micro-economics, thanks

Consider an exchange economy with 2 consumers whose preferences and endowments are represented by: I u1(E1, E2) = [(931)" + ($2)p]1/p and e1 = (8 + a, 11+ b) o u2(E1, E2) = [(3:1)p + (E2)p]1/p and 62 = (10 (1,4 b) where a El [ 810] and b E [ 11 4]. Consider the allocation E given byE1=(2 ,.ElO) '2 (6 5) (a) Assume p = 1/3. Find the demand function/correspondence of consumer 1 as a function of a. and b. [7] (b) Assume still p = 1/3. Are there values of a and I) such that E is a Walrasian equilibrium allocation? [8] (c) Assume now p = 3. Find the demand function/correspondence of consumer 1. [3] (d) Assume still p = 3. Are there values of a and b such that E is a Walrasian equilibrium allocation? Are there values of a and 5 such that E is in the Core? [7]