1. Consider a consumer who consumes. goods 1' = 1, . . . ,n and has preferences that are represented by the utility function use) = (Zuni so?) # i=1 Whl'pl 1, p :5 0, 1,- } U, and Sign = 1. (a) Show that the utility function is strictly quasiconcave assuming p :1 1. In the solution, note carefully where you use p Z} 11 and also where you use that o,- 3: D! The other case, p s\". 1 is very similar and you can see how to do it once you have understood the case p 23- 1. Hints: {1) try to simplify by using or monotonic tmnsfonnotion to oh~ loin out} = (n(x)), were p{) has :1 simpler fonn. Explain why o{) is strictly quasiconcave if and only if u{) is strictly quasiconcave. (2} quasiconcavity is implied by concavity which is oen easier to show. (h) Derive Marshallian demand for all goods. {You may assume that n{x} is strictly concave for this derivation)"