3. Consider the social welfare function W = 1=1 x;1/N , where x represents the income of each individual i = {1,...,N}. (i) Demonstrate mathematically, whether W satisfies the five desirable properties of social welfare functions, as discussed in class. [5 marks] (ii) Write down the mathematical expression of the inequality index that corresponds to W. Check that when all incomes are equal, W = 12-1 X. [3 marks] 3. Consider the social welfare function W = 1=1 x;1/N , where x represents the income of each individual i = {1,...,N}. (i) Demonstrate mathematically, whether W satisfies the five desirable properties of social welfare functions, as discussed in class. [5 marks] (ii) Write down the mathematical expression of the inequality index that corresponds to W. Check that when all incomes are equal, W = 12-1 X. [3 marks]