Consider a consumer with utility function u(x1; x2; x3) = x1x2x3, and income w. (a) Set up the consumers utility maximization problem and find the...

Consider a consumer with utility function u(x1; x2; x3) = x1x2x3, and income w.

(a) Set up the consumerís utility maximization problem and find the Walrasian de-

mands for each good.

(b) Let x1 + p2 /p1 x x2 = xc denote the units of a composite good. Set up the consumer's

utility maximization problem again, but now in terms of the composite good xc. Find the Walrasian demand function for the composite good xc.

(c) Show that the Walrasian demands you found in parts (a) and (b) are equivalent.