An adverse social welfare consequence of a rich-to-poor income transfer: A relative deprivation approach

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Aufrufstatistik

URI: http://hdl.handle.net/10900/78137
http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-781374
http://dx.doi.org/10.15496/publikation-19537
Dokumentart: Aufsatz
Date: 2017-09-22
Source: University of Tübingen Working Papers in Economics and Finance ; No. 102
Language: English
Faculty: 6 Wirtschafts- und Sozialwissenschaftliche Fakultät
Department: Wirtschaftswissenschaften
DDC Classifikation: 330 - Economics
Keywords: Economics
Other Keywords:
A rich-to-poor transfer
Relative income
Sen’s social welfare function
License: Publishing license excluding print on demand
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Abstract:

A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular - the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.

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