Problem 2 [20 points]. John and Jane consume nonnegative quantities of two goods, 1 and 2. Each has wealth w > 0 (they can have different wealth levels) and faces the same prices p1 = 1 and p2 = p > 0. John's preferences are described by the following utility function: uJohn (x1, X2) = X, + In x2, while Jane has utility function u Jane (x1, X2) = x1 + 4VX2. - 1) [7 points] Set up and carefully solve John's utility maximization problem to find his Marshallian demand for both goods. Do the same for Jane. 2) [7 points] Suppose p 2 4, and for both John and Jane, suppose w > 1. Find the aggregate demand functions for each good. Is this aggregate demand function independent of wealth distribution? Explain. 3) [6 points] Does your answer to part 2) change if p and w can take on any strictly positive value, including p = 4 and/or w - 1? Explain