2. Aggregation across goods Hicksian separability: no relative price change so p=tp,let p=t,x=px Define the indirect utility function v(p, g, w)=max u(x, z) X,Z s.t. pp x+gz=w As Roy's identity show Ov(p, q, w)/Op 2ov(pp, q, w)/Op x(p, q, w)av(p, q, w)/Ow av(pp, a, w)/OwpX(p, q, w)2.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