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Selected answers in Chapter 28

Selected answers in Chapter 28 - for country A is 0.74...

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income 100 62 56 46 16 12 8 4 0 28 26 A C B 45° Selected answers in Chapter 28 7 Plotting the Lorenz curves (LC) below indicates shows that Group B is the most equal set of incomes. For all percentages of households, the LC for Group B is closer to the 45 degree line of equity than are the other LC curves. Group A is the more unequal as the LC for Group A is always furthest from the line of equity. The LC curves do not cross at any point. 8 (i) Variance shows the extent of inequality in a country by measuring the square of the extent to which incomes diverge from the mean corrected for sample size. Using the formula in Equation 28.3, for country A the variance is 111,240 while for country B the variance is 124,450. Using this measure, country A has a slightly more equal distribution of income because incomes are closer to the mean than in country B. (ii) The coefficient of variation (CV) that normalises the variance on average income. Accordingly, the measure of inequality is not sensitive to the level of income. Using the formula in Equation 28.4, the CV
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Unformatted text preview: for country A is 0.74 while the CV for country B is 0.61. By this measure, Country B has a more equal distribution of income. (iii) These results show that the degree of inequality depends on the measure being used. Any inferences from mathematical measures of inequality must take account of the attributes of that measure. 9 Using the GC in Equation 28.7 and taking Ballarat males (60, 70, 80). ΣΣ | y i-y | = (10+20)+(10+10)+(20+10) = 80. So GC = 80/2n 2 y(bar) = 80/(2 × 9 × 70) = 0.0634. Using the same method for the other groups and for the combined male and females groups (with six members), we get the following GCs: Ballarat female 0.0952 Bendigo male 0.351 Bendigo female 0.386 All males 0.275 All females 0.267 This indicates that the: Ballarat female GC > Ballarat male GC Bendigo female GC > Bendigo male GC But Combined male GC > combined female GC....
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