Labor Economics 5th Edition by George Borjas

Exercise 13

Suppose the bottom 50 percent of a population (in terms of earnings) all receive an equal share of p percent of the nation's income, where 0 p 50. The top 50 percent of the population all receive an equal share of 1 - p percent of the nation's income.
a. For any such p, what is the Gini coefficient for the country
b. For any such p, what is the 90-10 wage gap