40
Chapter
2
consider
increasing
transformations,
Chelsea’s
ordering
of
bundles
4=(1,2)
and
B=(3,8)
is
unaffected
(i.e.,
she
still
prefers
B
to
4).
When
we
consider
decreasing
transformations,
show
that
Chelsca’s
ordering
of
bundles
4
and
B
may
be
affected.
(a)
vlx,y)=[u(x,y))
(b)
v(x,y)=In[u(x,y)]
(¢)
vix,y)=S5[u(x,y)]
@
v
=
g5
(e)
vlx,y)="Tlulx,y)]
-2
.
Finding
Properties-I
Eric’s
preferences
for
books,
x,
and
computers,
y,
can
be
represented
with
the
following
Cobb-Douglas
utility
function:
u(x,
y)
=x*y2.
(a)
Find
Eric’s
marginal
utility
for
books,
MUy,
and
for
computers,
MU,
(b)
Are
his
preferences
monotonic
(i.e.,
weakly
increasing
in
both
goods)?
(c)
For
a
given
utility
level
u,
solve
the
utility
function
for
y
to
obtain
Eric’s
indifference
curve.
(d)
Find
Eric’s
MRS
between
x
and
y
.
Interpret
your
results.
(e)
Are
his
preferences
convex
(i.e.,
bowed
in
toward
the
origin)?
(f)
Consider
a
given
utility
level of
10
utils.
Plot
his
indifference
curve
in
this
case.
.
Finding Properties-IL.C
Repeat
exercise
10,
but
assume
now
that
Eric’s
preferences
are
represented
with
the
following
(Stone-Geary)
utility
function:
u(x,y)
=2
(r3
-
1)
(v2
-
2)
:
(a)
Find
Eric’s
marginal
utility for
books,
MUy,
and
for
computers,
MUj.
(b)
Are
his
preferences
monotonic
(i.e.,
weakly
increasing
in
both
goods)?
(c)
For
a
given
utility
level
u,
solve
the
utility
function
for
y
to
obtain
Eric’s
indifference
curve.
(d)
Find
Eric’s
MRS
between
x
and
y.
Interpret
your
results.
(¢)
Are
his
preferences
convex
(i.e.,
bowed
in
toward
the
origin)?
(f)
Consider
a
given
utility
level
of
10
utils.
Plot
his
indifference
curve
in
this
case.
.
Finding
Properties-IIL%
Repeat
exercise
10,
but
assume
now
that
Eric’s
preferences
are
represented
with
the
following
(linear)
utility
function:
u(x,
y)
=
3x
+
4y.
(a)
Find
Eric’s
marginal
utility
for
books,
MUy,
and
for
computers,
MUy
(b)
Are
his
preferences
monotonic
(i.e.,
weakly
increasing
in
both
goods)?
(c)
For
a
given
utility
level
u,
solve
the
utility
function
for y
to
obtain
Eric’s
indifference
curve.
(d)
Find
Eric’s
MRS
between
x
and
y.
Interpret
your
results.
(¢)
Are
his
preferences
convex
(i.c.,
bowed
in
toward
the
origin)?
(f)
Consider
a
given
utility
level
of
10
utils.
Plot
his
indifference
curve
in
this
case.
