2. Aggregation across goods Functional separability Independence property (x, z)%(x,z)e(x,,)%(,z) Weakly separable utility function: (x 2)=0(v(x), 2) Then the problem is x∈maxw(x) S.t. pX=w2.Aggregation across goods • Functional separability: – Independence property – Weakly separable utility function: • Then the problem is ( ) ( ) ( ) ( ) x,z x ,z x,z x ,z % %      u U v ( ) ( ( ), ) x,z x z = max ( ) . . x x v s t p w  = , z x x x