Taxation and Economic Efficiency
                      Alan J. Auerbach
                University of California, Berkeley and NBER
                      James R. Hines Jr.
                  University of Michigan and NBER
                        February 2001
       This paper has been prepared for a forthcoming volume of the Handbook of Public Economics,
       edited by Alan Auerbach and Martin Feldstein.  We thank Charles Blackorby, Peter Diamond,
       Kenneth Judd, Louis Kaplow, Gareth Myles, Michel Strawczynski and Ronald Wendner for
       helpful comments on a previous draft.
                                         Taxation and Economic Efficiency
                                                 ABSTRACT
              This paper analyzes the distortions created by taxation and the features of tax systems that
              minimize such distortions (subject to achieving other government objectives).  It starts with a
              review of the theory and practice of deadweight loss measurement, followed by characterizations
              of optimal commodity taxation and optimal linear and nonlinear income taxation.  The
              framework is then extended to a variety of settings, initially consisting of optimal taxation in the
              presence of externalities or public goods. The optimal tax analysis is subsequently applied to
              situations in which product markets are imperfectly competitive.  This is followed by
              consideration of the features of optimal intertemporal taxation.  The purpose of the paper is not
              only to provide an up-to-date review and analysis of the optimal taxation literature, but also to
              identify important cross-cutting themes within that literature.
              JEL Classification: H21.
              Alan J. Auerbach                              James R. Hines Jr.
              Department of Economics                       Office of Tax Policy Research
              549 Evans Hall                                University of Michigan Business School
              University of California                      701 Tappan Street
              Berkeley, CA  94720-3880                      Ann Arbor, MI  48109-1234
              auerbach@econ.berkeley.edu                    jrhines@umich.edu
                 Table of Contents
                 1.   Introduction............................................................................................................................. 1
                   1.1. Outline of the chapter.......................................................................................................... 2
                 2.   The theory of excess burden.................................................................................................... 2
                   2.1. Basic definitions.................................................................................................................. 2
                   2.2. Variations in producer prices.............................................................................................. 7
                   2.3. Empirical issues in the measurement of excess burden.................................................... 10
                 3.   The design of optimal taxes.................................................................................................. 15
                   3.1. The Ramsey tax problem................................................................................................... 15
                   3.2. Changing producer prices.................................................................................................. 21
                   3.3. The structure of optimal taxes........................................................................................... 24
                   3.4. An example....................................................................................................................... 25
                   3.5. The production efficiency theorem................................................................................... 26
                   3.7. Distributional considerations............................................................................................. 27
                 4.   Income taxation..................................................................................................................... 30
                   4.1. Linear income taxation...................................................................................................... 30
                   4.2. Nonlinear income taxation: introduction........................................................................... 34
                   4.3. Nonlinear income taxation: graphical exposition.............................................................. 36
                   4.4. Nonlinear income taxation: mathematical derivation....................................................... 39
                 5.   Externalities, public goods, and the marginal cost of funds.................................................. 46
                   5.1. The provision of public goods and the marginal cost of public funds.............................. 47
                   5.2. Externalities and the “double-dividend” hypothesis......................................................... 51
                   5.3. Distributional considerations and the MCPF.................................................................... 54
                 6.   Optimal taxation and imperfect competition......................................................................... 57
                   6.1. Optimal commodity taxation with Cournot competition. ................................................. 57
                   6.2. Specific and ad valorem taxation...................................................................................... 63
                   6. 3. Free entry........................................................................................................................... 67
                   6.4. Differentiated products...................................................................................................... 72
                 7.   Intertemporal taxation........................................................................................................... 75
                   7.1. Basic capital income taxation: introduction...................................................................... 76
                   7.2. The steady state................................................................................................................. 78
                   7.3. Interpreting the solution.................................................................................................... 79
                   7.4. Human capital accumulation and endogenous growth...................................................... 82
                   7.5. Results from life-cycle models.......................................................................................... 90
                 8.   Conclusions........................................................................................................................... 94
       1. Introduction
          This chapter considers a subject at the very center of public finance analysis, the
       distortions introduced (and corrected) by taxation.  Tax-induced reductions in economic
       efficiency are known as deadweight losses or the excess burdens of taxation, the latter signifying
       the added cost to taxpayers and society of raising revenue through taxes that distort economic
       decisions.
          Taxes almost invariably have excess burdens because tax obligations are functions of
       individual behavior.  The alternative, pure lump-sum taxes, are attractive from an efficiency
       perspective, but are of limited usefulness precisely because they do not vary with indicators of
       ability to pay, such as income or consumption, that are functions of taxpayer decisions.  Thus,
       even though tax analysis often starts with the simple case of a representative household, it is
       household heterogeneity and the inability fully to observe individual differences that justify the
       restrictions commonly imposed on the set of tax instruments.  Designing an optimal tax system
       means keeping tax distortions to a minimum, subject to restrictions introduced by the need to
       raise revenue and maintain an equitable tax burden.
          The following sections discuss the theory and measurement of excess burden and the
       design of optimal tax systems.  The analysis draws heavily on the chapters by Auerbach (1985)
       and Stiglitz (1987) in the original volumes of this Handbook, interweaving the most important
       results contained in these two chapters with the additional insights and areas of inquiry that have
       appeared since their publication.  For more detailed analysis and a treatment of many other topics
       in this literature, the reader is referred to these original essays.