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Mathematical Formulation of Poverty Index 292 For example, Gini coefficient has been suggested by Bhattacharya et al. (1991) connecting the mean income and population size. It is given as follows: G(y) = 1 + (1/n) – (2/n z) ∑ i=1 n (n+1-i) yi Where, G (y) = Gini coefficient z = mean income n = population size But, none of these models existing in the literature catch the essence of poverty index for families of different sizes. Some of the work reported literature in this respect connects the poverty level to the prices of the commodities like sugar and rice. It is to be noted that these are indirect parameters that effect the poverty level. Further, the equation suggested by United Nations is a non-linear equation not very easy to use. Hence a need for new formulation of poverty index. 2. Description of new model PI = k f/e (3) Where, PI = poverty index e = economic level (family income) f = family size k = constant of proportionality The above relation is based on the inherent realistic assumption that PI is inversely proportional to economy level (e) or family income and directly proportional to the family size (f). Derivation of the formula for new model is given below: PI α 1/e (4) PI α f From the above, one can write the following equalities: (5) PI = k1/e (6) PI = k2 f Combining the above two equations, (7) PI = k f/e (8) Where, k = k1 k2 (9) In here k1 and k2 are the constant of proportionalities connected with family income (e) and family size (f). k is the combined constant of proportionality. It is to be noted that Eq.8 is the same equation as Eq.3. The constant of proportionalities can be evaluated based on the actual data. The data for family size and median family income can be either in terms of median or mean value. It can be said that this is a simple but realistic approach to calculate the poverty index. It is to be noted that eq.2 for calculation of poverty index is simple to use even though non-linear in nature. (2)
293 Chandra Putcha 3. Validation of the new model The above model (shown in eq.2) can be validated using the actual data existing in the literature. Table 1: Median Family Income in the past 12 months is given below by family size: State Median Income Estimate + Margin of Error Alabama $49,207 +/- 747 Alaska $69,872 +/-2,371 Arizona $55,709 +/-646 Arkansas $45,093 +/-813 California $64,563 +/-413 Colorado $64,563 +/-524 Connecticut $78,154 +/-951 Colorado $64,614 +/-975 Delaware $62,623 +/-2217 District of Columbia $61,015 +/-4029 Florida $54,445 +/-402 Georgia $56,112 +/-609 Hawaii $70,277 +/-1454 Idaho $51,640 +/-1028 Illinois $63,121 +/-529 Indiana $55,781 +/-459 Iowa $55,735 +/-577 Kansas $56,857 +/-698 Kentucky $48,726 +/-682 Louisiana $48,261 +/-794 Maine $52,793 +/-973 Maryland $77,839 +/-851 Massachusetts $74,463 +/-753 Michigan $57,996 +/-535 Minnesota $66,809 +/-485 Mississippi $42,805 +/-1,008 Missouri $53,026 +/-561 Montana $51,006 +/-829 Nebraska $56,940 +/-649 Nevada $61,466 +/-837 New Hampshire $71,176 +/-1,111 New Jersey $77,875 +/-649 New Mexico $48,199 +/-1,132 New York $62,138 +/-364 North Carolina $52,336 +/-481 North Dakota $55,385 +/-1,467 Ohio $56,148 +/-388 Oklahoma $47,955 +/-776 Oregon $55,923 +/-757 Pennsylvania $58,148 +/-361 Rhode Island $64,733 +/-1,971 South Carolina $50,334 +/-657 South Dakota $53,806 +/-936 Tennessee $49,804 +/-564 Texas $52,355 +/-275 Utah $58,141 +/-835 Vermont $58,163 +/-1,411 Virginia $66,886 +/-623 Washington $63,705 +/-650 West Virginia $44,012 +/-823 Wisconsin $60,634 +/-462 Wyoming $57,505 +/-1,708 Puerto Rico $20,425 +/-414
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