1. A Lorenz curve is a curve defined by some equation 1,- = LEI) on the interval [I], 1], where each :r-yalue represents the least wealthy :1! portion (i.e. lmif'b) of a society, and the corraponding yyalue represents the portion of the total wealth that is owned by that part of the society. Note that if two or more people are 'equally wealthy', then order them in any order. For example, Lf} = [1.10 would mean that the 'poorest' 30% of the population owns 1B% of the total wealth. The line 3; = :1! is called the line of perfect equality. Optional: Think about why this is a suitable name. The area of the region enclosed by y = :r and y = Life] is sometimes used as a measure of how [unjequitable a society is. (a) For any Lorenz curve, Lf} = I] and LE1} = 1. Explain briefly why this is. [b] Suppose that for the population of Narnia, the Lorenz curve can be modelled by L,~,r{:r} = or\". Find the area of the region between the cunures LNEI] = mg and y = :r. 1 [c] Suppose that for the population of Westerns, the Lorenz curve can be modelled by Lurk} = 2em\". 3 1 Find the area of the region between the curva Lwm} = Eme'jL and y = I. Make sure to justify how you know which curve is above the other. Find the area of the region between them. Make sure to justify how you know which curve is above the other. lfyou wish, you can do this with a graph, and using DESMDS {or other graphing softwarefcalculator] is aoceptable to produce the graph. (d) Aocording to these models, which society is more equitable - Narnia or Westeros? Explain briefly. (Dog a larger area represent a more or less equitable society? Why?}