Regulating dynamic congestion externalities with tradable credit schemes: Does a unique equilibrium exist?

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Abstract

Tradable credit schemes offer a potentially efficient, revenue-neutral policy alternative to classical dynamic pricing of congestion externalities. We show in this paper that the resulting equilibrium may not be unique for particular models of congestion, including the first-best solution for the conventional Vickrey's bottleneck model. This can have substantial detrimental impacts on social welfare and social acceptance of tradable credit schemes. The reason underlying this result is that the credit supply-demand condition can be satisfied for a continuum of credit prices. This is because any marginal change in the credit price will be matched by a compensating change in queuing times, keeping user price fixed but deviating from the first-best optimum in which no queueing should occur. We find that the problem of non-uniqueness does not occur for the dynamic flow congestion model proposed by Chu. A unique equilibrium can be obtained in the bottleneck model if the buying and selling of credits with a bank is allowed, against a pre-determined price. Credits are then still tradable so that the use can deviate from the initial distribution, but the credit price is determined by the perfectly elastic demand and supply from the bank.

Original languageEnglish
Pages (from-to)225-236
Number of pages12
JournalTransportation Research Part B: Methodological
Volume127
Early online date29 Jul 2019
DOIs
Publication statusPublished - Sep 2019

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credit
Sales
bank
supply
demand
selling
social welfare
Costs
pricing
revenue
acceptance

Keywords

  • Non-uniqueness
  • Road pricing
  • Tradable credits
  • Tradable permits
  • Traffic congestion

Cite this

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title = "Regulating dynamic congestion externalities with tradable credit schemes: Does a unique equilibrium exist?",
abstract = "Tradable credit schemes offer a potentially efficient, revenue-neutral policy alternative to classical dynamic pricing of congestion externalities. We show in this paper that the resulting equilibrium may not be unique for particular models of congestion, including the first-best solution for the conventional Vickrey's bottleneck model. This can have substantial detrimental impacts on social welfare and social acceptance of tradable credit schemes. The reason underlying this result is that the credit supply-demand condition can be satisfied for a continuum of credit prices. This is because any marginal change in the credit price will be matched by a compensating change in queuing times, keeping user price fixed but deviating from the first-best optimum in which no queueing should occur. We find that the problem of non-uniqueness does not occur for the dynamic flow congestion model proposed by Chu. A unique equilibrium can be obtained in the bottleneck model if the buying and selling of credits with a bank is allowed, against a pre-determined price. Credits are then still tradable so that the use can deviate from the initial distribution, but the credit price is determined by the perfectly elastic demand and supply from the bank.",
keywords = "Non-uniqueness, Road pricing, Tradable credits, Tradable permits, Traffic congestion",
author = "Yue Bao and Verhoef, {Erik T.} and Paul Koster",
year = "2019",
month = "9",
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language = "English",
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pages = "225--236",
journal = "Transportation Research. Part B: Methodological",
issn = "0191-2615",
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T2 - Does a unique equilibrium exist?

AU - Bao, Yue

AU - Verhoef, Erik T.

AU - Koster, Paul

PY - 2019/9

Y1 - 2019/9

N2 - Tradable credit schemes offer a potentially efficient, revenue-neutral policy alternative to classical dynamic pricing of congestion externalities. We show in this paper that the resulting equilibrium may not be unique for particular models of congestion, including the first-best solution for the conventional Vickrey's bottleneck model. This can have substantial detrimental impacts on social welfare and social acceptance of tradable credit schemes. The reason underlying this result is that the credit supply-demand condition can be satisfied for a continuum of credit prices. This is because any marginal change in the credit price will be matched by a compensating change in queuing times, keeping user price fixed but deviating from the first-best optimum in which no queueing should occur. We find that the problem of non-uniqueness does not occur for the dynamic flow congestion model proposed by Chu. A unique equilibrium can be obtained in the bottleneck model if the buying and selling of credits with a bank is allowed, against a pre-determined price. Credits are then still tradable so that the use can deviate from the initial distribution, but the credit price is determined by the perfectly elastic demand and supply from the bank.

AB - Tradable credit schemes offer a potentially efficient, revenue-neutral policy alternative to classical dynamic pricing of congestion externalities. We show in this paper that the resulting equilibrium may not be unique for particular models of congestion, including the first-best solution for the conventional Vickrey's bottleneck model. This can have substantial detrimental impacts on social welfare and social acceptance of tradable credit schemes. The reason underlying this result is that the credit supply-demand condition can be satisfied for a continuum of credit prices. This is because any marginal change in the credit price will be matched by a compensating change in queuing times, keeping user price fixed but deviating from the first-best optimum in which no queueing should occur. We find that the problem of non-uniqueness does not occur for the dynamic flow congestion model proposed by Chu. A unique equilibrium can be obtained in the bottleneck model if the buying and selling of credits with a bank is allowed, against a pre-determined price. Credits are then still tradable so that the use can deviate from the initial distribution, but the credit price is determined by the perfectly elastic demand and supply from the bank.

KW - Non-uniqueness

KW - Road pricing

KW - Tradable credits

KW - Tradable permits

KW - Traffic congestion

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