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Assume that the set of alternatives is X = R1 and consider a consumer with utility function Man, 332) = a3? + 3132. Fix prices (191,192) > 0 and wealth 'w > 0. (a ( Are the consumer's preferences locally nonsatiated? CT' Are the consumer's preferences convex? O Q. ( ( (e ) ) ) Write down the consumer's utilitymaximisation problem. ) Write down the Lagrangean and derive the rstorder necessary conditions. ) Does there exist a solution 33* to the rst-order necessary conditions with 33:20? (f) Does there exist a solution 33* to the rst-order necessary conditions with 33320? (g) Derive the consumer's demand correspondence 513(1), w)