Issue1. Vol.1 (April, 2013) - IIT Mandi

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ESSENT Society for Collaborative Research and Innovation, IIT MandiResults & DiscussionThe extent of relative poverty and inequality inthe study area has been measured with the helpof Head Count Ratio and Gini-coefficienfollows: asHead Count RatioLet n denote the total number of people in thecommunity and q * the number of people belowthe poverty line. The ‘Head Count Ratio’ (Hp)is then:Hp = q * / nq * = 234.6, n = 1448.5. Therefore: Hp = 234.6 /1448.5 = 16.19 percentThe percentage of poor comes out to 16.19percent on the basis of ‘Head Count Ratio’. Butas a measure of poverty head count method isconsidered insensitive to the extent of aggregateshortfall in income from the poverty line as wellas to the distribution of income amongst thepoor.percentages of income and population of samplehouseholds when plotted on a graph paper andthe resultant shape of the Lorenz Curve (seediagram -1) clearly indicates that the bottom32.83 percent of the population is sharing about11.26 percent of the total income at the one endand at the other end 46.76 percent of the totalincome is shared by the 70.04 percent of thepopulation.The Lorenz Curve and Gini-CoefficientTable- I (page 75) shows the Distribution ofmonthly income among the sample households.To find out the extent of income inequality inthe Lorenz curve technique the size of items andthe frequencies are both cumulated and takingthe total as 100, than percentages are calculatedfor the various cumulated values.Their percentages are plotted on a graph paper.If there were proportionately equal distributionof the frequencies over various values of avariant, the points would lie in a straight line.This line is called ‘line of equal distribution’. Ifthe distribution of items is not proportionatelyequal, it indicates variability and the curvewould be away from the line of equaldistribution. The farther the curve is from thisline the greater is the variability in the series. Ahigher Lorenz curve implies more social welfarefor the same total of income. The cumulatedDiagram -1Lorenz Curve of the Income Distribution of AllHouseholdsThe income of the poorest among the poor isvery low due to their small size of holdings andlack of regular non-farm employmentopportunities72 ESSENT|Issue1|Vol1
ESSENT Society for Collaborative Research and Innovation, IIT MandiTable- IDistribution of monthly income among the sample householdsIncome Monthly Cumulated Cumulated No. of Cumulated CumulatedClasses Household Income (Rs.) Percentage Persons Number Percentage(Rs.) Income (Rs.)0-200 4791.67 4791.67 0.26 35.6 35.6 2.46200-300 20815.84 25607.51 1.41 83.3 118.9 8.2300-400 41050.56 66658.07 3.67 115.7 234.6 16.2400-500 30030.4 96688.47 5.33 66.9 301.5 20.81500-600 22612.5 119301.0 6.57 40.8 342.3 23.63600-700 25602.3 144903.3 7.98 39.5 381.8 26.36700-800 59476.17 204379.4 11.26 93.8 475.6 32.83800-900 68541.6 272921.0 15.04 80.0 555.6 38.36900-1000 43591.65 316512.7 17.44 45.1 600.7 41.471000-1100 66368.33 382881 21.09 63.8 664.5 45.881100-1200 122532.5 505413.5 27.85 106.3 770.8 53.211200-1300 76299.16 581712.7 32.05 61.3 832.1 57.451300-1400 89337.5 671050.2 36.97 64.5 896.6 61.91400-1500 82726.66 753776.8 41.53 57.1 953.7 65.841500-1600 94931.25 848708.1 46.76 60.8 1014.5 70.041600-170084218.33 932926.4 51.4 51.5 1066.0 73.591700-2000128045.0 1060971 58.45 106.0 1172.0 80.912000-3000470286.6 1531258 84.36 198.3 1370.3 94.63000-above 283790 1815048 100.0 78.2 1448.5 100.0The value of Gini – coefficient of the incomedistribution among all households has beencalculated as follows:Let Z be the mean income, Yi be the income ofthe i th person when income arranged inascending order, so that Yi ≤ Yi +1 for all i andn be the total number of people in thecommunity.1 2 nG ( y)= 1 + − ∑ ( n + 1 − i)Yin 2, wheren z i = 1G(y) = Gini-coefficient of the incomedistribution of all households, n= populationsize (1448.5), z= mean income (1303.80),n∑ ( n + 1 − i)Yi = 863760661 , thusi = 112G(Y ) = 1 + −× 8637606611448.5 2(1448.5) × 1303.80= 36.92%The value of Gini-coefficient of the incomedistribution among the poor has beencalculated as follows:1 2 qG ( Y ) = 1 + − ∑ ( q + 1 − i)Yiq2q z i = 1G(y) = Gini-coefficient of the incomedistribution of poor households, q = number ofpoor below the poverty line (234.6), z = meanincome of the poor (Rs. 284.13),q∑ ( q + 1 − i)yi = 6294820 Thus1 = 173 ESSENT|Issue1|Vol1
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Issue1. Vol.1 (April, 2013) - IIT Mandi

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