2. Aggregation across goods Hicksian separability: no relative price change, so p=t plet: p=t, x=px Define the indirect utility function v(p, q, w)=max u(x, Z) s.t. ppx+gZ=w As Roy' s identity show: x(p, q, w)= Ov(p, q, w)/Op >ov(pp, q, w)/Op, px(p, q, w) av(p, q, w)/aw av(pp, q, w)/aw2.Aggregation across goods • Hicksian separability: no relative price change, so ,let: • Define the indirect utility function: • As Roy’s identity show: 0 p p =  t 0 p t x = = , p x 0 ( , , ) max ( ) . . v p w u s t p w = + = x,z q x,z p x qz 0 0 0 ( , , ) / ( , , ) / ( , , ) ( , , ) ( , , ) / ( , , ) / i v p w p v p w p x p w w v p w w v p w w     = − = − =     q  p q q p x p q q p q