What is the first-best allocation of water

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Problem: 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 π(w) = 4w - 1 2 w2. (I) 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? (II) What is the first-best allocation of water if w = 10?

Reference no: EM133614571

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