In this individual portion of the project, you will learn about two important tools for measuring inequality: the Lorenz curve and the Gini coefficient. These will be used in the pod project. 1. The Lorenz Curve: In this problem, we'll work step-by-step through constructing values of a Lorenz function from a set of raw data. This will help you to understand the meaning of the Lorenz curve, which you'll use in your pod project. (a) A small village has a population of 10 people. The yearly incomes, in thousands of CAD per year, for each of the 10 residents is listed below. 95, 46, 74, 150, 60, 110, 46, 34, 80, 105 Rearrange these incomes in increasing order, from smallest to largest. (b) What is the total sum of the income made by all people in this town each year? Answer: thousand CAD. (c) What fraction of the total income is made by top 20% of earners? Please express your answer as a decimal value between 0 and 1. Answer: (d) What fraction of the total income is made by bottom 20% of earners? Please express your answer as a decimal value between 0 and 1. (Note: Even if there is a tie for the second-lowest earner, you should only count two of the 10 people as the lowest-earning 20%.) Answer: (e) Please continue by filling in the chart below. All numbers in the second row should be in units of thousands of CAD, while all numbers in the third row should be decimal values between 0 and 1. Please round numbers in the third row to the nearest 0.01. Lowest-earning fraction r 0.0 0.2 0.4 0.6 0.8 1.0 Total income (thousand CAD) made by lowest-earning fraction r Fraction of income made by lowest-earning fraction r (f) The Lorenz function L(x) represents the fraction of the population's total income made by the lowest- earning fraction r of people in the population. In this case, the numbers that you wrote in the third row of the above table represent values of L(x). Please plot these points on the grid below. (When graphed, these become points on the Lorenz curve, which is the graph of the Lorenz function.) 1.0 0.8 y = L(x) 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 Note: It would be possible to also compute values of L(x) for r = 0.1, 0.3, ..., 0.9 etc, however, we are not asking you to compute any more values for this problem. Do not interpolate to sketch a curve