A Contribution to the Pure Theory of Taxation.

Currently serving as Directeur de Recherches at the Centre National de la Recherche Scientifigue and Directeur d'Etudes at the Ecole des Hautes Etudes in Sciences Sociales in Paris, French economist Roger Guesnerie adds this Econometric Society monograph to his quite substantial list of existing scholarly publications. Although his stated objective is to provide an analytical framework, familiar techniques, and interesting results concerning tax theory to public economists, the technical level of this treatise limits the potential market to a few Ph.D.'s with a current, state-of-the-art research interest in the theory of taxation. In fact, sections and subsections are labeled with a number of asterisks according to the level of technical difficulty and the mathematical appendix will be comprehensible only to a topologist.

In general, basic premises of this volume include the theories of second-best and incomplete markets as applied to optimal taxation theory, with specific emphasis on the academic contributions of P. Hammond, P. Diamond-J. Mirrlees, and J. Greenberg-S. Weber since 1971. Organizationally the fundamental, theoretical Diamond-Mirrlees model is examined analytically with respect to institutional status in chapter 1, "positive" aspects in chapter 2, "normative" implications in chapter 3, the problem of the relationship between social values and prices in chapter 4, and the structure of second-best Pareto optima as well as game-theoretic inferences in chapter 5. In particular, the institutional analysis of Chapter 1 relies on three significant polar assumptions namely:

1. individual characteristics are private rather than public knowledge;

2. no asymmetric information between the government and the production sector exist; and

3. transactions between the production and consumption sectors are costlessly observed.

In essence, this chapter provides one possible justification of the taxation model to be presented in chapters 2 and 3 in which commodity and factor taxes introduce wedges between production and consumption prices. To be specific, given the above assumptions, this model does not distort choices and create inefficiencies only if lump-sum transfers are unavailable and commodity taxes are the correct substitutes for the lump-sum taxes. Based on Guesnerie's 1981 unpublished material, the analytical framework consists of a central planner with full control of the production sector of an economy, but faced with informational and observational constraints in the consumption sector. Two types of planning conceptions are then introduced and compared. Expressly, a sophisticated or incentive mechanism planner costlessly acquires information via anonymous game forms, while an unsophisticated or tax-setting planner advocates linear taxes for commodities which can be traded among consumers and non-linear taxes for untradable commodities. Given that the distribution of private characteristics is public information, a sketchy proof of the equivalence of the incentive-mechanism and tax-system planners with respect to the achievement of equal social welfare as a Bayesian-Nash equilibrium solution is provided. Furthermore, the simplifying assumption of linear taxation is made and the general conditions under which unsophisticated planning organization is the best that can be achieved are established. Comprehension of these analytical results is difficult without the formal model specification which constitutes the majority of the following two chapters.

In chapter 2, the positive economics of taxation is explored utilizing a general equilibrium model developed from that of Diamond-Mirrlies in 1971. Although their model was initially used in a normative study on redistributive marion by Diamond-Mirrlees, Guesnerie extends this model to consider general tax equilibria based on his single- and co-authored research from 1977 to 1983. (Incidentally, this general extended model reduces to such familiar subcases as the Harberger (1962), Sheshinsky (1972), and Hellwig (1986) models.) Implementation of a tax equilibrium in this modified, more complex Diamond-Mirrlies model requires government intervention to determine public good levels, to disconnect consumption and production prices through tax systems which allows for linear (differentiated) taxation of different commodities, to impose a 100 percent tax on the pure profit of the production sector, and to transfer uniform lump sums. (Budget balance is not required by government since that balance will occur as a result of normal market clearance.) Furthermore, in this quite technical and theoretical chapter, Guesnerie outlines proofs of eleven theorems which contribute to the conceptual understanding of both the local and global tax structure with respect to both the regularity properties and parametrization of the set of tax equilibria. In addition, proofs of existence, continuity, and uniqueness of fixed-tax-system equilibria are offered.

In contrast to the positive perspective taken in the second chapter which was aimed at comprehension of the structure of the set of tax equilibria, the third chapter's complementary approach is normative and, therefore, concerned with the welfare effects of different tax policies and tax reform algorithms underlining the significance and limits of optimal tax formulas. In general, chapter three presents a comprehensive, though not exhaustive, discussion of the consequences of the condition for tax optimality for cost-benefit analysis, the provision of pure public goods, and a desirable tax structure. In particular, first, tax reform via infinitesimal changes which are later linked along a finite path is analyzed with respect to individual agents' welfare as a result of tax equilibria. Next individual agents' welfare is aggregated into a social welfare function and a specific gradient-projection or direction-of-steepest-ascent algorithm of tax reform is both proposed and interpreted. To conclude, second-best Pareto optima are characterized and rules for optimal taxation in a few special cases are discussed. Most of this quite scholarly chapter, which includes brief proofs of both theorems and several associated corollaries, is founded upon Guesnerie's 1977 to 1981 sole and jointly-authored publications and is continued with the less rigorous discussion of further normative issues in chapter four.

Because the simple conclusions from the special framework outlined in chapter 3 rely on extremely unrealistic assumptions, the fourth chapter first attempts to test the robustness of these results and then explores other applications of the model. These applications include the introduction of simple non-linearities due to rationing by quotas which either restrict or force consumption. In addition, a simple criterion involving the social values of commodities and a fictitious index of discouragement is given to show that, in general, such quota policies are desirable in a second-best world. Similarly, the last section in the chapter also focuses on the introduction of non-linearities such that linear taxes coexist with a non-linear tax schedule and provides a brief overview of the redistributive consequences of this non-linearity. Unfortunately, the remaining middle section of this mixed and disjointed fourth chapter is misplaced. In essence, this section is merely an extension of the discussion of tax reform and optimization problems of the final section of chapter 3 to the case of a single consumer or, equivalently, a large number of identical consumers. Given this model simplification, this section yields two major conclusions. Namely, primarily, the simple Ramsey rule that tax rates are inversely proportional to compensated elasticities is generally true if composite commodities are appropriately redefined. Also, secondarily, more intuitively appealing welfare-improving and distortion-reducing directions of tax changes exist in the single-consumer simplified model.

With the fifth chapter, this monograph returns to the consideration of the model presented in chapters 2 and 3 and focuses attention on the conflicts between agents in the determination of tax systems. Unlike chapter 4 which solves such conflicts by the introduction of an exogenous social welfare function, chapter 5 solves such conflicts politically via the endogenous determination of the tax system. In order to discuss this endogenization of an exogenous social welfare function, this chapter generally assumes that central authorities in charge of organizing the fiscal system face the incentive constraints outlined in chapter 1 and receive their instructions from the interested agents of the economy, that is households, through some political channels. Specifically, this chapter consists of four separate essays, the first two of which provide an assessment of the geometry of the set of second-best Pareto optima, as a subset of the set of tax equilibria in a low-dimensional model, and concludes that the relative number of households and commodities is a key determinant of the size of the set of second-best Pareto optima. In addition, the second essay concludes that there exist few theoretical restrictions on the social choice problem associated with tax decisions. The remainder of the chapter is concerned with the special case of the general model in which the set of tax equilibria is one-dimensional, that is, which assumes an economy with two private goods and one public good, as well as the game-theoretic approach to the political choice of a taxation system. Based mainly on the author's 1981 and 1991 research, proofs of nine theorems in this part of the chapter imply that, first, increasing returns to the size of society or, equivalently, decreasing per capita cost of public goods may be vulnerable to the increased difficulty of reaching a decision in a larger, more heterogeneous society and to credible secession threats from the coalitions. Consequently, conditions enumerated in theorems 5 through 8 must be met unless a stable structure of coalitions emerges.

In summary, this volume, based on previous work by the author, presents a stylized theoretical model in which public policies are constrained by incomplete, asymmetric information. In this context, tax systems are viewed as information extracting devices which generate complex tax equilibria, a tax reform methodology associated with optimal taxation is proposed, and the effects of social conflicts in the determination of taxes on social cohesion are examined. Thus, the general perspective of this monograph is derived from second-best tax systems. Although Guesnerie claims policy relevance for public economists, most practitioners will find that the technical level of this work precludes ease of application. Furthermore, the verbose and muddled writing style renders identification of major points exceptionally difficult without successive reading attempts. Other factors which contribute to this incoherence and, consequent, incomprehensibility include the careless and unsystematic definition of mathematical symbols and the incomplete and/or unrigorous proof of some theorems. Furthermore, references are inadequately and inappropriately cited. That is, although each chapter concludes with a section entitled "Bibliographical Note," this part consists of only vague, general references to entries in the bibliography instead of properly utilizing footnotes and/or endnotes. Even if the model were broadened to include the author's suggestions for future research of an open economy with dynamic properties, the existing lack of clarity of exposition and narrow market appeal would prevent the appearance of this treatise on the economics best-seller list.

Sandra L. Snow University of Wisconsin-Whitewater