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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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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 780.

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Date of creation: May 2013
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Handle: RePEc:ide:wpaper:27231

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  1. Cremer, Helmuth & Gahvari, Firouz, 1995. "Uncertainty, Optimal Taxation and the Direct versus Indirect Tax Controversy," Economic Journal, Royal Economic Society, vol. 105(432), pages 1165-79, September.
  2. Cremer, Helmuth & Gahvari, Firouz, 1998. "On Optimal Taxation of Housing," Journal of Urban Economics, Elsevier, vol. 43(3), pages 315-335, May.
  3. Baumol, William J & Bradford, David F, 1970. "Optimal Departures from Marginal Cost Pricing," American Economic Review, American Economic Association, vol. 60(3), pages 265-83, June.
  4. Atkinson, A. B. & Stiglitz, J. E., 1976. "The design of tax structure: Direct versus indirect taxation," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 55-75.
  5. P. A. Diamond, 1975. "A Many-Person Ramsey Tax Rule," Working papers 146, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Sandmo, Agnar, 1976. "Optimal taxation : An introduction to the literature," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 37-54.
  7. Cremer, Helmuth & Gahvari, Firouz & Ladoux, Norbert, 1998. "Externalities and optimal taxation," Journal of Public Economics, Elsevier, vol. 70(3), pages 343-364, December.
  8. Cremer, Helmuth & Gahvari, Firouz, 2002. " Nonlinear Pricing, Redistribution, and Optimal Tax Policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(2), pages 139-61.
  9. Laffont, Jean-Jacques & Tirole, Jean, 1990. "Optimal Bypass and Cream Skimming," American Economic Review, American Economic Association, vol. 80(5), pages 1042-61, December.
  10. Ware, Roger & Winter, Ralph A., 1986. "Public pricing under imperfect competition," International Journal of Industrial Organization, Elsevier, vol. 4(1), pages 87-97, March.
  11. Christiansen, Vidar, 1984. "Which commodity taxes should supplement the income tax?," Journal of Public Economics, Elsevier, vol. 24(2), pages 195-220, July.
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