Surge Pricing and Labor Supply in the Ride- Sourcing Market

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1 Surge Pricing and Labor Supply in the Ride- Sourcing Market Yafeng Yin Professor Department of Civil and Environmental Engineering University of Michigan, Ann Arbor *Joint work with Liteng Zha and Yuchuan Du (Tongji University) 1

2 Ride Sourcing Ride sourcing refers to an emerging urban mobility service that private car owners drive their own vehicles to provide for-hire rides (Rayle et al. 2014). Companies like Uber and Lyft provide ride-hailing apps that intelligently match participating drivers to riders. These apps are free to use but usually a commission is charged for each transaction/ride (20-25% of the fare paid by the rider). 2

3 Surge Pricing Since their advent in 2009, ride-sourcing companies have enjoyed huge success, but have created many controversies as well. One of them centered on dynamic pricing (e.g., Uber s surge pricing and Lyft s prime time pricing) that price is algorithmically adjusted for different geographic areas and updated periodically 3

4 Surge Pricing (Cont d) Spatially differentiated dynamic pricing Surge multiplier times a base price Both customers and drivers are informed before a transaction occurs Falls within 1-2 (most of the cases) but can soar to 7 times or even higher without a cap 4

5 Surge Pricing (Cont d) Advertised to be passively triggered to help balance supply and demand Unlimited price surge can be troublesome particularly when ride sourcing is one of the few viable options As platforms generally benefit from the surges, prices may surge unnecessarily higher or more frequently to exploit customers 5

6 Research Motivation It is thus necessary to investigate the impacts of surge pricing and derive insight on how to better manage or regulate the scheme Surge pricing directly influences the spatial and temporal distribution of ride-sourcing labor supply. Previous studies, e.g., Chen et al. (2015) and Zha and Yin (2017), have investigated its spatial impacts This paper focuses on investigating how surge pricing may temporally redistribute the supply of ride-sourcing vehicles 6

7 Research Objective We propose a mathematical framework to describe the equilibrium of ride-sourcing market while explicitly considering ride-sourcing drivers work scheduling behaviors under surge pricing The equilibrium framework is applied to investigate the impacts of surge pricing and then discuss potential management policies 7

8 Outline Basic Premise Equilibrium Model Modeling and Analysis of Surge Pricing 8

9 Basic Premise 9

10 Two-Sided Market 10

11 Platform Matching Matching Function (Yang and Yang, 2011) vt N c N c t vt c m = M( N, N ) : number of the vacant ride-sourcing vehicles at any moment : number of the waiting customers at any moment. It is assumed that, vt c M N > 0 M N > 0 11

12 Platform Matching (Cont d) Matching Function c t vt c m = M( N, N ) N = wt vt t vt N c = c w Q T w Q vt t w c is the arrival rate of vacant vehicles per hour is the average searching time for a driver to find a customer is the customers arrival rate per hour. is the average customer waiting time At the stationary state (, ) (, ) c t vt c t vt c m = M N N = M wt wq c t vt m = Q= T t c (, ) Q= M wq wq w c t = W( Q, w ) 12

13 Demand and Supply Customer Demand where: c (,, ) Q= f F w l c w :average waiting time of the riders l :average trip time Fleet Status Conservation vt o vt t t u = N + N = T w + Ql = Qw + Ql 13

14 Basic Modeling System System of Equations for Ride-for-Hire System w c t = W( Q, w ) ( c,, ) Q= f F w l u = Qw t + Ql Given F and u, we can solve the system to obtain Q, w t and w c. 14

15 System Adopted in This Paper w c = 2v k t wq u = Qw t + Ql S ( c ) ( ) Q = Qexp θ F + βw + τl Ru ( ) = ( 1 η ) u FQ (Daganzo, 1978; Arnott, 1996) The system implicitly defines a drivers revenue function R(u) 15

16 Revenue Function It is assumed that: Ru ( ) u < 0 This assumption is generally valid. However, it is possible that more vehicle hours would increase the average hourly revenue for the drivers. Such a scenario occurs with an unrealistically small size of ride-sourcing fleet (Yang et al., 2005; Yang and Yang, 2011). 16

17 Equilibrium Model 17

18 Labor Supply Whether, when and how long does a driver work? Ride-sourcing drivers enjoy flexibility in work hour scheduling Competing theories exist on how drivers respond to hourly wage variation. For example, the number of work hours: log hr = β0 + β1log wage + Xβ- β 1 > 0 β < 1 0 Drivers work longer as hourly wage increases: neo-classical hypothesis Drivers work less as hourly wage increases: income-targeting hypothesis (or more general reference dependent hypothesis) 18

19 Labor Supply (Cont d) Empirical evidences are mixed Neo-classical β 1 > 0 Jonathan et.al (2015) Farber (2004) Farber (2005) Farber (2008) Chen et.al (2016) Farber (2015) Chou (2000) β 1 < 0 Camerer et.al (1997) Crawford et.al (2011) Vincent (2016) Income-targeting 19

20 Time-Expanded Network 1 1' 2 2' A0 R a ( u a ) O 3 3' D A1 A2 4 4' A3 A ' 20

21 Cost Structure pm ϖ ( ) 2 m p pm m p m p C = caδa + c = caδa + ϖ1 h, p P, m M a A a A m Disutility when traversing each link (additive) Disutility of continuously working (path specific and non-additive) where PM ; : p δ a : m ϖ : 1 m ϖ 2 : set of paths; set of driver classes link-path incidence cost associated with cumulative working hours captures the aversion to working long hours 21

22 Utility Specification Neo-Classical: pm pm p U = R C, p P, m M Income Targeting (Farber, 2015): where m I : ( ρ )( ) ( ρ )( ) pm m p m p m 1 0, pm + R I C + U R < I U =, p P, m M m p m pm p m 1 R I C + U0, R I target income level p R m ρ : : average revenue of choosing path p controls the degree of loss-aversion and is assumed to vary between [0,1) 22

23 Market (Network) Equilibrium Drivers are assumed to choose work schedules to maximize their utilities At equilibrium, all chosen schedules would offer the same level of utility, which is higher than or equal to that of any unchosen schedule For each driver class, all paths that carry positive flows yield equal utility, which is no less than that of any unused path 23

24 Mathematical Definition where f pm : ( f ) U m U pm () f pm = 0, m M, p P m pm U U () f 0, m M, p P pm f 0, m M, p P p P pm m f = N, m M pm U : the pay-off of drivers of class m choosing path p; the number of drivers of class m choosing path p U m = pm max ( U ) p P m N : the number of drivers of class m 24

25 Variational Inequality Define Ω= f pm = N m, f pm 0, m M, p P p P The equilibrium solution can be found by finding that satisfies: f * Ω ( pm * )( pm pm f ) p m U ( ) f f 0, m M, p P, f Ω 25

26 Neo-Classical Formulation min u a a( ) a a a A m M a A p P m M Z = R w dw + c u + c f f 1 0 m m pm pm s.t. p P pm m f N, m M pm f 0, p P, m M pm p u = f δ, a A a m p a * *All ride-sourcing vehicles that provide service during a time period are assumed to be available for the following period. 26

27 Solution Algorithm Both formulations have two distinctive features. Namely, the revenue function is implicitly defined and path costs are not link-additive Various path-based solution algorithms can be applied to solve the formulations, in combination with a column generation scheme to avoid path enumeration 27

28 Numerical Experiments Base Demand (hour) 35,000 30,000 25,000 20,000 15,000 10,000 5, Starting hour ( θ ( β c τ )) 1 Q = Q exp F + w + l, b A b b b b b b b b We assume that 1) demand sensitivity of price ( θ b ) is lower in peak hours; 2) values of time ( βb, τb) are higher in peak hours. 28

29 Numerical Experiments (Cont d) We consider 4 driver classes and each of them has a fleet size of 2,000 vehicles: m = 1, prefer to start early (7:00-10:00 a.m.) work long hours ( ϖ 1 1 = 2 ) m = 2, prefer to start early (7:00-10:00 a.m.) work short hours ( ϖ 2 1 = 3 ) m = 3, prefer to start early (15:00-19:00 p.m.) work long hours ( ϖ 3 1 = 2 ) m = 4, prefer to start early (15:00-19:00 p.m.) work short hours ( ϖ 4 = ) 1 3 The income target for the corresponding driver class is assumed to be: I m $200, m = 2, 4 = $300, m = 1,3 29

30 Neo-classical Start time End time Work Rest Revenue hours (hr) hours (hr) ($) Cost ($) Profit ($) Path flow(veh) Class Class Class Class

31 Income-Targeting Start time End time Work hours (hr) Rest hours (hr) Class 1 Revenue ($) Cost ($) Utility ($) Path flow(veh) Class Class Class

32 Modeling and Analysis of Surge Pricing 32

33 Surge Multiplier Fare structure F F F b A b = 0 + γ, b b 1 where F 0 : F b γ b = ω l : b b : flag-drop fee time-based charge surge multiplier 33

34 Revenue-Maximizing Surge Pricing s.t. πλf,,, γ> 0 1 ( ) 0 b b b b A max J = η F + γ F Q where: G ( ) G πλf,, γ = 0 ( ) is a gap function used to characterize the equilibrium of drivers work scheduling 34

35 Numerical Example Surge Multiplier Hour 35

36 Impact of Surge Pricing 5 Average waiting time Average searching time 25 Average Waiting Time (min) Average Searching Time (min) Hour 0 36

37 Welfare Impacts Benchmark for comparison Optimal static revenue-maximizing pricing where the surge multiplier is 2.02 for all study periods Metrics Passengers: consumers surplus Platform and drivers: joint revenue 37

38 Welfare Impacts (Cont d) 4 2 $ x10, Change of consumers' surplus Hour Change of joint revenue 38

39 Regulation Policy Commission cap regulation, if the platform exhibits evident market power Fixed percentage -> fixed cap (e.g., 20%-> $4) Practically implemented as mile-based or timebased charge (i.e., $/mile, $/hour) With a properly chosen cap, a revenue-maximizing platform will have incentive to maximize the number of transactions (realized demand), which are positively related to consumers surplus; the additional revenue from price surge completely goes to the drivers 39

40 Impact of Regulation max Jˆ = ˆ ηbqb πλ,f,γ, > 0,ηˆ 0N, 0 s.t. b A ( πλf γηn ˆ ) G,,,, = 0 λ π R ˆ ηb η, b A 1 1 where R π : is the vector of the reservation profit levels (per work session); η : commission cap. 40

41 Regulation Outcome Ratio of Platform's Revenue to Total Revenue Revenue ratio Surplus ratio Commission Cap ($/trip) Ratio of Social Surplus to That in the Second-best A proper choice of commission cap (if necessary) should seek the balance between the profit margin of the ride-sourcing company and the market efficiency. 41

42 Summary We have proposed a modeling framework to capture the temporal effects of surge pricing on the ride-sourcing labor supply Drivers and platforms are better off under revenue-maximizing surge pricing while customers are worse off in highly surged periods Surge pricing can create a win-win situation in certain periods as compared with its static counterpart Capping the commission may enhance market efficiency 42

43 Thank You! Questions? 43

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