To Pool or Not to Pool: Equilibrium, Pricing and Regulation

42 Pages Posted: 19 Dec 2019 Last revised: 15 May 2020

See all articles by Kenan Zhang

Kenan Zhang

affiliation not provided to SSRN

Marco Nie

Northwestern University

Date Written: December 3, 2019


We study a monopoly transportation network company (TNC) in an aggregate market that offers on-demand solo and pooling e-hail services, while competing with transit for passengers. The market equilibrium is established based on a spatial driver-passenger matching model that characterizes the passenger wait time for both solo and pooling rides. We prove, under mild conditions, this system always has an equilibrium solution. Built on the market equilibrium, three variants of pricing problems are analyzed and compared, namely, (i) profit maximization, (ii) profit maximization subject to regulatory constraints, and (iii) social welfare maximization subject to a revenue-neutral constraint. A comprehensive case study is constructed using TNC data collected in the city of Chicago. We found pooling is desirable when demand is high, but supply is scarce. However, its benefit diminishes quickly as the average en-route detour time (i.e., the difference between the average duration of solo and pooling trips) increases. Without regulations, a mixed strategy—providing both solo and pooling rides—not only achieves the highest profit and trip production in most scenarios, but also gains higher social welfare. The minimum wage policy can improve social welfare in the short term. However, in the long run, the TNC could react by limiting the size of the driver pool, and consequently, render the policy counterproductive, even pushing social welfare below the unregulated level. Moreover, by maintaining the supply and demand of ride-hail at an artificially high level, the minimum wage policy tends to exacerbate traffic congestion by depressing the use of collective modes (transit and pooling). A congestion tax policy that penalizes solo rides promotes pooling, but consistently harms social welfare. However, it promises to increase both social welfare and pooling ratio, when jointly implemented with the minimum wage policy.

Keywords: e-hail,pooling,pricing,equilibrium,regulation,minimum wage,congestion tax

JEL Classification: R41, L51

Suggested Citation

Zhang, Kenan and Nie, Marco, To Pool or Not to Pool: Equilibrium, Pricing and Regulation (December 3, 2019). Available at SSRN: or

Kenan Zhang

affiliation not provided to SSRN

Marco Nie (Contact Author)

Northwestern University ( email )

2145 Sheridan Road
Evanston, IL 60208-1230
United States

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