Duality Graph
2
Mikro 1 CAU Kiel WS 2001/02 Raff/Willmann Overview of Duality U max s.t. BC Marshallian Di(p1, p2, I) Hicksian DiC(p1, p2, U) Expd. fct. E(p1, p2, U) p1x1+p2x2 min s.t. u=U(x1,x2) ind. U fct. V(p1, p2, I) down: plug into the objective fct Shephard’s Lemma Roy’s identity right to left and back: plug in expd. fct. for I or ind. U fct. for U to get from Di to DiC and vice versa. To move between V and E simply solve for I and U respectively.
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microeconomics duality graph marshallian and hicksian demand
Transcript of Duality Graph
![Page 1: Duality Graph](https://reader035.fdocuments.net/reader035/viewer/2022081816/55cf8ebe550346703b9522ff/html5/thumbnails/1.jpg)
Mikro 1 CAU KielWS 2001/02 Raff/Willmann
Overview of Duality
U maxs.t. BC
MarshallianDi(p1, p2, I)
HicksianDiC(p1, p2, U)
Expd. fct.E(p1, p2, U)
p1x1+p2x2 mins.t. u=U(x1,x2)
ind. U fct.V(p1, p2, I)
down: plug intothe objective fct
Shephard’sLemma
Roy’s identity
right to left and back:plug in expd. fct. for I orind. U fct. for U to get fromDi to DiC and vice versa.To move between V and E simply solve for I and Urespectively.
![Page 2: Duality Graph](https://reader035.fdocuments.net/reader035/viewer/2022081816/55cf8ebe550346703b9522ff/html5/thumbnails/2.jpg)
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