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Topology of utility possibility frontiers of economies with Ramsey taxation


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  • Murty, Sushama

    (Department of Economics, University of Warwick)


This paper establishes the generic size and structure of the second-best Pareto frontier and its various components in private ownership economies with Ramsey taxation. It provides conditions under which the second-best Pareto frontier of an economy with H consumers will have the expected structure of a H . 1-dimensional manifold. In a class of economies, it shows that, generically, while the jointly production and consumption ine cient component of the second-best Pareto manifold is a submanifold that also has a dimension equal to H . 1, the production e cient, consumption e cient, and the rstbest components are lower dimensional, and hence negligible in size, submanifolds. Thus, it formally demonstrates that the economies usually studied in the literature, where all second-best are production e cient, are extremely rare. Market prices cannot be used in lieu of social shadow prices in most economies for cost-bene t tests. This begs further research for recovering the true social shadow prices from the data in such economies.

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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 912.

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Date of creation: 2009
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Handle: RePEc:wrk:warwec:912

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Keywords: Ramsey taxation ; second-best ; production e ciency ; general equilibrium ; private ownership ; di erential topology ; transversality theorem.;

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  1. Keen, Michael & Lockwood, Ben, 2010. "The value added tax: Its causes and consequences," Journal of Development Economics, Elsevier, vol. 92(2), pages 138-151, July.
  2. Zeckhauser, Richard J & Weinstein, Milton C, 1974. "The Topology of Pareto-Optimal Regions with Public Goods," Econometrica, Econometric Society, vol. 42(4), pages 643-66, July.
  3. Blackorby, Charles & Murty, Sushama, 2009. "Constraints on Income Distribution and Production Efficiency In Economies with Ramsey Taxation," The Warwick Economics Research Paper Series (TWERPS) 908, University of Warwick, Department of Economics.
  4. Hahn, Frank H., 1973. "On optimum taxation," Journal of Economic Theory, Elsevier, vol. 6(1), pages 96-106, February.
  5. Atsushi Kajii & Antonio Villanacci & Alessandro Citanna, 1998. "Constrained suboptimality in incomplete markets: a general approach and two applications," Economic Theory, Springer, vol. 11(3), pages 495-521.
  6. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  7. Leslie J. Reinhorn, 2011. "Production efficiency and excess supply," Working Papers 2011_13, Durham University Business School.
  8. Guesnerie, Roger, 1979. "Financing Public Goods with Commodity Taxes: The Tax Reform Viewpoint," Econometrica, Econometric Society, vol. 47(2), pages 393-421, March.
  9. Guesnerie,Roger, 1998. "A Contribution to the Pure Theory of Taxation," Cambridge Books, Cambridge University Press, number 9780521629560, October.
  10. Robin Boadway, 1973. "Cost-Benefit Rules in General Equilibrium," Working Papers 137, Queen's University, Department of Economics.
  11. Carvajal, Andrés & Polemarchakis, Herakles, 2011. "Idiosyncratic risk and financial policy," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1569-1597, July.
  12. Fuchs, Gerard & Guesnerie, Roger, 1983. "Structure of Tax Equilibria," Econometrica, Econometric Society, vol. 51(2), pages 403-34, March.
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