The economy of Nintendo has ten people. Three of them live in the modern sector of Nintendo and earn $2000 per month. The rest live in the traditional sector and earn only $1000 per month. One day, two new modern sector jobs open up and two people from the traditional sector move to the modern sector.

(a) Show that the Lorenz curves of the income distributions before and after must cross. Do this in two ways:

(i) By graphing the Lorenz curves and

(ii) By first expressing both income distributions as divisions of a cake of size 1, and then showing that the two distributions are linked by “opposing” Dalton transfers.

(b) Calculate the Gini coefficients and the coefficients of variation of the two distributions.