Oded Hochman

Optimum and Market Equilibrium in a Model of a City without a Predetermined Center

Most of the recent theoretical literature on the internal structure of cities has assumed that a city is organized around a predetermined center, and that all traffic in the city is oriented toward that point. This is an oversimplification. It is not correct that all traffic in modern cities either goes to the center or comes from the center. In this paper we assume that every individual travels to every location in the city. The individuals choose locations that minimize the sum of their transportation and housing expenditures. Results are obtained for a social optimization and for a competitive equilibrium. In both cases there is a center where the density and land prices are higher; the density decreases with distance from this center. The optimal city is more dense than the ‘competitive’ one owing to externalities which are not taken into account in the latter case.

Land rents, optimal taxation and local fiscal independence in an economy with local public goods

Abstract A general equilibrium model of an economy with cities, farms and free migration of population is constructed. The cities produce internationally traded goods via production functions subject to economies of scale. They also produce housing and a local public good. Two areas are defined to be disjoint if households performing an economic activity in one area are not operating in the other. An area is exclusive if it is disjoint to its complement. The economic surplus of an area is then defined to be the value of the areas net export of goods and resources. Local efficiency of an area is defined to be a state in which its economic surplus attains its maximum value. This state is proved to be a necessary condition for Pareto optimality of the economy. It is then proved that beside Piguvian corrective taxes the only taxes necessary and sufficient to finance local government activities efficiently, are taxes on land rents. Furthermore, if jurisdiction of a local government is over an exclusive area no intervention of central government is necessary, and local authorities can be fully autonomous. If the economy can be divided into pairwise disjointed exclusive areas, those areas are optimal jurisdictions in the sense that efficiency in the economy can be achieved with local authorities only.

Costs of Adjustment and the Spatial Pattern of a Growing Open City

This paper investigates the effect of costs of adjustment on the dynamic characteristics of intra-urban resource allocation. The analysis is concentrated on the development pattern of an open city within a system of many cities both in steady-state and in variable-state economies. Competitive equilibrium of the urban system as a whole is also discussed and compared to Pareto optimum allocation. Some of the results that characterize the resource allocation under static analysis are reestablished for the dynamic case as well. But others that follow from comparative statics are shown to be incorrect under the dynamic analysis.

A theory of the behavior of municipal governments: The case of internalizing pollution externalities☆☆☆

Alt’hough Coase (1960) has argued that private arrangements bctwecn damaged and damaging parties may emerge to solve externality problems without outside intervent’ion, his arguments are not accepted as answers to the specific problem of pollution by economists who st,ress t#he nature of pollution as a negative public good. Even Demsetz, who argues (1967) that society internalizes externalities by the institution of property rights, considers pollution a problem not amenable to such solution; and most writers of more recent vintage concur t’hat it is impossible t,o decentralize pollution externalities without direct intervention to control market trends. Baumol (1972), Buchanan and Tullock (1975), Peltzman and Tideman (1972), and Tietcnberg (1974a, 1974b) all conclude that, this intervention should be effected by Pigouvian pollution t,axes rather t’han by regulatory standards ; and Peltzman and Tideman and Tietenberg

Congestable local public goods in an urban setting

Abstract In this paper, we recognize two types of unpure local public goods (LPGs): congestable and pollutable. This paper and the forthcoming one (Clubs in an urban setting, mimeo, 1980) are devoted to congestable LPGs (CLPG). In Part I we define, classify, and characterize CLPGs. CLPGs may vary in their degree of congestability between zero, in the case of a pure LPG, and one, in the case of a private good. Spatially, we recognize two types of LPGs: the dispersed LPG (DiLPG) and the concentrated LPG (CoLPG). The first is distributed throughout the residential ring and the second is provided in specific locations to which households must travel. The second part of this paper is devoted to the investigation of the properties of a CDiLPG in an urban setting. The properties of CoLPG are investigated in (Clubs in an urban setting, mimeo, 1980). A version of Samuelsons rule as to the optimal allocation of pure public goods is extended on one hand to local dispersed public goods and on the other hand to CLPGs. Two corrective Pigouvian taxes are identified: congestion tolls levied on households, and a residential land tax. These two taxes cover total government expenditure on the LPG. The fraction of the expenses on the LPG covered by congestion tolls is α, and that covered by land taxes is (1 − α), where α is the degree of congestability. Efficiency can also be achieved by zoning the residential ring and regulating the housing density in it. This procedure may replace taxation and its advantage is that we can control a large number of externalities by a single set of zoning rules and regulations. An a posteriori rule to guide the local government as to the desirability of its actions is provided.

COMPETITIVE EQUILIBRIUM OF TRANSPORTATION AND HOUSING IN THE RESIDENTIAL RING OF AN URBAN AREA

A general approach to competitive equilibrium within an urban area is suggested in this paper. The demand for transportation is incorporated into the equilibrium conditions of the household, and in turn the equilibrium conditions of the household are incorporated into the existing models of market equilibrium. The resulting relations are used to verify the characteristics of the prices of housing, rents, velocity, transportation costs, and densities. The implications of the model are consistent with the exponential form of the velocity function observed empirically by Angel and Hyman (1970). These implications illuminate the question of efficient resource allocation in improving the transportation system in the proximity of the CBD. Earlier explanations of the exponential density function given by Muth (1969) are verified and shown to be insufficient.

More on scale economies and cities

Abstract In this paper we develop a model of a closed economy with many types of traded (between cities) products of which the production functions are subject to scale economies internal to the industry as a whole. Workers are assumed to live in Muth type residential rings and commute to the center of the city where the industry is located. This setup leads to the creation of many types of cities. To each type of city, residential cost functions and output cost functions are constructed. From these cost functions all types of demand functions are derived. It is shown here that the introduction of cities into the economy leads to an equivalence between the demand for inputs and the demand for consumption goods, an equivalence which does not exist in models of economies without cities. Thus there are conditional-compensated, unconditional-compensated and Marshalian demand curves for both inputs and consumption goods. The efficiency conditions for this economy are in the short run marginal cost pricing, and for an interior solution in the long run, average cost pricing is also required. This last condition is equivalent to the Henry George rule. Marginal cost pricing remains an efficiency requirement in the case of natural monopoly cities. Next we investigate two cases of scale economies internal to the individual firms and to the industry as a whole. The first case is a model of regular products in perfectly competitive markets and the other model deals with differentiated products and monopolistic competition. These cases have been previously investigated in the literature. Here we generalize and expand previous results and gain additional insights.

REGENERATION, PUBLIC GOODS, AND ECONOMIC GROWTH

In this paper we discuss the (Pareto) optimal provision of a public good (desirable or undesirable) in an intergenerational model of an economy, where regeneration is an endogenous decision variable of the households in the economy. We show that in addition to providing desirable public goods and/or levying the well known Pigouvian taxes on polluting industries, a government must subsidize households who are consuming a desirable public good and tax consumers who are consuming an undesirable public good (pollution). In addition, we show that there is a public rate of return, distinct from the market rate of return, that should be used by the government for the evaluation of investments in public goods. This public rate of return is smaller than the market rate of return in a growing economy and larger than the market rate of return in a declining economy. We investigate biases in both the public and market rates of return, as well as in other parameters which characterize the economy, as a result of nonoptimal governmental behavior. We discuss the question of how to aggregate biases due to different public goods. 1. INTRODUCTION THE RENEWED INTEREST in the interrelationship between household behavior and economic growth has recently been emphasized by the contributions of Nerlove [15] and of Razin and Ben Zion [17], both of which offer an intergenerational model of population growth. In this paper we follow the lead of Razin and Ben Zion but add to the economy a public good (desirable or undesirable) and a government whose function is to insure the (Pareto) optimal provision of this public good. We assume a homogeneous population with respect to tastes, abilities, and initial endowments and thus we address only efficiency considerations.

Demand for investment in productive and financial capital

Abstract The paper deals with an entrepreneur who operates in imperfect capital markets, making rational decisions about productive and financial investment. Using the economic rule that the allocation of assets between productive and financial purposes is carried out according to the equality of the marginal productivity and the marginal factor costs of debt, the paper analyses the factors which determine the size of the firm, the size of debt, and the optimal dynamic path.

Cities, Scale Economies, Local Goods and Local Governments

This study utilises a precise diagrammatic exposition to analyse issues involving the existence and stability of cities, land rents, and private and public local finance. In spite of the limitations of the exposition (such as having only two dimensions) the model is very general, primarily due to the use of cost curves in the analysis. The main new results of this study are: (1) A generalisation of the Henry George law. In its extended form, this law expresses the sufficiency of land rents for the financing of efficient local government investments in local public goods (pure or not), Piguvian subsidies and taxes, and in the internalisation of external economies of scale (except for the case of natural monopoly cities). For this study, a further extension has been made to apply to an economy with many different population groups, industries, cities, and production factors. (2) That when the basic industry of a city has scale economies internal to the individual firm, the optimal local government policy is the subsidisation of a single firm in the industry and deterrence from entry of all other firms of the same industry. In this case and, unlike that of the natural monopoly city, there may exist many such cities. (3) The identification and characterisation of internal and external scale economies in real life, and the type of city evolving from each and actual actions and procedures used by local governments which can be (and often are) used to increase efficiency. (4) The study of a natural monopoly city and the actions to be taken by both federal and local governments that are needed to achieve efficiency. (5) The existence of a criterion for the (Pareto) desirability of marginal local government investments. The criterion is based on changes in net land values. (6) The possible existence of local optimum solutions to the problem of an efficient city, which indicate the possible efficiency of major changes in the use of land in an already existing city. When the investment in such a major project is broken into stages, the initial steps in the series of investments may appear to be inefficient according to the above criterion (5), although the investment as a whole is altogether desirable.