Suppose that there is a group of four individuals who have utility functionsu(y) =ywhereyis income. Suppose that the social welfare function has no intrinsic preference for inequality and that the income distribution isy={1,1,9,9}.

1.(a)Draw the Lorenz curve associated with this income distribution and illustrate a measure of in- equality using your graph.

2.(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{1,1,9,9}?

(ii)How does this government intervention impact average income?

(iii)What does your answer to(ii) tell us about the welfare consequences of income redistribution?

3.(c)Suppose the utility of the two individuals with an income of9is nowu(y) =ywith >1.

i) Does this alter the case for equalising incomes?

ii) Discuss how different criteria might be used to justify redistribution even whenis high.