Suppose we model a consumer who cares about the "practical value and style of Gucci products," dollars of other consumption, and the "prestige value" of being seen with Gucci products. Denote these as x1 , x2, and x3 respectively

B. Consider the same definition of x1, x2, and x; as in part A. Suppose that the tastes for our consumer can be captured by the utility function u(x1 , *2, x;) = or; In x, + x2. a. Set up the consumer's utility maximization problem, keeping in mind that x; is not a choice variable. b. Solve for the optimal consumption of x (which will be a function of the prestige value x3). C. Is x normal or inferior? Is it Giffen? d. Now suppose that prestige value is a function of p1 . In particular, suppose that x} = p1. Substitute this into your solution for x1 . Will consumption increase or decrease as p1 increases? e. How would you explain that x, is not a Giffen good despite the fact that its consumption increases as pj goes up