Denant-Boemont, Gaigné and Gaté (2018) built a closed-city spatial-equilibrium model with endogenous housing demand and endogenous job decentralization in which a polycentric city is ecologically and welfare-superior provided travel speed and road connectedness to the central business district are sufficiently high, and in which the spatial extension of the city is the critical variable for curbing commuting-related pollution. That result rests on two exogenous objects: a constant emissions-per-distance parameter and an exogenous average travel speed. The open problem is to extend this framework so that commuters choose between private car and public transport, travel speed responds to congestion, and the emissions intensity of travel depends on the mode mix and on the density-dependent viability of transit, and then to determine whether and when compact or polycentric urban forms still reduce transport emissions and raise welfare, and how the paper's conditions shift.

Background

In urban economics, a city is modeled as a spatial equilibrium in which households trade off housing costs against commuting costs: land rents fall with distance from employment centers while commuting costs rise (the bid-rent logic of the Alonso–Muth–Mills tradition). A monocentric city has all employment in a single central business district (CBD); a polycentric city additionally has secondary business districts (SBDs). In the model of Denant-Boemont, Gaigné and Gaté (2018, JEEM 89:29–45), a fixed population of workers allocates itself between a CBD and an SBD along a hub-and-spoke road network; housing consumption is endogenous, so cheaper land at the outskirts raises housing demand and pushes the city border outward; and each workplace location is endogenous through firms' labor demand and a wage gap between the centers. Commuting generates a pollution externality: total emissions equal an emissions-per-distance coefficient, epsilon, times mu, a road-connectedness parameter, times aggregate commuting distance. The paper's central findings are that a polycentric city is desirable from both welfare and ecological perspectives only when travel speed (the inverse of a time-per-distance parameter tau) and/or the number of roads directly connected with the CBD are sufficiently high, and that the spatial extension of the city (its physical size), rather than the mere number of centers, is the critical variable for curbing transport-related pollution. Several neighboring results frame the gap. Gaigné, Riou and Thisse (2012) showed in a related framework that compact cities are not unambiguously environmentally friendly once the composition and destination of trips adjust. Anas and Kim (1996) had already built general-equilibrium models of polycentric land use with endogenous congestion, but without an emissions dimension. Creutzig (2014) modeled how fuel prices shape public-transport infrastructure, modal shares and urban form, without a welfare analysis in this spatial-equilibrium sense. Borck (2016) studied building-height limits and urban greenhouse-gas emissions, and Borck and Brueckner (2018) optimal energy taxation in cities, both in monocentric settings without mode choice. What all of these leave open, and what the 2018 paper deliberately abstracts from, is that in reality both of its emission-relevant primitives are endogenous: commuters can shift between private car and public transport (and transit is viable mainly where density is high, so polycentric decentralization can shrink the transit market), and travel speed falls with congestion, which itself affects emissions non-linearly — vehicle-level studies such as Barth and Boriboonsomsin (2008) document a U-shaped relation between CO2 per kilometre and average speed, with hypercongested stop-and-go traffic near centers emitting heavily. The authors state this explicitly: additional work is needed to understand how modal choice and traffic congestion modify the relationship between urban form and social welfare.

Problem Statement

In the closed-city polycentric spatial-equilibrium framework of Denant-Boemont, Gaigné and Gaté (2018) — with endogenous housing demand, endogenous CBD/SBD job allocation along a hub-and-spoke road network, a wage gap between centers, and commuting emissions proportional to aggregate commuting distance through an exogenous emissions-per-distance coefficient ε\varepsilon (mediated by road connectedness), with travel speed 1/τ1/\tau an exogenous city-wide average — determine how the mapping from urban spatial structure to transport-related emissions and welfare changes when modal choice, congestion, and transit viability are made endogenous. Concretely: (i) extend the model so that commuters choose between private car and public transport, with the viability and service quality of transit depending on the density of the area it can serve, so that job decentralization and urban expansion feed back into modal shares; (ii) make travel speed depend endogenously on congestion and allow the emissions intensity of travel to depend on speed and mode (including the U-shaped speed–emissions relation documented for real traffic), so that ε\varepsilon is an equilibrium object rather than a constant; (iii) characterize, in the extended model, the conditions — on transit viability, road capacity and connectedness, travel speed, and housing demand — under which a polycentric or more compact/less spatially extended city reduces total transport emissions and raises welfare, and establish whether the source paper's conclusion (polycentricity desirable only when speed and road connectedness are sufficiently high; spatial extension the critical variable) is reinforced, weakened, or reversed. The source frames this as a research agenda with additional secondary directions (non-commuting trips, vacant land, heterogeneous preferences, richer networks); these are acknowledged limitations rather than part of the core question, which is the joint modal-choice/congestion/emissions question above. Related directions — the design of policy instruments (congestion pricing, fuel or emissions taxes, zoning or density regulation) that internalize the commuting and pollution externalities in the extended environment, and the empirical confrontation of the theoretical conditions with observed cities — belong to the surrounding literature in which the core question sits.

References

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