Describe any 3 measures of Inequality. For each measure, explain whether it sati

Question

Describe any 3 measures of Inequality. For each measure, explain whether it satisfies the axioms of 1) Anonymity, 2) Population invariance, 3) Relative income principle, 4) Dalton principle Explain how you will construct the Lorenz curve from the income data given below. What is the relationship between the Lorenz curve and the Gini coefficient? Using this relationship compute the Gini coefficient for the data given below [Data: 5-people economy with incomes, A: 500, B: 35, C: 220, D: 170, E: 310]

Explanation / Answer

Three measures of income inequality:

Briefly, the four principles of measuring inequality can be described as follows:

From the above mentioned measures of inequality, Range satisfies the first three principles, but fails to satisfy the Dalton’s principle.

Conceptually,Lorenz Curve depicts the distribution of income or wealth in the economy among the overall population size of the economy.The Lorenz Curve basically shows the concentration of income/wealth distributed from the poorest to the richest section of the population and in this process signifies how much overall income/wealth in the economy is distributed among the poor and rich section of the population.The x-axis for the Lorenze Curve denotes the Aggregate/Cumulative percentage of income distributed from the poorest to the richest section and the y-axis shows the overall/cumulative share of income earned in the economy.

Now,here notice that the population size of the economy is 5 with individual incomes of A=500,B=35,C=220,D=170 and E=310

Hence,the total income level in the economy=(500+35+220+170+310)=1235

Therefore,individual percentage or share of income for A=(500/1235)*100=40.5%

Individual percentage/share of income for B=(35/1235)*100=3% approximately

Percentage/share of income for C=(220/1235)*100=17.8%

Percentage/share of income for D=(170/1235)*100=13.76%

Percentage/share of income for E=(310/1235)*100=25.10% approximately

Now we have to classify the population size of the economy(in this case 5) according to poorest to richest based on the individual percentage of income that each person earned.For example,notice that based on above calculation the poorest person based on the individual percentage of total income is B and the richest person based on the same logic is A and the rest 3 would fall somewhere between A and B or the poorest and the richest.As mentioned the x-axis represents this classification of the population size based on the individual percentage of income and the y-axis denotes the actual inidvidual percentages/share of income earned by the members in the population.Hence,if we plot the calculations done above for 5 people economy we would derive the Lorenze Curve graphically.

We know by now,that the Lorenze Curve represents the distribution of income/wealth level in the economy among the entire population size in the economy and consequently lead to the economic classification of population such as "poor" or "rich" based on their percentage share of overall income level in the economy.

Now,using the graphical information from Lorenze Curve,we can construct the Gini Coefficient which essentially shows the statistical dispertion of the income/wealth distribution in an economy to reflect the measure/extent of income equality/inequality in the economy.Thus,based on percentage share of income distributed among the population as shown by Lorenze Curve,Gini Coefficient can represent the level of income equality/inequality in the economy.

Recall the individual incomes of the 5 people in the economy (A=500,B=35,C=220,D=170 and E=310).The mean income level in the economy=1235/5=247

Gini Coefficient can be mathematically represented as:-

G=(Mean Absolute Difference for all individual observations of the population/Population size(n))/Mean income level

G={[(500-247)]+[35-247]+[220-247]+[170-247]+[310-247]/5}/247

G={(253+212+27+77+63)/5}/247

G=126.4/247

G=0.51 approximately

A Gini Coefficient of 0 implies perfect income equality and 1 implies perfect income inequality in an economy.In this example a Gini Coefficient of 0.51 is somewhere in the middle reflecting not a perfect income equality and nor totally perfect income inequality either).

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