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An interpretation of the Gini coefficient in a Stiglitz two-type optimal tax problem

Abstract

In a two-type Stiglitz, J. Public Econ. 17, 213–240 (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income distribution of a utilitarian government. In this sense the optimal degree of income redistribution is determined by the severity of the incentive problem facing the policy-maker. Extensions of the benchmark model to allow for more general functional forms of the utility function and for more than two types of workers reveal that also in these cases the desired degree of income redistribution is positively correlated with the shadow prices of the incentive constraints.

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Correspondence to Bo Sandemann Rasmussen.

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Rasmussen, B.S. An interpretation of the Gini coefficient in a Stiglitz two-type optimal tax problem. J Econ Inequal 13, 17–26 (2015). https://doi.org/10.1007/s10888-014-9292-9

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Keywords

  • Optimal taxation
  • Income distribution
  • Incentive constraint
  • Gini coefficient