On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

机制设计理论综述

机制的新理解和激励相容概念使得机制设计框架得以确立,显示原理极大简化了分析框架。公共品经济难以有效权衡配置效率、自愿参与和激励相容。公共品提供的占优策略均衡机制,在拟线性环境和一般性经济环境下分别导致帕累托严格无效和独裁。在贝叶斯环境下,对于公共品经济和私人品经济,帕累托效率与自愿参与均难以兼容。其中,公共品不兼容性在极限角度仍成立。纳什执行及其拓展试图使在所设机制下的所有均衡结果对于社会选择目标而言都最优。放松关于信息结构和理性的假定,理论的最新发展围绕信息结构内生化、机制稳健化以及计算机制设计问题展开。     

Economies with Multiple Public Projects

This paper discusses a general equilibrium model of an economy with multiple separately provided public projects. We assume an additively separable cost structure and consider valuation equilibria with separated finance systems, one for each collective good. Under non-Euclidean representation we show the decentralization of Pareto efficient allocations by valuation equilibria and the equivalence of the core and the set of nonnegative valuation equilibria. In the case of Euclidean representation, every Pareto efficient allocation is shown to be supported as an affine valuation equilibrium that is characterized by a personalized price per unit of each public good and a personalized lump sum tax or subsidy. These results complement and clarify already established insights into Lindahl pricing and its generalizations developed in the literature.     

Commodity tax competition between member states of a federation: equilibrium and efficiency

The purpose of this paper is to characterize the outcome of tax competition between autonomous fiscal authorities. It treats the case of a two-region economy, where an origin-based commodity tax is levied by each region on some private good to finance a local public good. A second private good is untaxed.We first describe ‘regional market equilibria’, whereupon consumers of each region allocate their purchases of private goods between domestic and nondomestic ones according to the structure of relative prices, taxes, and transportation costs. Next, regional optimal tax levels and public good quantities are derived, the tax of the other region being held constant. Fiscal competition arises from the ability of one region in choosing its tax to alter the tax base of the other.A ‘noncooperative fiscal equilibrium’ (NCFE) is then defined as the pair of fiscal choices such that each region's tax and public good supply are optimal for itself, given those of the other region. After examining the conditions for the existence of a NCFE, its efficiency properties are considered. Pareto efficient tax levels are computed and compared with the NCFE ones, showing the sources and nature of fiscal externalities. Finally, it is established that, in this model, fiscal choices that are Pareto improving with respect to a NCFE never reduce the taxes in both regions, and always increase the tax of a tax importing region.     

Budget Balancedness and Optimal Income Taxation

We make two contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents' preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.     

Proportional income taxes and cores in a public goods economy

An equivalence relationship between cores and Pareto optimal allocations of a public goods economy where the public goods are to be provided through a proportional income tax is presented. For this purpose, the definition of the core is modified by allowing coalitions to tax their complements at any given rate. Also, a certain rule which specifies the rate is introduced.     

On the set of Pareto efficient allocations in economies with public goods

Summary We examine the set of Pareto-efficient allocations in economies with public goods. We show that even if preferences are continuous and strongly monotonic, it need not coincide with the set of weakly efficient allocations. We then study topological properties of the Pareto set. We show that it is neither connected nor closed in allocation space. Furthermore, if the public goods are local, the image of the Pareto set in utility space need not be closed or connected. We provide two independent sufficient conditions for the closedness of the Pareto set. The results are directly applicable to private goods economies with joint production. Our results should be of interest for general equilibrium and mechanism design theory; where for example, the properties of the efficient set are important for proving the existence of an equilibrium and for the study of the properties of monotone-path social choice correspondences.We thank Hideo Konishi, Tomoichi Shinotsuka, Nicholas Yannelis and an anonymous referee for valuable comments on previous drafts of this paper.     

OPTIMAL CAPITAL TAXES FOR PUBLIC GOOD PROVISION*

This paper constructs a general equilibrium trade model of a small open economy that produces many traded private goods and one non-traded public consumption good. Trade in goods is free, but the country taxes the internationally mobile capital to finance the provision of the public good. Within this framework, the paper identifies the conditions under which the optimal policy on the internationally mobile capital calls for a tax. Under the assumptions that (i) the welfare function is concave with respect to the tax rate, and (ii) the net revenue-maximizing capital tax rate is positive, it is shown that the marginal cost of the public good always understates its social marginal cost.     

Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries

We revisit the classical result that taxation of private consumption is distortionary and therefore precludes the efficient provision of public goods. We introduce a nonlinear consumption tax which we call a ‘tax lottery’. Under this scheme, an ad-valorem consumption tax is supplemented with a lottery in which consumers can win cash prizes. The winning probabilities in this lottery depend on all consumers' private good consumption decisions. We show that for a given ad-valorem tax, an appropriately designed lottery can implement an efficient allocation in pure-strategy Nash equilibrium. The lottery component corrects the distortion in private consumption due to the ad-valorem tax, while the resulting tax revenue is sufficient to efficiently provide the public good and pay out the lottery prize.     

Old‐age Social Security versus Forward Intergenerational Public Goods Provision

This paper introduces an overlapping‐generations model with earnings heterogeneity and borrowing constraints. The labour income tax and the allocation of tax revenue between social security and forward intergenerational public goods are determined in a bidimensional majoritarian voting game played by successive generations. The political equilibrium is characterized by an ends‐against‐the‐middle equilibrium where low‐income and high‐income individuals form a coalition in favour of a lower tax rate and less social security while middle‐income individuals favour a higher tax rate and greater social security. Government spending then shifts from social security to public goods provision if higher wage inequality is associated with a borrowing constraint and a high elasticity of marginal utility of youth consumption.     

Pigouvian Taxes in General Equilibrium with a Fixed Tax Redistribution Rule

This paper establishes existence of a first-best emission tax in a general equilibrium model with pollution, when the redistribution rule of the tax income is chosen fixed and independently of the Pigouvian tax rate. It is known that under standard convexity assumptions each Pareto efficient allocation can be implemented by simultaneously choosing a Pigouvian tax rate and an appropriate lump sum redistribution of income. In real politics, however, tax redistribution schemes are often restricted to a small feasible set. Nonetheless we show that for any given lump sum redistribution rule, being continuous in overall tax income, an emission tax rate exists that leads to a Pareto efficient equilibrium.     

The “second economy” and resource allocation under central planning

A formal model of intermediate product reallocation through Second Economy markets in a centrally planned economy is discussed. The principal result is that there exists an equilibrium allocation determined in these Second Economy markets in spite of fixed official prices and centrally monitored trading at these prices. It is always a constrained Pareto optimum with respect to the initial plan-generated allocation. Hence, Second Economy markets can effectively and “second best” efficiently ration the intermediate-product “sellers' market” of a centrally planned economy.     

Distribution of tastes and skills and the provision of local public goods

This paper introduces into the Tiebout model individuals with different skills. It is shown that the production techniques, the distribution of tastes and skills and intercommunity trade will affect the pattern of communities. In the suggested model competition with local public goods is Pareto optimal: communities will not be composed of identical people. The optimal solution requires that every community will tax everybody according to his marginal social cost. A Pareto efficient redistribution policy can be carried out only by a central government using lump-sum taxes. A federal income tax will affect community patterns and therefore is inefficient.     

The theory of reform and indian indirect taxes

Given a set of value judgements, an initial state, and a model of the economy, one can ask whether some feasible tax change would increase welfare. We do this by defining the marginal cost in terms of welfare of raising an extra rupee from the ith good. The inverse optimum problem is the calculation of non-negative welfare weights on households which imply that the initial state is optimum. If no such welfare weights exist, then a Pareto improvement is possible. We illustrate the concepts and results using data from the Indian economy for 1979–1980. Directions of tax reform for a number of specific social welfare functions and for Pareto improvements are presented.     

Congestion with heterogeneous commuters

We study a congestion model where a continuum of heterogeneous commuters make a binary choice between riding a bus and driving private vehicles for their commutes. Formulating the model as a large game, we establish the existence and uniqueness of a nontrivial Nash equilibrium and analyze how a gasoline tax affects the allocation of commuters between public transportation and private vehicles at the equilibrium. Based on the analysis, we provide a sufficient condition under which a gasoline tax is Pareto improving. We also prove the existence of a socially optimal policy that minimizes the aggregate loss to all commuters.     

A Core‐Equilibrium Convergence in a Public Goods Economy

This paper shows a core‐equilibrium convergence in a public goods economy where consumers' preferences display warm glow effects. We demonstrate that if each consumer becomes satiated to other consumers' provision, then as the economy grows large the core shrinks to the set of Edgeworth allocations. Moreover, we show that an Edgeworth allocation can be decentralized as a warm glow equilibrium.     

Multiplicity in general financial equilibrium with portfolio constraints

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.     

Optimal tax perturbations

The paper considers an economy with H households, N+1 commodities and M fixed factors with commodity taxes and government expenditures on goods and services. The paper studies under what conditions (small) Pareto improving tax changes exist, i.e., tax changes which increase the utility of each household in the economy. The basic analytical technique used is just the usual comparative statics apparatus, except that duality theory is used in order to simplify the computations. The paper derives both the changes in prices and in real incomes that are induced by (small) changes in exogenous tax variables (differential real income balanced budget incidence analysis).     

Public good provision rules and income distribution: Some general equilibrium calculations

A central issue in the analysis of public goods is the relationship between the optimal provision level and the distribution of income. Theoretical research has stressed the conditions under which the optimum is independent of the distribution of income. Here we focus on numerical analysis of more policy-relevant concerns. Specifically, to what extent is a given redistribution of income likely to affect the optimal level of public good supply? And how significant are the welfare costs of not adjusting public good supply when income distribution changes? We use an applied general equilibrium (AGE) model of the Australian economy and public sector to generate numerical estimates of the impacts of redistributive policies on these variables. Results suggest that the traditional separation of allocation and distribution in determining the level of public good supply may be a justifiable empirical simplification, except where very dramatic redistributions are involved.