قیمت گذاری بهینه، امور مالی و تامین حمل و نقل شهری در تعادل عمومی: نمایشگاه تئوریک

We present a general equilibrium framework of optimal allocation treating the pricing, finance and supply of urban transportation. Uncongested public transportation technology with economies of scale supports the city's existence; and a congested road system subject to constant returns limits urban size. Optimal investment in public transit and in roads follow Samuelson's rule. With optimally determined urban population, roads are fully financed by Pigouvian congestion tolls while aggregate differential land rents fully finance public transit and any other activity with internal or external economies of scale (Henry George Theorem). Marshallian agglomeration from production in the core and the suburbanization of jobs to avoid congestion are treated. We also see how the optimal rules and the Henry George Theorem are modified when the demand for location is determined by a random utility model. Highlights ► Optimal allocation of roads and public transit in urban general equilibrium. ► Congestion pricing, land rent surplus and redistribution for optimal allocation. ► The Samuelson rule and Henry George Theorem: how they apply to roads and to public transportation. ► Idiosyncratic taste heterogeneity and the optimal finance rules.

It is hard to imagine any model of the urban economy with any level of spatial detail that can ignore personal transportation. Conversely, ignoring the urban economy in transportation studies leads to wrong predictions. The generation of travel is strongly linked to land use, to housing and job location decisions and to the pricing, finance, modal mix and supply of transportation. This interdependence and feedback between transportation and the urban economy has been center stage in urban economic theory ever since theoretical models of urban land use have been formulated in the1960s. The purpose of this article is to present in a nutshell and in a form that is stripped from unnecessary details, the most fundamental results on the interrelationships between urban economics and transportation that have emerged out of five decades of theory. The extant theoretical literature contains only some of these results. The unified extended treatment exposited here has not appeared anywhere and the simplicity, generality and power of the basic results has become largely obscured by the demanding analytical requirements of the “workhorse of urban economics”: the monocentric model. The monocentric model assumes that all jobs are pinned at the central business district (CBD) and treats the urban space around the CBD as a continuous dimension.1 The analytical difficulty from treating space as continuous has limited the scope of many contributions and the eagerness of scholars to engage in extending broadly this basic workhorse model. In particular, extensions of partial equilibrium models to general equilibrium ones have lagged and several issues have been considered relatively intractable. This has been especially true for analytical models with decentralized employment and job sub-centers that conform to realistic patterns and go beyond straightforward extensions of the monocentric framework2; and for models with more than one mode of urban travel (e.g. roads and public transportation).3 To make it possible to obtain fundamental results with little if any loss of generality, this article embraces an approach that holds the promise of making urban economics at once more digestible, more communicable and more analytically pleasant, and quite easily extendable compared to the continuous workhorse model. The approach treats space as discrete. Once this is accepted, then a natural starting point is that of a core–periphery setup of just two discrete urban land areas. The core is an area within a metropolis that represents the CBD and the inner or central city; the periphery is a surrounding area that represents the suburbs.4 This undeniably fits urban reality all around the world, quite well. In this article, we generalize the core–periphery setup and show how to exploit its potential. Given the limited space available to this article, we focus on the most basic issues. First, in Section 2, we use the core–periphery setup to model monocentric urban spatial equilibrium with public transit in the core and roads in the periphery. We do a comparative static analysis of this core–periphery model in general equilibrium, showing that its qualitative properties are consistent with the corresponding analysis of the continuous monocentric model obtained by Wheaton (1974) who first did the comparative statics analysis of the continuous-space Alonso model with a homogeneous urban population. Second, in Section 3, we deal with optimal allocation when there are two modes of transportation. We do this by extending the general equilibrium model of Section 2. The obvious choices are public transportation in the form of subways and private transportation which requires roads. Although transportation economists have long recognized the consumer's choice between these two modes especially after the seminal work of McFadden (1974), what is really important here but neglected in the theoretical literature is a crucial difference between the two modes in their cost-structure on the supply side. Public transport infrastructure is subject to great economies of scale arising from the high fixed costs of tunneling or of surface high capacity corridors.5 The higher the investment in such infrastructure, the lower the private cost of individual users of public transportation becomes. The reason for this reduction in private cost is not only the higher speeds induced by the higher investment but also the shorter access when the number of tunnels and lines increases (Anas and Moses, 1979), each serving a narrower urban area. It is reasonable, in a theoretical setting such as ours, to follow the dominant convention treating public transportation as not congestible. Our second mode, roads and bridges accessed by private cars, is assumed – again following the dominant convention – to be constant returns to scale, requiring an extensive land input. With congestion, the private cost of road transportation increases with its use and at an increasing rate and its marginal social cost is above the average private cost. In Section 3, armed with the above two-mode context we exploit the question of the optimal pricing, finance and supply of public transit and roads. To make sure there is no confusion, throughout this paper pricing refers to road charges. It would refer more generally to gasoline taxes, public transit fares, or any instruments that prices travel per trip, per mile, per passenger or per gallon of fuel. Finance refers to the source of the funds that cover the public provision cost of a road or public transit system. In general, such funds may come from the pricing or tax instruments, but also from sources such as land taxes, income taxes or head taxes. Supply refers to the quantity, or quality, extent and location of a transport system that is provided. In a general equilibrium context, pricing–finance–supply are treated in a unified manner and are jointly determined. Since both forms of transport infrastructure are public goods and externalities are also present, markets cannot optimally resolve pricing, finance and supply. A variety of planning regimes are then potentially available, and they vary from minimalist public intervention to first-best optimality with many lower-best regimes in the middle. These regimes are distinguished from one another according to the optimal provision rules and the pricing/tax instruments available and actually used to finance the supply of transportation that is provided. Our main focus in this article is on first-best optimality.6 We formulate the social optimum as a mixed regime, in which the planner controls the fiscal instruments and the markets allocate resources and determine prices subject to the values of the fiscal instruments chosen by the planner. The first-best allocation is found by the planner optimizing the choice of the fiscal instruments, taking into account how the markets will respond. A central result original to this paper is that the economy of scale in public transportation is one of the unsung reasons that support a larger optimal urban population size. That is, as people concentrate in the same area where they can share a public transit infrastructure, the cost per trip of that infrastructure decreases with the number of trips made on it. Therefore, a public transport system provides a second-nature cause for a city to be formed at a larger size.7 An associated central result, but this one over sung in the existing literature, is that congestion on urban roads increases with urban population. Since, in road transport, there are no or only small economies of scale but rising congestion, this diseconomy offsets the benefits from further gains on the public transit side. At an optimal allocation, the level of investment in public transit and in roads are each determined according to Samuelson's rule for the supply of a public good (Samuelson, 1954), that is expansion of such investments continues until the sum of the private marginal benefits over all users of each infrastructure just equals the marginal cost of supplying more of that infrastructure. An optimal city size is reached where the marginal benefits of public transit and the marginal costs of road transportation are balanced. At an optimally sized population for a region or an urban area the Henry George Theorem holds (Flatters et al., 1974 and Arnott and Stiglitz, 1979).8 We will see that in our basic model this means that the aggregate rent surplus generated by the urban concentration completely pays for the total social cost of the public transport infrastructure, while the aggregate revenue from Pigouvian tolling of road congestion completely pays for the cost of roads.9 The basic model of Section 3 which includes within a planner's social optimization problem the spatial equilibrium model of Section 2 yields the results described in the above paragraph and is offered as a framework for examining a number of extensions. In Section 4 we consider what happens if there are Marshallian externalities in the core's production process, often cited as the reason for the existence of cities. The results of Section 3 extend nicely to this case and we show how the Henry George Theorem generalizes: the rent surplus from the core now finances not only the social cost of the public transportation system but also a Pigouvian subsidy to each worker, closing the gap between the worker's marginal social product and his average private product. That is the rent surplus again covers all social costs when urban population is optimally chosen. Section 5 allows suburban residents to work either in the core where they benefit from a Marshallian production externality from other workers in the core (as in Section 4), or to choose lower private commuting costs by working in the suburbs where they cannot benefit from other workers. When this new margin is allowed, then the urban area can grow by accommodating suburban jobs, but is limited by suburban congestion. Section 6 is where the earlier insights are generalized to a setting in which consumers differ in tastes according to a random utility model of idiosyncratic tastes for location. This model is inspired by the use of random utility models in transportation econometrics since the seminal work of McFadden (1974). Since these are used with success in transportation planning, it is important to ask whether and how the optimal allocation results of theoretical urban economics are modified by idiosyncratic heterogeneity. We formulate a general equilibrium problem of social welfare maximization in which consumers choose between locating their residence in the core or in the suburbs of a monocentric city in part according to their idiosyncratic attachments to these locations. We then show that optimality requires not only Pigouvian tolling of road congestion and optimal sizing of roads and of public transit infrastructure, but also location-specific redistribution of public income to equalize the marginal utility of income for consumers residing in the core and in the suburbs. The pricing, finance and supply rules are modified significantly and so is the Henry George Theorem. In Section 7 we informally summarize the results on urban sprawl and the urban growth boundary that have recently appeared in the literature using the core–periphery setup of this article in order to give a flavor of second-best efficient allocations. Section 8 briefly identifies only several of the many ways in which the present theoretical approach may be extended.