7. a. Show that if Evgeny Evgenievich's preferences are homothetic, then the cross-price effects on Marshallian demand are symmetric. That is, given a system of demand equations D(P, I) arising from homothetic preferences, the cross-price derivatives for any two goods i and j must satisfy aDi(PD) aDi(PD) api aPi b. Show by counter example that the result in part (a) does not hold for non-homothetic preferences