Pricing in the Stochastic Bottleneck Model with Price-Sensitive Demand

Qiumin Liu, Vincent van den Berg, Erik T. Verhoef and Rui Jiang
Additional contact information
Qiumin Liu: Beijing Transport Institute, Beijing Jiaotong University and VU Amsterdam
Erik T. Verhoef: VU Amsterdam and Tinbergen Institute
Rui Jiang: Beijing Jiaotong University

No 24-011/VIII, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We analyse time-varying tolling in the stochastic bottleneck model with price-sensitive demand and uncertain capacity. We find that price sensitivity and its interplay with uncertainty have important implications for the effects of tolling on travel costs, welfare and consumers. We evaluate three fully time-variant tolls and a step toll proposed in previous studies. We also consider a uniform toll, which affects overall demand but not trip timing decisions. The first fully time-variant toll is the ‘first-best’ toll, which varies non-linearly over time and results in a departure rate that also varies over time. It raises the generalised price (i.e. the sum of travel cost and toll), thus lowering demand. These outcomes differ fundamentally from those found for first-best pricing in the deterministic bottleneck model. We call the second toll ‘second-best’: it is simpler to design and implement as it maximises welfare under the constraint that the departure rate is constant over time. While a constant rate is optimal without uncertainty, it is not under uncertain capacity. Next, ‘third-best’ tolling adds the further constraint to the second-best that the generalised price should stay the same as without tolling. It attains a lower welfare and higher expected travel cost than the second-best scheme, but a lower generalised price. All our other tolls raise the price compared to the no-toll case. In our numerical study, when there is less uncertainty: the second-best and third-best tolls achieve welfares closer to that of the first-best toll, and the three schemes become identical without uncertainty. As the degree of uncertainty falls, the uniform and single-step tolls attain higher welfare gains. Also, when demand becomes more price-sensitive, the uniform and single-step tolls attain relatively higher welfare gains. Our step toll would lower the generalised price without uncertainty but raises it in our stochastic setting.

Keywords: stochastic bottleneck model; price-sensitive demand; time-varying toll; step toll; uncertainty (search for similar items in EconPapers)
JEL-codes: D62 D80 R41 R48 (search for similar items in EconPapers)
Date: 2024-02-08, Revised 2024-10-22
New Economics Papers: this item is included in nep-tre
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://papers.tinbergen.nl/24011.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20240011

Access Statistics for this paper

More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Bibliographic data for series maintained by Tinbergen Office +31 (0)10-4088900 ().