2. (2 points) Consider a pure exchange economy. (a) (1 point) Suppose this economy is made up of two consumers, A and B. Both consumers face a generic CES function over two goods, ⃗xi = [xi 1, xi 2], such that ui(x1, x2) = (xρ 1 +xρ 2) 1 ρ . Assume both agents face the same generic linear budget constraint, ⃗p⃗xi = yi. Given the Marshallian Demand Functions for each consumer, find the price vector ⃗ p∗ that constitutes aWalrasian Equilibrium along with the Marshallian Demand Function vector ⃗ x∗. (b) (1 point) Now consider the addition of a new consumer to this economy, C, who faces a generic Cobb-Douglas utility function over the same two goods as A and B, such that uc(x1, x2) = xα1 x1−α 2 . Assume further that agent C faces the same generic linear budget constraint, ⃗p⃗xi = yi, as the other two agents. Find the new price vector ⃗ p∗ that constitutes a Walrasian Equilibrium along with the Marshallian Demand Function vector ⃗ x∗.