1. Puzzle Piece #2: The purpose of this question is to construct a market demand curve \"from the ground up." Consider a market with three consumers: Bruce, Clark, and Diana. They each have income of Y = 120. Their utility functions are: 0 Bruce: U = $053,105 . Clark. U = IU-Z'Syj 0 Diana: U = 10'75y'25 (a) If the price of good 3; is pg = 10, derive the equation for the market demand curve for good 1'. (b) How much will each consumer purchase if the price of good I is p1 = 5? Why are they different? Does it make sense? (c) Draw the three individual demand curves and the market demand curve on the same graph. Indicate the quantities when pm = 5