-based charge (as currently implemented in NYC). Under the time-based charge, the TNC platform earns a higher profit. For drivers, the time-based congestion charge does not affect their surplus in the first regime as the same number of drivers are hired at the same wage. For passengers, the time-based charge leads to a lower ride fare but a longer waiting time. However, the time-based congestion charge also has higher passenger arrival rate (Figure (ref)). Since the demand function $F_p(c)$ is monotonic, this implies that the total travel cost $c$ is lower and the passenger surplus is higher under the time-based congestion charge.
In summary, the time-based congestion charge leads to higher passenger surplus and higher platform profit (Figure (ref)), which benefits all participants of the transportation system. This is because the time-based congestion surcharge penalizes idle vehicle hours and motivates the TNC to increase the occupancy rate of the vehicles (see Figure (ref)). Based on the data for San Francisco, the surplus resulting from increased vehicle occupancy will be distributed to all market participants, including the passengers, the TNC platform, and the city.
While the aforementioned results do not necessarily hold for all levels of targeted tax revenues, the conclusion is indeed applicable for a large range of model parameters in the regime of practical interest. To formally present this claim, we define $N_t^*, w_t^*, \lambda_t^*, c_t^*, P_t^*, Tr_t^*$ as the optimal solution to ((ref)) and denote $N_h^*, w_h^*, \lambda_h^*, c_h^*, P_h^*, Tr_h^*$ as the optimal solution to ((ref)). They are respectively the optimal number of drivers, driver wage, passenger arrival rate, total travel cost, platform profit, and city tax revenue. Note that all variables with subscript $t$ depend on $p_t$ and $w_0$, and all variables with subscript $h$ depend on $p_h$ and $w_0$. We suppress this dependence to simplify the notation whenever it is clear from the context.
The proof of Theorem (ref) can be found in Appendix E. It shows that there exists a regime where a time-based charge offers a Pareto improvement over a trip-based one. In this regime, for any trip-based charge, one can find an appropriate time-based charge for which the same number of drivers is hired, more passengers take TNC rides at a lower cost, the platform earns more profit, and the city collects more tax revenues to subsidize public transit. For the case of San Francisco, we calculate $w_3=\$29.20$/hour, and $\bar{p}_t=\$2.1$/trip when $w_0=\$26.35$/hour.
This section reports a sensitivity analysis to test the robustness of our results with respect to the model parameters. We vary the model parameters of ((ref)) and evaluate the impact of the time-based congestion charge under distinct parameter values. The nominal values of the parameters are set to be the same as in Section (ref). We perturb $\lambda_0, N_0$ and $\alpha$ by $5\%$ and investigate how these perturbations affect passengers, drivers, and the TNC platform under the time-based charge.
Figure (ref)-(ref) show the number of drivers, passenger arrival rate, and the platform profit as functions of the time-based congestion charge under different $\lambda_0$ (the nominal value is 1049). Clearly, there are two regimes. When $\lambda_0$ increases, the TNC platform has more passengers, and therefore enjoys a higher profit. However, we note that in the first regime, the number of drivers is not affected by $\lambda_0$. This is because in the first regime, both ((ref)) and ((ref)) are active, which determines $N$ as $N=N_0F_d(w_0)$.
Figure (ref)-(ref) show the number of drivers, passenger arrival rate, and the platform profit as functions of the time-based charge for different $N_0$ (the nominal value is 10K). There are clearly two regimes for the three values of $N_0$. When $N_0$ increases, the platform hires more drivers, attracts more passengers and collects a higher profit. Platform profit is insensitive to the number of potential drivers.
Figure (ref)-(ref) show the number of drivers, passenger arrival rate, and the platform profit as functions of the time-based charge for different $\alpha$ (the nominal value is 2.33). When $\alpha$ increases, both passenger arrival rate and platform profit drop. We note that the platform profit is much more sensitive to $\alpha$ than it is to $\lambda_0$ and $N_0$.
This paper describes the impact of two proposed congestion charges on TNC: (a) a charge based on vehicle trips, and (b) a charge based on vehicle hours. We used a market equilibrium model to assess the joint effect of minimum wage with either of these two charges. Surprisingly, we find that neither charging scheme significantly affects the number of TNC vehicles since their effect is mitigated by the wage floor on TNC drivers. Furthermore, we find that the time-based charge is Pareto superior compared with the trip-based charge that is currently imposed in New York City. Under the time-based charge, more passengers take TNC rides at a cheaper overall travel cost, drivers remain unaffected, the platform earns a higher profit, and the city collects more tax revenue from the TNC system to subsidize public transit.
The policy implication of these results are profound. First of all, our results imply that the TNC driver minimum wage mitigates the effectiveness of the congestion charge (either time-based or trip-based) in reducing the TNC traffic. Therefore, when a driver minimum wage is imposed, the city can not merely count on the congestion charge to reduce the number of TNC vehicles on the city's street, unless the charge is significant and exceeds certain threshold. Second, { the TNC profit is rather sensitive to regulations such as minimum wage and congestion charges. Based on calibrated model parameters, we showed that the tax burden mainly falls on the ride-hailing platform as opposed to passengers and drivers. We argue that this effect should be taken into account in policy formulation, and an interesting research direction is to synthesize more effective policies that achieve the regulatory objective without jeopardizing the TNC business model, e.g., li2020off. } Third, our result suggests that the time-based congestion charge is superior to the trip-based congestion charge. While most city selects the trip-based congestion charge as a natural candidate of its charge scheme (e.g., NYC, Chicago, Seattle), a shift to the time-based congestion charge is not difficult to implement: the city only needs to periodically audit the operations data of the TNC and collect the charge based on the accumulated vehicle hours on the platform.
Future research directions include determining the optimal level of congestion charge that maximizes social welfare, extending the model to capture temporal and spatial aspect of the TNC market, and characterizing the impact of regulatory policies on TNC competition.
This research was supported by the Hong Kong Research Grant Council project HKUST26200420 and National Science Foundation EAGER award 1839843.