Abstract
A structure of taxes and transfers that keep the income distribution unchanged even after positive or negative shocks to an economy, is referred as a Distribution Neutral Fiscal Policy. Marjit and Sarkar (Distribution neutral welfare ranking-extending pareto principle, 2017, [14]) referred this as a Strong Pareto Superior (SPS) allocation which improves the standard Pareto criterion by keeping the degree of inequality, not the absolute level of income, intact. In this paper we show the existence of a SPS allocation in a general equilibrium framework, and we provide a brief survey of distribution neutral fiscal policies existing in the literature. We also provide an empirical illustration with Indian Human Development Survey data.
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This can also be interpreted as the desired level of inequality the policy maker is anticipating.
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Note that per-capita income data is available in this survey. However, income data have standard problems in the sense that people often misreports their income. Furthermore, the poverty line in India is usually constructed using the per-capita consumption figures. Thus using such figures for income data might be incomplete.
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An Wikipedia entry argues that “It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution.” (https://en.wikipedia.org/wiki/Pareto_efficiency).
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Acknowledgements
Sugata Marjit is indebted to the participants of the conference titled “The Economy as a Complex System IV: Can economics be a physical science?” arranged by the Institute of Mathematical Sciences (IMSc). We are also grateful to the seminar participants at IMF, Washington D.C. in July 2017, for helpful comments. We would also like to acknowledge the helpful comments by Sanjeev Gupta of the Fiscal Affairs Department of the IMF. The usual dissimilar applies.
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Mathematical Appendix
Mathematical Appendix
Let \(\{W^i\} :\) endowment vectors \(i=1,2,\ldots ,n;\sum \limits _{i} W^i=W\).
Utility functions, real valued, assumed to be continuous, increasing, strictly quasiconcave : \(\{\bar{U}^i\}\) The consumption possibility set is \(\mathfrak {R}^n_+\) the non-negative orthant. The set of feasible allocation vectors \(\mathfrak {F}=\{\{Y^i\}: Y^i\ge 0, \sum _i Y^i \le W\};~\{W^i\}\in \mathfrak {F}\); \(\mathfrak {U}=\{\{U^i\} : \exists \{Y^i\}\in \mathfrak {F},U^i(Y^i)=\bar{U}^i\forall i\}\) is the set of feasible utilities. Notice \(\{U^i(W^i)\}\in \mathfrak {U}\).
Statement 1 \(\mathfrak {U}\) is a nonempty compact subset of \(\mathfrak {R}^n_{+}\)
Proof: The above follows given the continuity of \(U^i\) over a compact set \(\mathfrak {F}\).
Let \(U^i(W^i)=\hat{U}^i\forall i\); there is a \(P^*=(P^*_1,P^*_2,\ldots ,P^*_n)\) which is a competitive equilibrium i.e., \(X^{i*}\) solves the problem \(max U^i(.)\) subject to \(P^*x\le P^*.W^i \forall i\) and \(\sum _{i}X^{i*}=W\). Let \(U^i(X^{i*}) = U^{i*}\).
Define \(\mathfrak {U}^\mathfrak {P}=\{\{\bar{U}^i\} : \{\bar{U}^i\}\in \mathfrak {U},~\exists \{U^i\}\in \mathfrak {U} ~\text {such that}~,U^i>\bar{U}^i\forall i\}\): Pareto Frontier. The First Fundamental Theorem assures us that \(\{U^{i*}\}\in \mathfrak {U}^\mathfrak {P}\).
Consider next \(\bar{\theta }<\hat{\theta }\); from the property of the supremum, there is \(\tilde{\theta }>\bar{\theta }\) such that \(U(\tilde{\theta })\in \mathfrak {U}\) i.e., there is \(\tilde{Y}^i\) such that \(\{\tilde{Y}\}\in \mathfrak {F}\) and \(U^i(\tilde{Y}^i)=\tilde{\theta }U^i(W^i) \forall i\). Now there must be a scalar \(1>\alpha _i\ge 0\) such that \(U^i(\alpha _i \tilde{Y}^i)=\bar{\theta }.U^i(W^i)\) since by shrinking the scalar \(\alpha _i\) we can make the left hand side go to zero (U is increasing), whereas for \(\alpha _i=1\), the left hand side is greater; also then we can claim \(\{\alpha _i \tilde{Y}^i\}\in \mathfrak {F}\) since
and
\(\quad \square \)
Statement 3 \(U(\hat{\theta })\in \mathfrak {V}\)
Thus one may conclude that \(\{\hat{Y}^i\}\) is a Pareto optimal configuration with the property that \(U^i(\hat{Y}^i)=\hat{\theta }U^i(W^i)\forall i\). And since \(\hat{\theta }\) is uniquely determined, so is the configuration \(\{\hat{Y}^i\}\).
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Marjit, S., Mukherji, A., Sarkar, S. (2019). Pareto Efficiency, Inequality and Distribution Neutral Fiscal Policy—An Overview. In: Abergel, F., Chakrabarti, B., Chakraborti, A., Deo, N., Sharma, K. (eds) New Perspectives and Challenges in Econophysics and Sociophysics. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-030-11364-3_13
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