a. Explain how you will construct the Lorenz curve from the income data given be

Question

a. 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]

b. Explain the basic facts describing increasing inequality a la Picketty. What explanations does Picketty provide for this phenomenon? In particular, does the condition “r>g” contribute to growing inequality? Present your arguments both in the context of the Solow model and by stepping outside the standard Solow model.

Explanation / Answer

a) 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).

b) Thomas Piketty examined the mai attributes of income inequality in many instances and generally concluded that one of the foremost factors causing increasing income inequality is the unrestrained accumulation of capital assets by certain section of the population compared to the economic growth.As empirically asserted by Piketty,if the rate of capital return is evidently higher than the rate of economic growth it would wventually cause greater income inequality as well and cause much concentrated didtribution of income/wealth.As a remedial fiscal action to prevent burgeoning income inequality Piketty suggested imposition of welfare tax on capital assets to redistribute wealth/income more equally and equitably among the entire population.Hence,Piketty mainly points out at the redistributive policy through tax imposition to attain a more stable and equitable wealth distribution.

As stated above,Piketty identifies that if the rate of return on capital investment(r) is greater than the rate of economic growth or GDP growth rate(g) then greater income inequality would prevail.Ideally from the perspective of Solow Growth Model,it implies that even though the capital accumulation in significantly high in an economy it is not being utilized for any productive capacity to enhance the output growth.The rate of investment is not proportional to the capital accumulation and much of the capital assets remain in the hand of wealthy section of the population which are used mainly for personal purposes and not for overall economic growth.Hence,contrary to what Solow advocated,in this instance,capital accumulation is higher but it is only concentrated in the hands of few which prevents the employment of the capital resources for productive purposes and overll economic progress.

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