The following utility functions are defined over three goods, x, y, and z. Calculate the demand functions for each good, h, for j = x, y, z, as functions of the prices px, P (a) u(x, y, z) = xyz hylPx, Py. Pz, m) 3p. hylPx. Py, Pz, m) 3p. %3D hz(Px. Py. Pz. m) (b) u(x, Y, z) = x + In(y) + In(2) 3 2 m if m > Px hylPx, Py. Pz, m) if m sPx Px Ру if m > hylPxı Pyi Pzi m) %3! if m sPx Px if m > h-(Px. Py. Pz, m) %3D If ms20. E
The following utility functions are defined over three goods, x, y, and z. Calculate the demand functions for each good, h, for j = x, y, z, as functions of the prices px, P (a) u(x, y, z) = xyz hylPx, Py. Pz, m) 3p. hylPx. Py, Pz, m) 3p. %3D hz(Px. Py. Pz. m) (b) u(x, Y, z) = x + In(y) + In(2) 3 2 m if m > Px hylPx, Py. Pz, m) if m sPx Px Ру if m > hylPxı Pyi Pzi m) %3! if m sPx Px if m > h-(Px. Py. Pz, m) %3D If ms20. E
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.8P
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Please help me with Question (b), for the two parts I got wrong.
Transcribed Image Text:The following utility functions are defined over three goods, x, y, and z. Calculate the demand functions for each good, h, for j = x, y, z, as functions of the prices px, py. Pz and income, m.
(a)
u(x, y, z) = xyz
m
hy(Pxı Py. Pz. m) =
3p.
m
hy(Px, Py. Pz, m) =
3p,
h-(Px. Py. Pz, m) = 3p.
(b)
u(x, y, z) = x + In(y) + In(z)
m
2
if m> 흑px
hylPx, Py. Pz, m) =
if msPx
Px
Py
if m >
hy(Pxr Pyr Pz m) =
if ms 측px
+
Px
if m > 흑px
2p-
hz(Px. Py. Pz, m) =
If ms
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