Exercise 8. Cookies and Ice Cream: Substitutes of Complements? (CES function)

Your brother's utility from Cookies (x₁) and Ice Cream (x₂) is v_B = (x₁ + x₂)². Your sister's utility is v_S = (x₁^- + (1- )x₂^-)^-2. Can you tell which sibling believes Cookies and Ice Cream must be eaten together (complements), and which sibling instead either eats Cookies or eats Ice Cream (substitutes)?

a)Find your sister's MU₁, MU₂ and MRS. What is her MRS at bundles (1,2), (2,2), (2,1)?

b)Find your brother's MU₁, MU₂ and MRS. What is his MRS at bundles (1,2), (2,2), (2,1)?

c)Find the elasticity of substitution between x₁ and x₂ for your brother, and your sister.