Imagine a country divided into four equally sized classes, poor, lower middle, upper middle, and upper. Within each class, incomes are the same. Imagine incomes of the poor class increase by 20%, of the lower middle class increase by 30%, of the upper middle class increase by 27%, and of the upper class increase by 23%. Assume the average increase in income is 24.5%. Further, assume the class orderings are unchanged, and that population size has not change. Has inequality increased, decreased, or changed in an unrestricted way, according to the Lorenz criterion? Justify your answer fully.
[Hint: beware of solving this question using an example distribution. For example, if you use (100,200,300,400) and then apply the changes, you realize the mean went up by 25.3%, not 24.5% as stated in the question. This exercise can be solved just by using the definition of the Lorenz curve; it helps to focus on the bottom and top income segments.]