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Financing Productive Local Public Goods

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Financing Productive Local Public Goods European Regional Science Association 36th European Congress ETH Zurich, Switzerland 26-30 August 1996 Gilles Duranton London School of Economics London, UK [email protected] Stéphane Déo CEME, Université Paris I Paris, France [email protected] FINANCING PRODUCTIVE LOCAL PUBLIC GOODS Abstract: Local public economics typically assumes that local public goods only affect the utility of consumers. We assume on the contrary that local public goods are purely productive. The implications of this assumption are analyzed within standard dynamic growth models. Investment in the public good is enhancing productivity only in the jurisdiction where it takes place. Capital as well as people are perfectly mobile. After characterizing the first-best equilibrium, we show that its decentralization is more demanding than with consumptive local public goods. In particular, efficient decentralization cannot be obtained with competing land developers providing the public good through a simple land capitalization scheme. I. INTRODUCTION How can an economy achieve optimal provision of local public goods (LPG)? Traditional public economics, originating from Samuelson [1954], stresses the difficulty of the question. Basically, a decentralized scheme cannot be implemented because of a standard free-rider problem. Moreover, the first order conditions for the central planner to achieve first-best require him to observe the consumers' marginal rates of substitution. So, even with a benevolent planner, the optimum is difficult to reach. However, Tiebout [1956] came with a clever alternative solution. His answer to the pivotal question raised above was to rely on the local aspects of some public goods. The idea is to use competition among the jurisdictions. In his original paper, assuming an optimal number of jurisdictions led by profit-maximizing developers, people by voting with their feet, can choose between different levels of provision for the public good and the associated head-taxes. Then the equilibrium attained in a perfectly competitive framework is the first-best. Yet the assumption of an ex-ante optimal number of jurisdictions and the possibility of head- taxes are rather restrictive. However, the subsequent literature (see Wildasin [1987] or Mieszkowski and Zodrow [1989] for complete surveys on this issue) managed to relax them elegantly1. The Tiebout idea relies on the strong analogy between fiscal competition and the competition to supply private goods. Consequently free-entrance of developers leads to the first-best just as free-entrance of producers can achieve the first welfare theorem for private goods. As for the head-tax, the idea is to replace it by using the land market. Implementation of the first-best just requires the developer to be able to take advantage of the differential land rent in her jurisdiction since public spendings are capitalized in the land value. This differential2 land rent stems from the agents' competition for space. The profit function of each developer in the most direct case is equivalent to total differential land rent (TDR) minus expenses for the public good (G). Then an immediate implication of the zero-profit condition is TDR = G. This result is known as the Henry George Theorem (George [1879]). Then the only informational requirement to implement the first-best in a decentralized way is the observation of the land market. This result appears in Flatters, Henderson and Mieszkowski [1974], Vickrey [1977] or Arnott and Stiglitz [1979] among others. Of course it relies on strong assumptions. It is not valid with: - Imperfect competition, see Scotchmer [1986] and Duranton [1996]. - Imperfect geography (if the land-rent is not well-defined at the border of the city), see Arnott and Stiglitz [1979] and Pines [1991]. - Congestion, see Scotchmer [1986] and Fujita [1989]. 1 - Imperfect taxation (if only a property tax is available instead of a land tax), see Mieszkowski [1972] or Hoyt [1991]. - Imperfect mobility (if agents cannot vote with their feet at zero cost). - Economy-wide externality, see Henderson and Abdel-Rahman [1991]. Despite all this, Tiebout's idea seems to receive some empirical support: Oates [1969], Edel and Sclar [1974], Hamilton [1976], Meadows [1976] or more recently Wassmer [1993] all draw favorable conclusions. Moreover, some important projects are explicitly funded by land capitalization schemes. One can think for instance of the railways in Tokyo (Kanemoto [1984], Kanemoto and Kiyono [1993], Midgley [1994]) or the public transports in Hongkong (Midgley [1994]). Strange as it might be, most potential applications of the capitalization hypothesis (i.e., financing the public goods with the differential land rent) are dealing with infrastructures (which are 'productive public goods'3), whereas the theoretical analysis seems to focus mainly on 'consumptive' public goods (which enter directly the utility function). It is possible to stress that user-charges can usually provide convenient albeit not always simple pricing schemes for infrastructures. A general synthesis on these aspects is provided by Laffont and Tirole [1993]. But, the stylized fact we want to put forward here is that public infrastructures do matter and do matter locally. So, the main problem is that for most infrastructure, distances seem to matter (be it a road network, an airport facility or even electricity or water distribution), whereas perfect spatial discriminatory pricing is seldom available. Consequently producers tend to favor some localizations at the expense of others (see World Bank [1994]). Hence, the local aspect is hard to ignore. Our aim in what follows is to assess in what measure the land market can contribute to the financing of productive local public goods. Another possible perspective is to consider that most local public goods usually treated as consumptive public goods also have a productive aspect. Indeed, only purely recreational public goods such as parks and museums can be considered as purely consumptive public goods. Even in these extreme cases, it may be argued that they have some productive aspects: museums can improve education, whose productive role is obvious4. The quality of leisure has also an impact on production. A last motivation is that local public economics typically recommends that local expenses should be financed through land taxation or property taxation. However property taxes represent only a fraction of local public finances (see Prud'Homme [1987] and Henderson [1995] for evidences). The problem is to know why non land-based instruments are used at the public level with such a pervasive insistence. For consumptive public goods, the economic analysis is one of partial equilibrium by nature. 2 We just need to consider an exogenous income, which generates a demand for the public good mediated by the land markets. Then, the problem is to see how the public good can be financed through the land market. On the contrary, in our case of productive public good, the initial income generates a demand for private goods, for land and for savings. Using the demand for land, it is possible to finance local public goods but the story does not end here, since the savings and the amount of public good determine the production at the next period. A dynamic general equilibrium model is thus a natural tool. In other words, the analysis of productive public goods is inherently dynamic, because public capital can be accumulated and influences further production. Since we can reasonably assume that private producers operate with constant returns to scale, taking into account public capital which increases their productivity amounts to considering increasing returns at the aggregate level. For these reasons, our dynamic model embodies increasing returns. Then we test whether the classical results are still valid as the productive aspect of all public goods is taken into account. It is shown that although Tiebout style (i.e., first-best) results can be obtained, they are very demanding and must rely on strong assumptions. The Henry George Theorem does not hold in the usual sense. Simple capitalization schemes do not work because the marginal product of public investment benefits to both the workers who live in the jurisdiction and also to capital holders who need not live where their savings are invested. Land rent capitalizes the increase in wages caused by public investment only up to the share of housing in expenditures. On the contrary, increased public investments raise the interest rate and thus the income of everyone and the demand for land in all jursidictions. In section II, we propose a simple framework of a competitive production economy with productive public goods. In section III, we analyze various decentralized frameworks. Finally the last section ends the analysis with some considerations concerning the provision of local public goods. II. ECONOMIES WITH PRODUCTIVE PUBLIC GOODS: THE FIRST-BEST We consider a large economy of surface S populated by individuals of mass N such that S > N L* , where 1 L* is the minimal amount of land to be consumed in order to enjoy a positive instantaneous utility. According to standard assumptions, we consider that each unit of land can be considered as a separate island. Our individuals are infinitely-lived or finitely- lived with a dynastic utility function and they supply continuously one unit of labor inelastically : 3 1−σ +∞ (u ) −ρ U = ∫ t e tdt 0 1−σ = x ≥ * with ut zt.st if st 1 L (1) = < * ut 0 if st 1 L σ > 1 Instantaneous utility is a Cobb-Douglas function5 of z, the consumption of the good and s, the quantity of land. For each 'island' of surface one, we face the production function: β 1−α α α ≥β> Yt = A.Gt . Kt .Lt with x (2) Note that s = 1 L since we suppose that people should live and work on the same unit of land. For the sake of simplicity any unit of capital (K), labor (L) or public spending (G) can be used only in one island (there is no overlap6) and we ignore depreciation.
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