1. Consider a social welfare function W = =EN x 1 - In(* , where x, 2 0 represents the income of each individual i = {1, ..., N} and # = #> (i) Demonstrate mathematically, whether W satisfies the five desirable properties of social welfare functions, as discussed in class. [10 marks] (ii) Write down and identify the mathematical expression of the inequality index that corresponds to W. [4 marks] (iii) Suppose all individual incomes are equal. In this case, what development indicator would W resemble? Explain. [2 marks]