Andrea maximizes the following utility function: subject to the budget constraint u(x1, x2) = x ² x ² P1x1 + ₂x2 = I where p1, p2, x1, x2, I > 0 (a) Find the (x₁, x2) that maximizes u(x₁, x2). (b) Show that the maximizer x (P1, P2, I) is decreasing in p2 and increasing in I (Hint: Use the partial derivatives). (c) Does x (P1, P2, I) change if p₁ changes? (Hint: partial derivatives).

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