1. Consider the utility function where the parameters and all the 3 are positive. For simplicity, ignore the case = = 1. a. Given the vector of prices p = (p₁.....PN),

define U(.....) = 1/4-21-1/4" P(p) can be written as for n = 1,..., N. = min (EN) c. Determine V(p.x). (i) Set up the Lagrangian. Write down the first-order conditions and use the constraint U (₁,...,CN) = 1 to simplify these conditions to p = µ(3/₂)¹/, for n = 1,..., N, where is a positive Lagrange multiplier. (ii) Determine the consumption choices (c₁,..., CN) that solve (1). (iii) Verify that V(p, x) = n=1 N {Σ P.C. : U(C... (x) ≥ 1}. P(p) = b. Show that the consumption choices that solve max 1/(1-1/2) (CEN) N 1/(1-x) Eve-)* N ;, {U ( ... ) : Σ PC ≤ 2} Cn = Bn B. (P(p)) P(p) (1) (2)