A linear programming model of housing market equilibrium

This paper reviews Wheaton's assertion that the Herbert-Stevens Linear Programming Model produces solutions which do not meet Alonso's criteria for market equilibrium. It demonstrates that, although Wheaton's criticism is valid in general, under certain conditions an alternative specification of the objective function coefficients and the dual variables in the linear program produces a model whose solutions satisfy Alonso's criteria. Finally, this paper shows that the NBER model is an application in which a linear programming problem computes market equilibria.     

The Lowry Model Revisited: Incorporating a Multizonal Input-Output Model into an Urban Land Use Allocation Model

This paper formulates a new generation of Lowry-style models that combine a multizonal input-output model and an urban land use allocation model. Three different types of models are proposed: 1) an unconstrained model, 2) a primal of a linear programming approach that includes land supply constraints, and 3) a modified dual of the linear programming approach that allocates land based on additional conditions of economic efficiency. The modified dual formulation improves upon the limitations of Lowry models and their derivatives. First, the proposed model has sound theoretical underpinnings that incorporate the production theory of input-output models and the behavioral theory of optimization models. Second, the proposed model allocates land on the basis of economic efficiency by imposing a procedure that equalizes shadow prices. And third, the proposed model is an optimization model that fully accounts for the spatial and sectoral relationships of multiplier effects determining land use demand.     

A linear programming model of the urban housing and land markets: Static and dynamic aspects

An extension of the Herbert-Stevens model is presented which incorporates the dynamic aspects of the housing market in order to simulate the filtering process. An open city is assumed with an exogenously given welfare level of the households and constant returns to scale in production. The bid-rent function can thus de defined independently of the resource allocation within the city. The maintenance policy of the landlords is endogenously determined allowing conservation, deterioration, as well as upgrading. Although the model has a normative formulation, the resulting allocation stipulates a competitive equilibrium. The model can be employed to show that discontinuous development can represent an efficient resource allocation.     

Implications for food production potential of future urban expansion in Ontario

The paper describes the application of an evaluation system to assess the flexibility that would exist in the use of Ontario's agricultural land resources under alternative urban growth scenarios. A programming method is employed, but the analysis does not yield a “best” or “predicted” allocation of land use; rather, the system gauges the degree to which options in the use of land are affected by changes in conditions, and identifies those land areas which are strategically important for particular uses given the specified conditions. The conditions are specified to reflect possible patterns of urban and exurban development, both with and without policy controls. The analysis provides evaluations of both the pressures on the land resources if food production requirements are to be met, and the importance of particular land units for agriculture if the requirements are to be met, under the alternative urban growth scenarios.     

Modeling the density variations of urban land uses with transportation network congestion

Perhaps the single most distinctive character of urban activity that distinguishes it from rural and regional activities is the intensive use of urban land. While the nature of density variations of urban land uses and their associated land rents are well understood, there have been few operational urban models that explicitly address the density variations of land uses. The paper presents a combined land use-transportation model, in which transportation congestion costs on networks of various transportation modes are simultaneously determined with the efficient intensity level of land uses. The procedure uses a nonlinear programming approach within the context of a multicommodity flow/input-output model.     

Spatial equilibrium with local public goods: Urban land rent,optimal city size and the Tiebout hypothesis

This paper extends the standard model of urban land rent to consider the spatial equilibrium conditions in a local public goods market as hypothesized by Charles M. Tiebout. An analysis is made of the spatial dimensions of public goods, their degree of ‘localness’ and their impact on land values. It is shown that the optimal population size of the community (Tiebout's sixth assumption) is simultaneously derived with the optimal supply of local public goods and local taxes. It is also shown that land rent is a poor output indicator of Tiebout's equilibrium conditions and that the capitalization assumption is not the appropriate test for his hypothesis.     

Spatial patterns of urban growth: Optimum and market

The optimum spatial pattern of urban growth for a problem which is essentially a dynamic version of von Thünen model of land use is first studied by using a notion of bid land price curves, which is a dynamic extension of bid rent curves by Alonso [1]. Then a competitive market of which equilibrium growth path coincides with this optimum one is obtained by examining demand side properties. It is hoped in this way to throw some light for the future development of dynamic theory of urban land use.     

Spatial majority voting equilibria and the provision of public goods

This paper develops general equilibrium conditions for urban areas where a pure public good is provided at a level decided upon by majority voting. Models with a property tax and a head tax and external land ownership are analyzed, and equilibrium solutions are compared using a specific form for the utility function. Optimal cities are characterized and compared to those emerging from the majority voting equilibria. Models where aggregate land rent is divided equally among the urban residents are also developed.     

The periurban city: why to live between the suburbs and the countryside

The last 30 years have witnessed the emergence of a new pattern of urban development in France, called the periurban belt. It is defined as a belt outside the city occupied both by households and farmers. We develop a residential model in which households commuting to an employment center may choose to live with farmers in this mixed belt because they value the rural amenities created by farming activities. Both types of agents compete on the land market and the equilibrium conditions allow us to obtain an analytical solution and to provide some insights about the robustness of the periurban form against decreases in commuting costs. Finally, the model is calibrated on French data.     

Environmental management costs using a best available control technology bact in the electrical generating industry

As pollution control programs become an increasingly important part of government regulatory activities there also arises the question of the economic impacts of these activites. The purpose of this paper is to illustrate the use of a computable general equilibrium model for measuring the economic impacts of imposing a Best Available Control Technology (BACT) on the Electric Utilities industry. This application is intended only to demonstrate the feasibility of the approach—and is not designed for immediate policy purposes. The particular model used in this study is structured after a recently developed mathematical programming system which is designed to compute a general equilibrium solution. This system combines activity analysis with downward-sloping demand curves, and solutions are obtained with a ‘single-pass’ linear programming algorithm. The model's objective function plays the central role of driving the model to market-clearing values.     

土地财政与最优城市规模

土地是有限的,完全依靠土地收入的发展模式是不可持续的。本文主要考察土地财政作为地方政府的一种融资渠道,城市建设用地规模的使用是否与城市人口规模的增加相协调,是否存在过度扩张城市面积促进地区经济发展的现象。为了分析土地出让收入(地租)、公共品供给以及城市规模之间的关系,本文以乔治亨利定理为基础,并引入林达尔均衡条件建立起最优城市人口密度理论模型。采用1999～2009年31个省面板数据对中国城市成本收益模型进行计量分析,结果表明全国26个省低于估算的最优城市人口密度,验证了中国存在城市面积的扩张与人口的增加不协调发展的情况。     

The effects of the property tax: A general equilibrium simulation

This paper uses a general equilibrium model of residential land use to study the effects of the property tax in a closed city. Two different specifications of the production technology for housing are used, and are found to yield similar results. The model is too complicated to be solved in closed form, but an efficient computational technique which utilizes a simplicial search algorithm was developed to solve it numerically. This type of model and computational technique can be applied to a wide variety of practical issues in urban economics.     

The accuracy of changes of urban land values as a measure of social benefits from public programs

This paper extends the standard model of urban land rent to consider the impact of the output of public programs on the spatial equilibrium and to analyze the accuracy of changes of urban land values as a measure of social benefits from public investment. Two consistent output indicators of public investment are advanced: the individual's welfare and total land values. The general results of the comparative analysis are that there is a lack of correspondence between both output indicators, and that changes in land values are, in general, not an accurate measure of the benefits of such programs.     

Congestion,agglomeration, and the structure of cities

Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities. The long-run equilibrium outcomes in economies with multiple correlated but offsetting externalities have yet to be fully explored in the literature. Therefore, I develop a spatial equilibrium model of urban structure that includes both congestion costs and agglomeration externalities. I then estimate the structural parameters of the model using a computational algorithm to match the spatial distribution of employment, population, land use, land rents, and commute times in the data. Policy simulations based on the estimates suggest that congestion pricing may have ambiguous consequences for economic welfare.     

Optimal density of radial major roads in a two-dimensional monocentric city with endogenous residential distribution and housing prices

This paper proposes an analytical urban system equilibrium model for optimizing the density of radial major roads in a two-dimensional monocentric city. The proposed model involves four types of agents: local authorities, property developers, households and household workers (i.e. commuters). The local authorities aim to maximize the total social welfare of the urban system by determining the optimal density of radial major roads in the city. The property developers seek to determine the intensity of their capital investment in the land market to maximize the net profit generated from the housing supply. The households choose residential locations that maximize their utility within a budget constraint, and the commuters choose the radial major roads that minimize their individual costs of travel between home and workplace. A heuristic solution procedure is developed to find the urban system equilibrium solution. A system optimum model is also proposed to optimize the density of radial major roads that maximizes the social welfare of the urban system. The proposed model can endogenously determine household residential distribution and land values across the city, along with the housing market structure in terms of housing prices and space. Numerical comparative static analyses of congestion pricing and road infrastructure investment (adding a new radial major road) are carried out together with evaluation of the effects of the service level of radial major roads, urban population size, and household income level on the urban economy.     

林业投资估价

分析了确定性条件下的林地估价的传统的Faustmann模型。用随机动态规划方法,建立了不确定性条件下林地估价模型,探讨了用LCP方法求解的问题,并得出有关结论。     

Convexity and duality properties of a quadratic intraregional location model

This paper has two main purposes. The first one is to analyse the convexity and duality properties of a quadratic intraregional location model that has been developed for long-term indicative planning in the Stockholm region. The second one is to review the results of Koopmans and Beckmann (1957) about the inadequacy of a linear price system in sustaining an optimal assignment of plants to locations when the costs of transporting intermediary commodities are taken into consideration. At the outset a model is formulated which is a transposition of a continuous Koopmans-Beckmann model into the urban scene. It is shown that this quadratic programming model is non-convex in all practical cases of interest, due to the simple fact that transportation costs increase with distance. A modification of the model is proposed in which the centralising transportation cost criterion is traded of against a decentralising so called congestion cost which penalizes over-exploitation of urban space. It is shown that the modified model tends to be convex. In the light of these results Kuhn- Tucker theory is used to derive a set of conditions that will ensure that the optimal solution is stable relative to all potential moves by individual decision-makers. This result forms the basis for the conclusion that the failure of the price system in the Koopmans-Beckmann model is rather due to properties of the quadratic criterion function than the integral restrictions on the variables.     

城市扩展的两个均衡条件及其政策含义

论文认为中国的快速城市化侵占了大量的耕地,是迫使粮食在质量差的土地上生产的重要因素之一,造成了巨大的外部成本,应将其整合到城市扩展的代价中,以提高农业对土地的竞争性,求得城乡之间良好平衡.在这个基础上,还应在市区改造和新区建设之间取得平衡,即边缘地块上地租的净增加值应相等.收取的外部费用要用于土地的农业生产外部不经济性治理.土地管理应城乡整合,包括都市更新与新区建设通盘考虑.论文的研究等价于说,如果做到了如上所迷,那么城市扩展导致的土地价值上升部分就能够覆盖它的社会代价:基础设施建设的投入、拆迁投入、土地生产力建设投入和消除土地的农业生产外部不经济性投入.城市发展用地和农业用地会处在一个比较公平的竞争环境中,取得良好的平衡.     

Mode choice,transport structure and urban land use

A theoretical model of the urban land market is solved to examine the impact of bimodal passenger transportation on equilibrium residential land use. In this model travel to the central business district occurs on a dense system of radial roads or bus routes and a competing system or radial expressways or mass transit lines fed by a subsidiary system of densely spread access streets. Under rational behavior assumptions for households, it is shown that various basic urban forms can result depending on the relative generalized cost characteristics of the competing dense and sparse radial networks. The basic urban forms yield fundamental shapes, differing as to the relative geometry and position of the market areas for the two modes. The standard Alonso-Muth model of unimodal travel and circular urban form is found to result as a special case in several of these cases. American urbanized areas of various sizes and modal mix provide plausible examples for each of the basic forms. The paper concludes with a discussion of the model's implications as a framework for examining optimum urban transport structure and the proliferation of transport routes as a function of urban size.     

A study in using linear programming to design non-urban attendance areas

A great deal of recent work has been directed toward using mathematical programming to achieve racial balance in urban schools. However, with the ever increasing cost of fuel for buses, there also appears to be a need to apply these techniques in non-urban school districts to reduce the use of fuel. This paper describes the development of a linear programming model to assign students to schools in such a way, as to minimize student-miles. Using data gathered in a non-urban school district, this model was tested on a large scale linear programming package with encouraging results. The resulting computational results are presented and discussed along with comments on the additional work necessary to implement this model.