1. (5 marks) A country's Lorentz curve, 3; = L(.r,), provides us with insight into the country's income inequality. In particular, if the point (i L) is on the Lorentz curve, then this 100' 100 means that the bottom a% of households receive b% of the country's total income. In this context, the line y = m is called the perfect equality line (do you see why?). The Gini index of a country is dened to be the area of the region between the line y = :1: and the country's Lorentz curve 3/ = L(:n) on the interval [0, 1], and can be used to measure the income inequality of the country. Suppose there are two hypothetical countries A and B with Lorentz curves: LA($) = 1133, , 7T 1r 71' LB(:I:) s1n (Ex) 5:6 cos (53:) . (a) We can see that the point (0.5, 0.125) is on country A's Lorentz curve 3; = LA(:c). From this, what can we conclude about the income distribution of the country A? (b) Compute the Gini indices of the countries A and B. Round your answers to the nearest 10th. (c) Based on your previous result, which country has higher income inequality? (Resource: https : / / en . wikipedia . org/wiki/Gini_coefficient) (You may wonder how your country is doing: https : //en.wikipedia. org/wiki/List_o:f_ countries_by_income_equality)