On the Optimal Taxation of Capital Income

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116 JONES, MANUELLI, AND ROSSI of labor and multi-sector settings in which the price of capital in the steady state is endogenous. Finally, the model in section 2 suggests that given the linearity assumption and a rich tax code, the Ramsey problem has very strong implications about both the timing of tax revenues and the structure of the tax system: Under the optimal scheme, revenue is `front-loaded' and all factors are treated symmetrically in the limit. This revenue front-loading is a disturbing but essential feature of the optimal tax code. Reasonable restrictions on the time path of deficits (e.g., period by period budget balance) can be shown to undo the zero limiting tax result. In essence, this is another type of restriction on tax codes not unlike that described in section 3 (b). This example highlights the interdependence of the initial behavior of the optimal tax code and its limiting properties. Because of the delicacy of the mapping between the features of the economy and the structure of optimal tax codes, further progress will necessitate a detailed analysis of the entire time path of taxes as in section 3 (c). Even for relatively simple examples, this will require a reliance on numerical methods. REFERENCES 1. A. B. Atkinson and A. Sandmo, Welfare implications of the taxation of savings, Econom. J. 90 (1980), 529 549. 2. A. J. Auerbach, The theory of excess burden and optimal taxation, in ``Handbook of Public Economics, Vol. II'' (A. J. Auerbach and M. Feldstein, Eds.), Elsevier, Amsterdam, 1985. 3. A. J. Auerbach and L. J. Kotlikoff, ``Dynamic Fiscal Policy,'' Cambridge Univ. Press, Cambridge, UK, 1987. 4. R. J. Barro, Government spending in a simple model of endogenous growth, J. Polit. Econom. 98, No. 2 (1990), S103 S125. 5. N. Bull, ``When the Optimal Dynamic Tax is None,'' Working paper, Federal Reserve Board of Governors, 1992. 6. C. Chamley, Efficient taxation in a stylized model of intertemporal general equilibrium, Internat. Econom. Rev. 26, No. 2 (1985), 451 468. 7. C. Chamley, Optimal taxation of capital income in general equilibrium with infinite lives, Econometrica 54, No. 3 (1986), 607 622. 8. V. V. Chari, L. J. Christiano, and P. J. Kehoe, Optimal fiscal policy in a business cycle model, J. Polit. Econom. 102, No. 4 (1994), 617 652. 9. I. Correia, Dynamic capital taxation in small open economies, forthcoming, J. Econom. Dynam. Control, in press. 10. P. A. Diamond and J. Mirrlees, Optimal taxation and public production I: Production efficiency and II: Tax rules, Amer. Econom. Rev. 61 (1971), 8 27 and 261 278. 11. S. J. Grossman and O. D. Hart, An analysis of the principal agent problem, Econometrica 51, No. 1 (1983), 7 45. 12. J. J. Heckman, A life-cycle model of earnings, learning, and consumption, J. Polit. Econom. 84 (1976), S11 S44.
CAPITAL INCOME TAXATION 13. L. E. Jones, R. E. Manuelli, and P. E. Rossi, Optimal taxation in models of endogenous growth, J. Polit. Econom. 101, No. 3 (1993), 485 517. 14. K. L. Judd, Redistributive taxation in a simple perfect foresight model, J. Public Econom. 28 (1985), 59 83. 15. K. L. Judd, The welfare cost of factor taxation in a perfect foresight model, J. Polit. Econom. 95, No. 4 (1987), 675 709. 16. K. L. Judd, `Òptimal Taxation in Dynamic Stochastic Economies,'' Working paper, Stanford University, 1990. 17. R. G. King, `Òbservable Implications of Dynamically Optimal Taxation,'' Working paper, University of Rochester, 1990. 18. Chang Gyu Kwag and Walter W. McMahon, `Èlasticities of Substitution Among Inputs: Comparison of Human Capital and Skilled Labor Models,'' Faculty working paper, University of Illinois Urbana Champaign, 1992. 19. R. E. Lucas, Jr., On the mechanics of economic development, J. Monet. Econom. 22 (1988), 3 42. 20. R. E. Lucas, Jr., Supply side economics: An analytical review, Oxford Econom. Pap. 42 (1990), 293 316. 21. R. E. Lucas, Jr. and N. L. Stokey, Optimal fiscal and monetary policy in an economy without capital, J. Monet. Econom. 12 (1983), 55 93. 22. J. A. Mirrlees, ``The Theory of Moral Hazard and Unobservable Behavior Part I'' Working paper, Nuffield College, Oxford, 1975. 23. J. A. Mirrlees, The theory of optimal taxation, in ``Handbook of Mathematical Economics'' (K. J. Arrow and M. D. Intrilligator, Eds.), Elsevier, Amsterdam, 1986. 24. F. P. Ramsey, A contribution to the theory of taxation, Econom. J. 37 (1927), 47 61. 25. J. Stiglitz and P. S. Dasgupta, Differential taxation, public goods and economic efficiency, Rev. Econom. Stud. 38 (1971), 151 174. 26. J. E. Stiglitz, `Ìnequality and Capital Taxation,'' IMSSS technical report, 1985. 27. J. E. Stiglitz, Pareto efficient and optimal taxation and the new welfare economics, in ``Handbook of Public Economics, Vol. II'' (A. J. Auerbach and M. Feldstein, Eds.), Elsevier, Amsterdam, 1987. 28. C. Yuen, ``Taxation, Human Capital Accumulation and Economic Growth,'' Working paper, University of Chicago, 1990. 29. X. Zhu, Optimal fiscal policy in a stochastic growth model, J. Econom. Theory 58 (1992), 250 289. 117
Page 1 and 2: journal of economic theory 73, 93 1
Page 3 and 4: CAPITAL INCOME TAXATION of feasible
Page 5 and 6: We consider the simplest infinitely
Page 7 and 8: Using (1.e) and rearranging we obta
Page 9 and 10: The first constraint is similar to
Page 11 and 12: From the planner's problem, Hence,
Page 13 and 14: CAPITAL INCOME TAXATION choosing th
Page 15 and 16: Letting + t be the Lagrange multipl
Page 17 and 18: function of the after-tax real wage
Page 19 and 20: where we used the property that u^
Page 21 and 22: non-zero result we have to assume t
Page 23: CAPITAL INCOME TAXATION 4. EXTENSIO

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