1. Integrability expenditure function, preference Proposition6: differentiable e(p, u) is the expenditure function of sets V(a)={x∈9:p·x≥e(p,)vp>0} We need to prove e(p, u is the support function of y(u), that is elp, u)=min(px xEv(u) see the fi1.Integrability • expenditure function→ preference. • Proposition6: differentiable e(p,u) is the expenditure function of sets: • We need to prove e(p,u) is the support function of V(u) ,that is see the fig. ( ) { : ( , ) 0} n V u e u =     + x p x p pe u V u ( , ) min{ : ( )} p p x x =  