Suppose that there is a group of four individuals who have utility functions u[y} = J? where y is income. Suppose that the social welfare function has no intrinsic preference for inequality and that theincome distribution is y = {111,Q,Q}. {a} Draw the Lorenz curve associated with this income distribution and illustrate a measure of in- equality using your graph. {b} Suppose that the government intervenes and equalizes income in the economy. i) At what equal level of income per capita is total utility the same as with {1, 1,919}? ii) How does this govemment intervention impact average income\"!II iii) What does your answer to [ii] tell us about the welfare consequences of income redistri- bution? {c} Suppose the utility of the two individuals with an incomeon is now eiy} = EVE? with H :=- 1. i) Does this alter the case for equalising incomes? ii) Discuss how different criteria might be used to justify redistribution even when 5' is high