If Utility Is Separable in a Three-Good Utility Function Then for Changes In

Multiple Choice

If utility is separable in a three-good utility function $\left[ U \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = U _ { 1 } \left( x _ { 1 } \right) + U _ { 2 } \left( x _ { 2 } \right) + U _ { 3 } \left( x _ { 3 } \right) , U _ { i } ^ { \prime } > 0 \quad U _ { i } ^ { \prime } < 0 \right]$ then for changes in $p _ { 1 } , x _ { 2 } \text { and } x _ { 3 } \text { must }$

A) both be gross substitutes for x₁ .
B) both be gross complements for x₁ .
C) be such that if one is a gross substitute for x₁ ,the other is a gross complement for x₁ .
D) both be gross substitutes or both be gross complements for x.