Arrakis is a planet without much water. There are two uses for water: consumption by local inhabitants, which creates local utility u(w) = 8w 1 2 w2 for w units of water, and spice mining, which creates profits (w) = 4w 1 2 w2. (a) Suppose that we care equally about utility and profits and that there is a total of w = 4 units of water on Arrakis. What is the first-best allocation of water? (b) What is the first-best allocation of water if w = 10