How to read this
(UMP): with income , reach the highest indifference curve; the answer is Marshallian demand , with utility . (EMP): to reach utility , find the cheapest budget line; the answer is Hicksian demand , at cost .
- Switch between the two views: when they pick the same bundle, .
- Change : the four duality identities, among them Roy's identity and Shephard's lemma, hold at every price.