UNDP introduced the human development report in 1991, a radical change in its approach in terms of multi-step fragmenting of the utility function and a concept of threshold income level, which was followed till 1998 by following an ill-structured Atkinson based multi-step utility function. Realizing the weaknesses in it formulation, the UNDP abandoned the approach abruptly from 1999 onwards. As a viable substitute for erroneous Atkinson based multi-step formulation of utility function used in UNDP's human development reports till 1998, we provided a generalized family of the utility functions under the premise of multi-step formulation while adhering to the concept of threshold income level and have showed in the present study that the earlier proposed two alternative formulations due to Bhatnagar (2001, 2002a) turn out to be particular cases.

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