Working Time under Alternative Pay Contracts in the Ride-Sharing Industry

Filippo Belloc

doi:10.1515/bejte-2020-0026

Published by De Gruyter October 5, 2020

Working Time under Alternative Pay Contracts in the Ride-Sharing Industry

Filippo Belloc

From the journal The B.E. Journal of Theoretical Economics

https://doi.org/10.1515/bejte-2020-0026

Showing a limited preview of this publication:

Abstract

We study hours worked by drivers in the peer-to-peer transportation sector with cross-side network effects. Medallion lease (regulated market), commission-based (Uber-like pay) and profit-sharing (“pure” taxi coop) compensation schemes are compared. Our static model shows that network externalities matter, depending on the number of active drivers. When the number of drivers is limited, in the presence of positive network effects, a regulated system always induces more hours worked, while the commission fee influences the comparative incentives towards working time of Uber-like pay versus profit-sharing. When the number of drivers is infinite (or close to it), the influence of network externalities on optimal working time vanishes. Our model helps identifying which is the pay scheme that best remunerates longer working times and offers insights to regulators seeking to improve the intensive margin of coverage by taxi services.

Keywords: working time; Uber; network effects; ride-sharing; pay schemes

JEL classification: L91; J22; J33

Corresponding author: Filippo Belloc, Department of Economics and Statistics, University of Siena, Piazza San Francesco 7, 53100 Siena, Italy, E-mail: filippo.belloc@unisi.it

Acknowledgments

The content of this paper previously circulated as part of a larger working paper titled “Why isn’t Uber Worker-Managed?”, which was presented at the 2019 CESifo Workshop on the Gig Economy (San Servolo – Venice). I wish to thank the participants to this Workshop for valuable suggestions. I am also grateful to participants at the 2018 IAFEP Conference (Lubjiana), the 2018 SIE Conference (Bologna), the 2019 STILE Workshop (Rome) and participants at the Economic Seminar Series at the University of Parma. The usual disclaimers apply.

Appendix

A.1 Proof of Proposition 1

As for the first part of Proposition 1, by comparing Equations (4) and (6) and manipulating, it is straightforward to observe that, for any φ > 0, h i m > h i e when p ( h i , h L − 1 ) + p ′ ( h i , h L − 1 ) h i > 0 . This is verified for any p ′ ( h i , h L − 1 ) > 0 and when | p ( h i , h L − 1 ) | > | p ′ ( h i , h L − 1 ) h i | . As for the second part of Proposition 1, we need to compare Equations (4) and (8). We obtain that h i m > h i w when p ( h i , h L − 1 ) + p ′ ( h i , h L − 1 ) h i > p ( h i , h L − 1 ) / L + p ′ ( h i , h L − 1 ) h i , with h _i = h. This always holds if L > 1.

A.2 Proof of Proposition 2

Manipulating Equation (10), φ ‾ can be expressed as 1 − ( 1 / L ) − δ + ( δ / L ) , with δ = [ p ′ ( h ) h i ] / [ p ( h ) + p ′ ( h ) h i ] . When h < h ‾ , p ′ ( h ) > 0 . Thus, we have that 0 < δ < 1. This implies that 1 − ( 1 / L ) − δ + ( δ / L ) < 1 .

A.3 Proof of Proposition 3

Denote again [ p ′ ( h ) h i ] / [ p ( h ) + p ′ ( h ) h i ] with δ. Then, from φ ‾ = 1 − ( 1 / L ) − δ + ( δ / L ) it results that φ ‾ = 1 when δ is lower than zero and precisely equal to 1/(1 − L). δ < 0 when p ′ ( h ) < 0 , that is when h > h ‾ .

A.4 Proof of Proposition 4

As for the first part of Proposition 4, it is sufficient to notice that Equations (11)–(13) do not include p ′ ( h ) . As for the second part of Proposition 4, we need to compare Equations (11)–(13). With φ > 0, h i M > h i E . Moreover, h i E > h i W when ( 1 − φ ) p ( h ) > p ( h ) / L , i.e. when φ < ( L − 1 ) / L , with lim L → ∞ ( L − 1 ) / L = 1 .

References

Alonso-González, M., N. van Oort, O. Cats, S. Hoogendoorn-Lanser, and S. Hoogendoorn. 2020. “Value of Time and Reliability for Urban Pooled On-Demand SCCervices.” Transportation Research Part C: Emerging Technologies 115: 102621, https://doi.org/10.1016/j.trc.2020.102621.Search in Google Scholar

Angrist, J. D., S. Caldwell, and J. V. Hall. 2017. “Uber vs. Taxi: A Driver’s Eye View.” NBER Working Paper No. 23891.10.3386/w23891Search in Google Scholar

Bai, C. E., and C. G. Xu. 2001. Ownership, Incentives and Monitoring. LSE Discussion Paper No. te/01/413. London: London School of Economics.Search in Google Scholar

Barzel, Y. 1973. “The Determination of Daily Hours and Wages.” Quarterly Journal of Economics 87 (2): 220–38, https://doi.org/10.2307/1882185.Search in Google Scholar

Berger, T., C. Chen, and C. B. Frey. 2018. “Drivers of Disruption? Estimating the Uber Effect.” European Economic Review 110: 197–210, https://doi.org/10.1016/j.euroecorev.2018.05.006.Search in Google Scholar

Camerer, C., L. Babcock, G. Loewenstein, and R. Thaler. 1997. “Labor Supply of New York City Cabdrivers: One Day at a Time.” Quarterly Journal of Economics 112 (2): 407–41, https://doi.org/10.1162/003355397555244.Search in Google Scholar

Cramer, J., and A. B. Krueger. 2016. “Disruptive Change in the Taxi Business: The Case of Uber.” The American Economic Review: Papers and Proceedings 106 (5): 177–82, https://doi.org/10.1257/aer.p20161002.Search in Google Scholar

Farber, H. S. 2005. “Is Tomorrow Another Day? The Labor Supply of New York City Cabdrivers.” Journal of Political Economy 113 (1): 46–82, https://doi.org/10.1086/426040.Search in Google Scholar

Farber, H. S. 2015. “Why You Can’t Find a Taxi in the Rain and Other Labor Supply Lessons from Cab Drivers.” Quarterly Journal of Economics 130 (4): 1975–2026, https://doi.org/10.1093/qje/qjv026.Search in Google Scholar

Guda, H., and U. Subramanian. 2019. “Your Uber Is Arriving: Managing On-Demand Workers through Surge Pricing, Forecast Communication, and Worker Incentives.” Management Science 65 (5): 1995–2014.10.1287/mnsc.2018.3050Search in Google Scholar

Hall, J. V., and A. B. Krueger. 2018. “An Analysis of the Labor Market for Uber’s Driver-Partners in the United States.” Industrial and Labor Relations Review 71 (3): 705–32, https://doi.org/10.1177/0019793917717222.Search in Google Scholar

Hall, J. V., J. J. Horton, and D. T. Knoepfle. 2018. “Pricing Efficiently in Designed Markets: Evidence from Ride-Sharing.” Mimeo.Search in Google Scholar

Harding, S., M. Kandlikar, and S. Gulati. 2018. “Taxi Apps, Regulation, and the Market for Taxi Journeys.” Transportation Research Part A: Policy and Practice 88: 15–25 https://doi.org/10.1016/j.tra.2016.03.009.Search in Google Scholar

Hu, M. 2019. Sharing Economy: Making Supply Meet Demand. Berlin: Springer.10.1007/978-3-030-01863-4Search in Google Scholar

Rochet, J. C., and J. Tirole. 2003. “Platform Competition in Two-Sided Markets.” Journal of the European Economic Association 1 (4): 990–1029, https://doi.org/10.1162/154247603322493212.Search in Google Scholar

Rochet, J. C., and J. Tirole. 2006. “Two-sided Markets: A Progress Report.” The RAND Journal of Economics 37 (3): 645–67, https://doi.org/10.1111/j.1756-2171.2006.tb00036.x.Search in Google Scholar

Sayarshad, H. R., and J. Y. Chow. 2015. “A Scalable Non-myopic Dynamic Dial-A-Ride and Pricing Problem.” Transportation Research Part B: Methodological 81: 539–54, https://doi.org/10.1016/j.trb.2015.06.008.Search in Google Scholar

Spulber, D. F. 2019. “The Economics of Markets and Platforms.” Journal of Economics and Management Strategy 28 (1): 159–72, https://doi.org/10.1111/jems.12290.Search in Google Scholar

Sun, H., H. Wang, and Z. Wan. 2019. “Model and Analysis of Labor Supply for Ride-Sharing Platforms in the Presence of Sample Self-Selection and Endogeneity.” Transportation Research Part B: Methodological 125: 76–93, https://doi.org/10.1016/j.trb.2019.04.004.Search in Google Scholar

Wang, H., and H. Yang. 2019. “Ridesourcing Systems: A Framework and Review.” Transportation Research Part B: Methodological 129: 122–55, https://doi.org/10.1016/j.trb.2019.07.009.Search in Google Scholar

Xu, Z., Y. Yin, and J. Ye. 2020. “On the Supply Curve of Ride-Hailing Systems.” Transportation Research Part B: Methodological 132: 29–43, https://doi.org/10.1016/j.trb.2019.02.011.Search in Google Scholar

Yang, H., S. C. Wong, and K.I. Wong. 2002. “Demand-supply Equilibrium of Taxi Services in a Network under Competition and Regulation.” Transportation Research Part B: Methodological 36 (9): 799–819, https://doi.org/10.1016/s0191-2615(01)00031-5.Search in Google Scholar

Zha, L., Y. Yin, and H. Yang. 2016. “Economic Analysis of Ride-Sourcing Markets.” Transportation Research Part C: Emerging Technologies 71: 249–66, https://doi.org/10.1016/j.trc.2016.07.010.Search in Google Scholar

Zha, L., Y. Yin, and Z. Xu. 2018a. “Geometric Matching and Spatial Pricing in Ride-Sourcing Markets.” Transportation Research Part C: Emerging Technologies 92: 58–75, https://doi.org/10.1016/j.trc.2018.04.015.Search in Google Scholar

Zha, L., Y. Yin, and D. Yuchuan. 2018b. “Surge Pricing and Labor Supply in the Ride-Sourcing Market.” Transportation Research Part B: Methodological 117: 708–22, https://doi.org/10.1016/j.trb.2017.09.010.Search in Google Scholar

Received: 2020-02-18

Accepted: 2020-09-02

Published Online: 2020-10-05

Working Time under Alternative Pay Contracts in the Ride-Sharing Industry

Abstract

Acknowledgments

A.1 Proof of Proposition 1

A.2 Proof of Proposition 2

A.3 Proof of Proposition 3

A.4 Proof of Proposition 4

References

Journal and Issue

Articles in the same Issue