Second-best Pricing Research Articles

Minimize population exposure to vehicle-generated emissions by road pricing

Vehicular emissions, as a major source of urban air pollution, are threatening public health. With a goal to regulate population exposure to vehicular emissions, three bilevel road pricing models are established to minimize the exposure to vehicular emissions for on-road travelers, near-road residents, and all populations in the study network. A simulated annealing-based method is applied to solve these models based on a first-best pricing scheme. For ease of implementation, a second-best pricing scheme is then proposed and solved based on a meta-heuristic approach coupled with genetic algorithm with elitism and simulated annealing. The proposed method is tested using the Nguyen-Dupuis network and the Sioux Falls network. It is found that a tradeoff exists between the objectives of minimizing the emission exposure levels of travelers and near-road residents. Another tradeoff is found between the objectives of minimizing total population exposure and total travel time. Results from the numerical example indicate that the optimality results obtained in the first-best pricing scheme may also be approximated by the second-best pricing scheme with fewer tolling locations and less toll collection. The conclusions drawn from the paper could potentially assist policymakers in formulating road pricing policies that prioritize environmental concerns.

The impact of bus punctuality on users’ decisions and welfare

ABSTRACT This paper proposes a public transport users’ scheduling model that considers crowding inside vehicles, waiting time, and punctuality as a reliability measure. Commuters simultaneously make two choices: the preferred bus and the timing to arrive at the bus stop (on time or late). Public transport punctuality is the probability of being on time or late, generating a parameter of public transport reliability. We compute users’ equilibrium, social optimum, and first-best pricing and analytically devise a methodology to obtain the second-best pricing. Using numerical analysis, we show that (i) punctuality plays an essential role in the commuter strategy modifying according to its level, (ii) commuters’ strategy changes according to how reliable the system is, and (iii) second-best pricing is efficient only for limited cases.

Incentives to implement personalized medicine under second-best pricing.

We characterize the socially optimal pricing policy inducing the implementation of personalized medicine. As a benchmark, we analyze the first-best allocation and the second-best optimal policy when only one treatment is available. Then, we characterize the optimal policy that a Health Authority can design to induce the firm to bear an investment and testing cost allowing it to tailor treatment to patients' needs. We show how optimal prices increase with treatment quality and effectiveness. We characterize the conditions under which these prices yield higher social welfare than in the benchmark case. Moreover, we address some policy and industrial organization issues and characterize the pricing policy inducing the firm to choose the optimal level of treatment effectiveness.

Emission pricing, emission rebound, and the coverage scope of incomplete regulations

This paper studies the emissions pricing of incomplete regulations when accurate firm-level information is unavailable. In an economy with monopolistically competitive heterogeneous firms, the equilibrium can be sufficiently characterized by an aggregate statistic, which we call the “coverage scope”. Given the coverage scope, emissions leakage to the unregulated firms results in a “U-shaped” relationship between the aggregate emissions and emissions price. As the coverage scope expands, the second-best emissions price increases. Firm heterogeneity and market power, the two defining features of the monopolistically competitive economy, affect emissions pricing differently. While both of them affect the second-best emissions price indirectly through coverage scope, market power has an additional direct effect. As a result, the optimal emissions price does not always decrease in market power, which contrasts the traditional wisdom on emissions pricing under complete regulations. A multi-sector model is numerically simulated using parameters for five Chinese manufacturing sectors to be incorporated into a proposed national carbon emissions pricing program. Quantitatively, the second-best price varies substantially with coverage scope and market conditions.

Optimal Electricity Demand Response Contracting with Responsiveness Incentives

Demand response programs in retail electricity markets are very popular. However, despite their success in reducing average consumption, the random responsiveness of consumers to price events makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. This paper aims at designing demand response contracts that allow to act on both the average consumption and its variance. The interaction between a risk-averse producer and a risk-averse consumer is modelled as a principal–agent problem, thus accounting for the moral hazard underlying demand response contracts. The producer, facing the limited flexibility of production, pays an appropriate incentive compensation to encourage the consumer to reduce his average consumption and to enhance his responsiveness. We provide a closed-form solution for the optimal contract in the linear case. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline and where the consumer is charged a price for energy and a price for volatility. The first-best price for energy is a convex combination of the marginal cost and the marginal value of energy, where the weights are given by the risk-aversion ratios, and the first-best price for volatility is the risk-aversion ratio times the marginal cost of volatility. The second-best price, for energy and volatility, is a decreasing nonlinear function of time inducing decreasing effort. The price for energy is lower (respectively, higher) than the marginal cost of energy during peak-load (respectively, off-peak) periods. We illustrate the potential benefits issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data.

Aggregate modeling and equilibrium analysis of the crowdsourcing market for autonomous vehicles

Autonomous vehicles (AVs) have the potential of reshaping the human mobility in a wide variety of aspects. This paper focuses on a new possibility that the AV owners have the option of “renting” their AVs to a company, which can use these collected AVs to provide on-demand ride services without any drivers. We call such a mobility market with AV renting options the “AV crowdsourcing market”. This paper establishes an aggregate equilibrium model with multiple transport modes to analyze the AV crowdsourcing market. The modeling framework can capture the customers’ mode choices and AV owners’ rental decisions with the presence of traffic congestion. Then, we explore different scenarios that either maximize the crowdsourcing platform’s profit or maximize social welfare. Gradient-based optimization algorithms are designed for solving the problems. The results obtained by numerical examples reveal the welfare enhancement and the strong profitability of the AV crowdsourcing service. However, when the crowdsourcing scale is small, the crowdsourcing platform might not be profitable. A second-best pricing scheme is able to avoid such undesirable cases. The insights generated from the analyses provide guidance for regulators, service providers and citizens to make future decisions regarding the utilization of the AV crowdsourcing markets for serving the good of the society.

Airport pricing and capacity: Schedule versus congestion delays

This study investigates airport pricing and capacity investment when passengers face schedule and congestion delays. Two countries' airports are served by each country's home carrier. Airports choose their charges on a per-flight and/or per-passenger basis. Given the general observation that carriers that compete on parallel international routes often form codeshare alliances to increase the schedule they are able to provide, we find the following. First, the first-best movement-related per-flight charges do not necessarily need to charge congestion delay costs if there is a positive externality that happens to compensate for the negative congestion externality. Second, when positive and negative externalities cancel out, choosing per-passenger charges alone (known as the second-best approach, in which per-flight charges are weight-related and become equivalent to per-passenger charges) can also lead to the first-best outcome. However, choosing movement-related per-flight charges alone (another second-best approach) cannot do so. Third, under the former second-best pricing approach, capacity investment could be globally efficient. However, under the latter second-best pricing approach, each airport overinvests.

A discrete-time second-best dynamic road pricing scheme considering the existence of multiple equilibria

When multiple equilibria exist, the desired traffic equilibrium, may not be reached through a day-to-day dynamic adjustment process. Han et al. [“Discrete-Time Day-to-Day Dynamic Congestion Pricing Scheme Considering Multiple Equilibria.” Transportation Research Part B: Methodological 104: 1–16.] proposed a day-to-day dynamic pricing scheme charged on all links to ensure the desired traffic equilibrium can be achieved even when multiple equilibria exist. However, due to many practical constraints, the second-best pricing scheme has more practical interests. This study first discussed the issues of existing congestion pricing schemes for second-best case. Then, this study developed a second-best dynamic road pricing scheme that is implemented on a dynamic subset of the road links in the network. Our rigorous theoretical proof and numerical tests prove that the dynamic pricing scheme can drive the traffic state evolution towards the desired second-best traffic user equilibrium state from any initial traffic state.

The merits of privileged parking

The paper investigates under what conditions it is optimal to exclude some motorists searching for parking from occupying a vacant parking bay. Privileged parking is found to be optimal if motorists are heterogenous and can steer their search towards or away from such parking. The socially optimal allocation of privileges and search strategies are characterized. The second-best pricing policies in the presence of cruising-for-parking externality are described; short-term parkers should always be allowed to take the first vacant bay they find. A model extension studies technologically modified “special needs” parking. Unlike existing policies that make such parking exclusive for special-needs motorists, the optimal policy makes it available for an extra fee to anyone, while increasing the number of special-needs bays so that even the initial users are better off.

Airport Pricing and Capacity: Schedule versus Congestion Delays

This study investigates airport pricing and capacity investment when passengers face schedule and congestion delays. Two countries’ airports are served by each country’s home carrier. Airports choose their charges on a per-flight and/or per-passenger basis. Carriers choose both quantities and frequencies. Given the general observation that carriers that compete on parallel international routes often form codeshare alliances to increase the schedule they are able to provide, we find the following. First, the first-best per-flight charges (rules) do not necessarily need to charge congestion delay costs if there is a positive externality (an increase in one carrier’s flights can reduce the schedule delay costs for its allied carriers’ passengers) that can compensate for the negative congestion externality. Second, when positive and negative externalities cancel out, choosing per-passenger charges alone and fixing the per-flight charges (known as the second-best approach) can also lead to the first-best outcome. However, choosing per-flight charges alone and fixing the per-passenger charges (another second-best approach) cannot do so. Third, under the former second-best pricing approach, each airport underinvests (overinvests) when the congestion delay effect dominates (is dominated by) the schedule delay effect. Interestingly, when the positive and negative externalities cancel out, capacity investment is globally efficient. However, under the latter second-best pricing approach, each airport overinvests.

The impact of potential-based physics models on pricing in energy networks

Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the underlying transport infrastructures. We introduce a general pricing framework for potential-based energy flows in arbitrarily structured transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results and compare different pricing outcomes of potential-free and potential-based energy flow models. Our results show that considering nonlinear laws of physics leads to significantly different pricing results on networks and that these differences can only be seen in sufficiently complex, e.g., cyclic, networks as they can be found in real-world situations.

Autonomous Cars and Dynamic Bottleneck Congestion Revisited: How In-Vehicle Activities Determine Aggregate Travel Patterns

We investigate the impacts of in-vehicle activities of commuters in the autonomous car on aggregate travel patterns. We allow for an autonomous car to affect the utility difference between being at home and being in the vehicle differently than the utility difference between being at work and being in the vehicle, compared to the differences experienced with a normal car. This affects the relative importance of values of travel delays, schedule delays early, and schedule delays late. Hence multiple possible changes in travel patterns may occur when autonomous cars become available. Switching to an autonomous vehicle may impose a net negative or positive externality, by raising the marginal external cost of autonomous cars themselves while lowering that of normal cars. We examine three provision regimes: marginal cost pricing, second-best pricing and profit-maximizing pricing by a private monopoly. The second-best mark-up (over marginal cost) rises with the price sensitivity, due to the increasing marginal external cost. Surprisingly, for the monopoly, mark-up may rise or fall with the price sensitivity, depending on the relative strength of the externality and of market power, where the former tends to raise it, and the latter tends to reduce it. Furthermore, the difference of the mark-up between private monopoly and second-best public provision falls as the demand becomes more price-sensitive.

How to road price in a world with electric vehicles and government budget constraints

In this paper we examine what characterizes second-best road prices targeting external costs from driving electric (EV) and conventional (ICEV) vehicles when there are distortionary labor taxes and binding government budget constraints. Further, we examine how this second-best pricing fits with government set goals of reducing CO2 emissions. The paper further develops an analytical framework for assessing first- and second-best road prices on vehicle kilometers, extending it to include EVs and externalities that vary geographically and by time of day. We find that optimal road prices largely vary with external cost, but are also significantly affected by the interactions with the rest of the fiscal system. Not surprisingly, the highest road prices should be for ICEVs in large cities during peak hours due to high external costs. More surprisingly, we find that the road price for ICEVs in rural areas should be lower than that for EVs due to large fiscal interaction effects. These road prices give large welfare gains, but they lead to no reduction in carbon emissions when applying the currently recommended social cost of carbon.

Preference heterogeneity and congestion pricing: The two route case revisited

This paper studies first-best and second-best congestion pricing in the presence of unobserved and observed preference heterogeneity using a stylised stochastic user equilibrium choice model. Travellers choose between multiple alternatives, have heterogeneous values of travel times, and may differ in their valuation of variety. We derive first-best and second-best tolls taking into account how the overall network demand responds to expected generalized prices, including tolls. For second-best pricing, we show that with homogeneous values of times the welfare losses of second-best pricing are smaller when route choice is probabilistic than when route choice is deterministic. Furthermore, we find that with heterogeneous values of times and benefits of variety, uniform second-best tolls and group-differentiated tolls can be very close, implying potentially low welfare losses from the inability to differentiate tolls. Finally, we show that there are cases where all groups benefit from second-best congestion pricing, but that these cases are likely to be politically unacceptable because tolls are then higher for low income groups.

ARAAC: A Rational Allocation Approach in Cloud Data Center Networks

The expansion of telecommunication technologies touches almost all aspects life that we are living nowadays. Indeed, such technologies have emerged as a fourth essential utility alongside the traditional utilities of electricity, water, and gas. In this context, Cloud Data Center Networks (cloud-DCNs) have been proposed as a promising way to cope with such a high-tech era and with any expected trends in future computing networks. Resources of cloud-DCNs are leased to the interested users in the form of services, such services come in different models that vary between software, platform, and infrastructure. The leasing process of any service model starts with the users (i.e., service tenants). A tenant asks for the service resources, and the cloud-provider allocates the resources with a charge that follows a predefined cost policy. Cloud resources are limited, and those cloud providers have profit objectives to be satisfied. Thus, to comply with the aforementioned promise, the limited resources need to be carefully allocated. Existing allocation proposals in the literature dealt with this problem in varying ways. However, none proposes a win-win allocation model that satisfies both the providers and tenants. This work proposes A Rational Allocation Approach in Cloud Data Center Networks (ARAAC) that efficiently allocates the available cloud resources, in a way that allows for a win-win environment to satisfy both parties: the providers and tenants. To do so, ARAAC deploys the Second Best-Price (SBP) mechanism along with a behavioral-based reputation model. The reputation is built according to the tenants’ utilization history throughout their previous service allocations. The reputation records along with the adoption of the SBP mechanism allows for a locally free-equilibrium approach that allocates the available cloud-DCN resources in an efficient and fair manner. In ARAAC, through an auction scenario, tenants with positive reputation records are awarded by having the required resources allocated at prices that are lower than what they have offered. Compared to other benchmark models, simulation results show that ARAAC can efficiently adapt the behavior of those rational service-tenants to provide for better use of the cloud resources, with an increase in the providers’ profits.

Reducing traffic externalities by multiple-cordon pricing

The second-best congestion pricing schemes including common optimum, one cordon, and multiple cordons schemes are compared with the first-best optimum pricing scheme. A cross-subsidy effect exists in these second-best pricing models. However, the scheme with more cordons will diminish the cross-subsidy and approach an efficient and equitable outcome. The relative efficiency of a cordon pricing scheme for the case of Taipei metropolis is very high. One single cordon yields excellent performance of 93% relative efficiency. There might be some factors causing the good results: the uncongested traffic condition, the linear unit distance cost in traffic flow forming a nonlinear cost function, and the trip demands with continuous space and the same destination (the central business district) in the network.

Optimal policies in cities with congestion and agglomeration externalities: Congestion tolls, labor subsidies, and place-based strategies

This paper develops a spatial general equilibrium model that accommodates both congestion and agglomeration externalities, while firms’ and households’ land-use decisions are endogenous across continuous space. Focusing on the interaction between externalities and land use patterns, we examine the efficiencies of first-best policies and second-best pricing and place-based strategies using numerical simulations. A first-best policy must combine both Pigouvian congestion tolling (PCT) and Pigouvian labor subsidies (PLS) instruments, or design an optimal toll (or subsidy) internalizing agglomeration externalities (or congestion externalities). We also examine second-best pricing policies if only one instrument is adopted. Congestion pricing policies alone (e.g., a partial PCT or a flat-rate toll) can improve social welfare only in heavy-congestion cities, and their welfare gains may be insignificant (e.g., below 10% of the welfare improvement achieved by first-best policies). In contrast, second-best labor subsidy policies alone are a more effective alternative to first-best policies. As to place-based policies, the firm cluster zoning (FCZ) regulation is more efficient than the urban growth boundary (UGB) policy. UGBs only have small effects on the agglomeration economy but could worsen land market distortions via residential rent-escalation effects. These findings suggest that it is important to internalize business land use decisions and relax monocentricity assumptions, in order to appreciate the interplay of both urban externalities, since spatial adaptations to policy interventions can distort system efficiencies.

On revenue recycling and the welfare effects of second-best congestion pricing in a monocentric city

This paper examines congestion taxes in a monocentric city with pre-existing labor taxation. When road toll revenue is used to finance labor tax cuts, 35% of the optimal road tax in our numerical model does not reflect marginal external congestion costs, but rather functions as a Ramsey–Mirrlees tax, i.e. an efficiency enhancing mechanism allowing for an indirect spatial differentiation of the labor tax. This adds a quite different motivation to road pricing, since welfare gains can be produced even in absence of congestion. We find that the optimal road tax is non-monotonic across space, reflecting the different impacts of labor supply elasticity and marginal utility of income, which both vary over space. The relative efficiencies of some archetype second-best pricing schemes (cordon toll, flat kilometer tax) are high (84% and 70% respectively). When road toll revenue is recycled lump-sum, the optimal toll lies below its Pigouvian level. Extensions in a bimodal framework show that the optimality of using road toll revenue to subsidize public transport depends on the initial inefficiency in public transport pricing.

The Impact of Physics on Pricing in Energy Networks

Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the transport infrastructures. We introduce a general pricing framework for potential-driven and arbitrarily structured energy transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results and compare different pricing outcomes of potential-free and potential-driven energy flow models. Our results show that regarding the laws of physics leads to significantly different pricing results on networks and that these differences can only be seen in sufficiently complex networks as they can be found in real-world situations.

Tolled multi-class traffic equilibria and toll sensitivities

We review properties of tolled equilibria in road networks, with users differing in their time values, and study corresponding sensitivities of equilibrium link flows w.r.t. tolls. Possible applications include modeling of individual travellers that have different trip purposes (e.g. work, business, leisure, etc.) and therefore perceive the relation between travel time and monetary cost in dissimilar ways. The typical objective is to reduce the total value of travel time (TVT) over all users. For first best congestion pricing, where all links in the network can be tolled, the solution can be internalized through marginal social cost (MSC) pricing. The MSC equilibrium typically has to be implemented through fixed tolls. The MSC as well as the fixed-toll equilibrium problems can be stated as optimization problems, which in general are convex in the fixed-toll case and non-convex in the MSC case. Thus, there may be several MSC equilibria. Second-best congestion pricing, where one only tolls a subset of the links, is much more complex, and equilibrium flows, times and TVT are not in general differentiable w.r.t. tolls in sub-routes used by several classes. For generic tolls, where the sets of shortest paths are stable, we show how to compute Jacobians (w.r.t positive tolls) of link flows and times as well as of the TVT. This can be used in descent schemes to find tolls that minimize the TVT at least locally. We further show that a condition of independent equilibrium cycles, together with a natural extension of the single class regularity condition of strict complementarity, leads to genericity, and hence existence of said Jacobians.