Question

Here’s a weird but easy to calculate economy. Suppose everybody in the economy experiences exactly same life story: start working for free at age 1 for $1/hour, and then has a wage increase $1 every year until age 100. That is, a person who is 20 years old makes $20/hour, a person who is 45 years old makes $45/hour, and so on. Every year, one person is born, and 1 person reaches age 100 and dies. Everyone lives for 100 years. That is, at any point in time, the economy is made of 100 people, 1 person who is aged 0 (been born in the current year), 1 person aged 1, 1 person aged 2, 1 person aged 3, …, all the way to 1 person aged 99, each earning their age in dollars per hour.

a. Calculate the Gini coefficient for this economy. b. The current estimates of Gini around the world ranges from (the lowest in the world) 23.7 in Slovenia to (the highest in the world) 63.2 in Lesotho. How does our imaginary economy compare to the real-world countries? (that is, is it unusually high, unusually low, or about average?) c. In your opinion, is the income inequality in our imaginary economy a bad thing and requires that the government redistributes incomes? Explain why or why not.

Answer 1

b. Our imaginary economy has a gini coefficient of .33 (ie. Score of 33, when measured on a scale from 0 to 100). A gini coefficient of less than 0.2 represents perfect equality and above 0.5 shows severe inequality. Any score between 0.3 and 0.4 represents adequate equality. So our imaginary economy is about average when compared with real world countries ( neither too bad nor too good, but adequate enough). But we cannot judge a country's position merely on the basis of gini idex as it is not an absolute measurement of income or wealth. Nevertheless gini coefficient among the poor can be important because the impact on poverty of economic shocks can differ greatly depending on the level and distribution of resources among those who are poor.

c. As we have seen a gini coefficient of .33 is not bad at all. But if we look at it their is huge gap between the first decile (1 to 10 age group) and the last decile (91 to 100 group). So just by looking at the gini coefficient we cannot say there is not necessity for a government redistribution. If there is a possibility to redistribute without disturbing economic balance it should be welcomed