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, we have made: 1 ? 12282.4 34218.2 = 0.641, where the numerator is the households' income in the second decile after the transfer and the denominator is the households' income in the ninth decile after the transfer. To reach the loss of the proportional transfer of 4%, we have made: 35644 ? 34218 is the households' income (in Euros) in the second decile, and 35, 644 is the households' income in the ninth decile Transfer principles and inequality aversion, with an application to optimal growth, 6 To reach the upper bound on the loss in the transferred benefit, pp.1-11, 2001.

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