T4 - Übungen PDF

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x1

x

u(x1 , x2 ) =

x12 ·x2

x

y

y

a, b > 0

u1 (x1 , x2 ) = a · x1 + b · x2 ,

x2

x1 , x2 ≥ 0

u2 (x1 , x2 ) = min{a · x1 , b · x2 }, vi (x1 , x2 )

u3 (x1 , x2 ) = x1a + b · x2 , a, b > 0

ui (x1 , x2 ) i = 1, . . . , 4 v1 (x1 , x2 ) =

a b

· x1 + x2 a

v3 (x1 , x2 ) = x1b + x2

v2 (x1 , x2 ) = min a

a b

v4 (x1 , x2 ) = x1b · x2

· x1 , x2



u4 (x1 , x2 ) = x1a · x2b .

x1 u(x1 , x2 ) = f (7 · x1 + x2 )

x2 f (·)

f (·) > 0 ′

MRS = −7 v(x1 , x2 ) = − (7 · x1 + x2 )−2...