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Atkinson-Stiglitz and Ramsey reconciled: Pareto efficient taxation and pricing under a break-even constraint

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  • Cremer, Helmuth
  • Gahvari, Firouz

Abstract

The Ramsey tax problem examines the design of linear commodity taxes to collect a given tax revenue. This approach has been seriously challenged by Atkinson and Stiglitz (1976) who show that (under some conditions) an optimal income tax makes commodity taxes redundant. In the meantime, the Ramsey setting has had a second life as model of regulatory pricing. Boiteux (1956) studies linear pricing of a regulated multi-product monopoly that has to cover some "fixed cost" through markups on the different products (equivalent to taxes). While the scope of regulation has declined, Ramsey-Boiteux pricing continues to play an important role. This paper examines if the optimal tax and regulatory pricing approaches to Ramsey pricing can be reconciled. We incorporate the two objectives of revenue raising for financing the government's expenditures and a regulated firm's fixed cost into a single framework. The first major lesson is that the existence of a break-even constraint not only requires taxation of goods produced by the regulated firm, but also the taxation of other goods. Next, we consider the cases of independent Hicksian and Marshallian demand curves. In both the Ramsey solution imply so-called inverse elasticity rules. In the separable Hicksian demand case, the private goods (not included in the break-even constraint) continue to go untaxed as in the Atkinson and Stiglitz setting. In the case where Marshallian demands are independent, the effect of the break-even constraint spills over to the other goods which no longer go untaxed. We continue to get inverse elasticity rules; however, there is no covariance (or similar) term that captures redistributive considerations. Finally, we study the most celebrated general result obtained in the Ramsey model; namely, the (un)equal proportional reduction in compensated demands property. We find that the redistributive considerations are once again replaced by tax revenue terms.
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  • Cremer, Helmuth & Gahvari, Firouz, 2013. "Atkinson-Stiglitz and Ramsey reconciled: Pareto efficient taxation and pricing under a break-even constraint," IDEI Working Papers 780, Institut d'Économie Industrielle (IDEI), Toulouse.
    • Handle: RePEc:ide:wpaper:27231
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    1. Cremer, Helmuth & Pestieau, Pierre & Rochet, Jean-Charles, 2001. "Direct versus Indirect Taxation: The Design of the Tax Structure Revisted," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 781-799, August.
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    4. Diamond, P. A., 1975. "A many-person Ramsey tax rule," Journal of Public Economics, Elsevier, vol. 4(4), pages 335-342, November.
    5. Helmuth Cremer & Firouz Gahvari, 2002. "Nonlinear Pricing, Redistribution, and Optimal Tax Policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(2), pages 139-161, April.
    6. Diamond, Peter A & Mirrlees, James A, 1971. "Optimal Taxation and Public Production: I--Production Efficiency," American Economic Review, American Economic Association, vol. 61(1), pages 8-27, March.
    7. Helmuth Cremer & Firouz Gahvari & Norbert Ladoux, 2002. "Externalities and Optimal Taxation," Chapters, in: Lawrence H. Goulder (ed.), Environmental Policy Making in Economies with Prior Tax Distortions, chapter 14, pages 210-232, Edward Elgar Publishing.
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    9. Cremer, Helmuth & Gahvari, Firouz, 1995. "Uncertainty, Optimal Taxation and the Direct versus Indirect Tax Controversy," Economic Journal, Royal Economic Society, vol. 105(432), pages 1165-1179, September.
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    1. Helmuth Cremer & Firouz Gahvari, 2017. "Restoring Ramsey tax lessons to Mirrleesian tax settings: Atkinson–Stiglitz and Ramsey reconciled," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 11-35, June.

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    JEL classification:

    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

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