Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency

This paper establishes the existence and efficiency of equilibrium in a local public goods economy with spatial structures by formalizing Hamilton's [Hamilton, B.W., 1975. Zoning and property taxation in a system of local governments Urban Studies 12, 205–211] elaboration of Tiebout's [Tiebout, C., 1956. A pure theory of local public expenditures. Journal of Political Economy 64, 416–424] tale. We use a well-known equilibrium concept from Rothschild and Stiglitz [Rothschild, M., Stiglitz, J.E., 1976. Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Quarterly Journal of Economics 40, 629–649] in a market with asymmetric information, and show that Hamilton's zoning policy plays an essential role in proving the existence and efficiency of equilibrium. We use an idealized large economy following Ellickson, Grodal, Scotchmer and Zame [Ellickson, B., Grodal, B., Scotchmer, S., Zame, W.R., 1999. Clubs and the market, Econometrica 67, 1185–1217] and Allouch, Conley and Wooders [Allouch, N., Conley, J.P., Wooders, M.H., The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibria, (2004), mimeograph]. Our theorem is directly applicable to the existence and efficiency of a discrete spatial approximation of mono- or multi-centric city equilibria in an urban economy with commuting time costs, even if we allow the existence of multiple qualities of (collective) residences, when externalities due to traffic congestion are not present.     

Voluntary contributions to multiple public goods in a production economy with widespread externalities

In a production economy, multiple public goods are produced by firms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers’ consumption and contributions and all firms’ production enter into utility functions. Public goods can be imperfect substitutes or complements, and they can be local public goods or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the differentiable approach. Applying the transversality theorem for smooth economies in a regular parameterization, we obtain the existence of equilibrium in such an economy, and generically equilibria are regular and locally unique.     

Competitive General Equilibrium with network externalities

We identify sufficient conditions for existence of competitive equilibrium with network externalities and indivisibilities. Such combination of externalities and indivisibilities is present in many goods and services with network effects, and it makes existence of equilibrium non-trivial. We provide an existence theorem in a model with a measure space of consumers. Key conditions for existence are anonymity of network effects and dispersion in the economy’s income distribution.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

Neighborhood amenities: An economic analysis

A spatial model of household and firm demand and supply of market goods is developed. Housing and neighborhood amenity markets are explicitly considered in deriving market equilibrium. The equilibrium relationships are empirically investigated, yielding important insights into the functioning of the urban economy. Attention is focused on externalities involved in neighborhood markets and the simultaneous determination of housing and amenity market equilibrium. The effect of neighborhood amenities on household equilibrium is of a major magnitude and effects of “externality” variables on both housing and amenity equilibrium are substantiated. The degree of neighborhood homogeneity and the extent of government programs aimed at neighborhood development are found to have significant impacts on housing and amenity markets.     

Congestible public goods and local indeterminacy: A two-sector endogenous growth model

This paper shows that the congestible public goods can generate local indeterminacy in a two-sector, constant-return human capital enhanced growth model. While the productive public good exerts positive sector-specific externalities, the congestion effect generates negative aggregate externalities. The sector-specific externalities alone arising from productive public goods cannot establish local indeterminacy without the combination of negative externality in a model with social constant return technology. Congestible public good generates local indeterminacy if the degree of productive public good externality and the degree of congestion effect are large enough. The condition for indeterminacy is independent of the factor intensity rankings. The conditions are quantitatively assessed and the required parameter values for the degrees of public good externality and congestion are consistent with the estimated values in existing literature.     

Monetary and fiscal policy under deep habits

Allowing habits to be formed at the level of individual goods – deep habits - can radically alter the fiscal policy transmission mechanism as the counter-cyclicality of mark-ups this implies can result in government spending crowding-in rather than crowding-out private consumption in the short run. We explore the robustness of this mechanism to the existence of price discrimination in the supply of goods to the public and private sectors. We then describe optimal monetary and fiscal policy in our New Keynesian economy subject to the additional externality of deep habits and explore the ability of simple policy rules to mimic fully optimal policy. We find that the presence of deep habits at empirically estimated levels can imply large externalities that significantly affect the conduct of monetary and tax policy. However, despite the rise in government spending multipliers implied by deep habits, government spending is barely used as a stabilisation tool under the optimal policy.     

Uniqueness of competitive equilibrium with solvency constraints under gross-substitution

Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infinite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi’s welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points.     

The welfare economics of city bigness

Money wages will vary among cities in an economy with perfect labor mobility, due to differences in costs of producing nontraded goods. Commuting costs contribute to making money wages higher in large cities. Increasing negative technological externalities, such as pollution and congestion, also make money wages higher in larger cities. Such externalities tend to make big cities too big, because marginal is greater than average externality. Internalizing the externalities would be likely to make a city larger if the externalities emanate from production of nontraded goods, but might make the city smaller if the externalities emanate from export production.     

‘Market failure’ arguments are a poor guide to policy

‘Market failure’ is frequently offered as a justification for government intervention in the economy. Proponents of interventions can point to almost limitless examples of markets which do not meet all the criteria for Pareto optimality and argue that government taxation, subsidies or regulation can perfect them, maximising social welfare. But comparing market outcomes with an unattainable and unidentifiable ideal is not useful in a world of imperfect knowledge and government failure. It is better to compare market outcomes against realistic alternatives. Furthermore, even within the market failure paradigm, concepts such as ‘public goods’ and ‘negative externalities’ are routinely misunderstood and inconsistently applied. This leads to predictably poor policy outcomes.     

Public housing units vs. housing vouchers: Accessibility,local public goods,and welfare

We develop a general equilibrium model of residential choice and study the effects of two housing aid policies, public housing units and housing vouchers. Land is differentiated by both residential accessibility and local public goods, and the provision levels of local public goods are determined by property tax revenues and neighborhood compositions. Households differ in their incomes and preferences for local public goods. Housing aid policies are financed by general income taxes. We discuss how the location of public housing units is a fundamental policy variable, in addition to the numbers and sizes of units, and argue that vouchers not only cause less distortion for social welfare compared to public housing, but may also improve overall welfare.     

General competetive equilibrium of the spatial economy

The spatial economy is analyzed in the general equilibrium framework by considering the production and the utility functions depending on spatial distribution and sets. The geometric constraint between the location and the extension of goods supplies the equilibrium condition for space. The existence of an equilibrium is demonstrated by extending the Gale-Nikaido theorem to the case under examination. Consequently, the competetive equilibrium exists, under the assumptions of the theorem, although each point of space is heterogeneous with any other point (because of the different location): the existence is allowed by the perfect partibility of space.     

Existence of a competitive equilibrium when all goods are indivisible

This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack.     

Existence of maximal elements and equilibria in linear topological spaces

We present some mathematical theorems which are used to generalize previous results on the existence of maximal elements and of equilibrium. Our main theorem in this paper is a new existence proof for an equilibrium in an abstract economy, which is closely related to a previous result of Borglin–Keiding, and Shafer–Sonneschein, but allows for an infinite number of commodities and a countably infinite number of agents.     

Refinements and incentive efficiency in Walrasian models of insurance economies

The literature on Walrasian markets in large economies with adverse selection has used various equilibrium refinements, but has obtained no general incentive efficiency of equilibrium, namely when cross-subsidies are needed for efficiency. We show that the same refined equilibria may also be incentive inefficient even when general mechanisms that allow for such cross-subsidies are priced and can be traded. In the process, we also prove existence of some type of forward induction equilibria in this context.     

Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational.     

Fiscal policies in open cities with firms and households

This paper provides an equilibrium numerical model of an open city economy with mobile firms and resident workers. Given household preferences and firm technologies and an exogenous configuration of city tax rates and national grants and fiscal mandates, the model calculates equilibrium values for aggregate city economic activity, factor prices, and finally, local tax bases, revenues, and public goods provision. The model is calibrated to the Philadelphia economy for Fiscal Year 1998. We then explore the economic and fiscal consequences of raising city tax rates and the city’s ability to finance rising local welfare payments. We find the city to be incapable of bearing significant increases in local responsibility for welfare transfers.     

Club theory and household formation

The relationship between our general equilibrium model with multi-member households and club models with multiple private goods is investigated. The main distinction in the definitions consists in the equilibrium concepts. As a rule, competitive equilibria among households where no group of consumers can benefit from forming a new household and valuation equilibria prove equivalent in the absence of consumption externalities, but not in their presence.     

Consumer surplus analysis under uncertainty: A general equilibrium perspective

This paper derives an exact form of partial equilibrium efficiency measure under uncertainty which is consistent with expected utility maximization in a general equilibrium situation with ex-post spot markets for many goods and asset markets which are in general incomplete.We consider that the good under consideration tends to be negligibly small compared to the entire set of commodity characteristics which is assumed to be a continuum, and look into the limit property of preferences over state-contingent consumption of the good and state-contingent income transfer associated to it. We show that the limit preference exhibits risk neutrality, not only that it exhibits no income effect, meaning that the two conditions are tied together. We also show that the marginal rate of substitution between extra income transfers at different states of the world converges to the ratio between the Lagrange multipliers associated to those states. When the asset markets are complete such ratios are equalized between consumers, but it is not the case in general when the asset markets are incomplete. This means that using the aggregate expected consumer surplus as the welfare measure will be in general inconsistent with individuals’ expected utility maximization in the general equilibrium environment or with ex-ante Pareto efficiency.     

Can platform competition support market segmentation? Network externalities versus matching efficiency in equity crowdfunding markets

We investigate whether, in spite of the existence of cross‐market network externalities, platform competition can lead to segmentation of the two sides of the market served by the platforms. We address this question in the context of competition between two equity crowdfunding platforms that connect startups looking for capital with prospective investors. Given the heterogeneity in the populations of startups and investors in terms of the riskiness of the former population and the degree of risk aversion of the latter population, we investigate whether there exists an equilibrium where the two populations are segmented to ensure an improved match between them. We find that the segmenting equilibrium can arise only when compatibility in terms of their risk profiles is of high importance to both populations, and compatibility is significantly more important than the size of the network externality considered by startups. Segmentation is likely to improve the welfare of both populations when the basic benefit from any kind of match is relatively high.