0n the planet Melancholia, consumers minimize utility subject to an equality income constraint as well as nonnegativity constraints. (Other than that, things are the same for an individual Melancholian as here on Earth: the utility functions have the same propertiesand you should assume monotonocity and differentiability, y e R\" and p e Rn++') Consider an individual consumer on Melancholia. Suppose that at his optimum, he conSumes both good i and good j. Derive the relationship between and at the individual's optimum. Now suppose that at his optimum, he conSumes good i and but not good k. Derive the relationship between and at the individual's optimum