Consider an initial income distribution {5, 12, 17, 20, 30, 40, 50, 100}. Let the poverty line z=40. The government's poverty alleviation budget is 40, which it distributes as a one-off cash transfer (as a grant) to individuals.

(1a) Suppose the government wants to reduce the number of the poor. Provide the final (or 'after grant') income distribution and discuss the optimal distribution of the grant.

(1b) Now suppose the government wants to reduce the squared poverty gap. How would the final (or 'after grant') income distribution change and why?