Economics 11, Winter 2006; Homework Assignment #2
Due
Thursday January 26, 3PM.
1. Which of the following utility functions represent the same preferences
as
u
(
x, y
) =
x
1
/
2
y
1
/
2
? Explain briefly.
v
1
(
x, y
)
=
xy
v
2
(
x, y
)
=
x
4
y
4
v
3
(
x, y
)
=
sin(
xy
)
v
4
(
x, y
)
=
log
x
+ log
y
v
5
(
x, y
)
=

1
xy
2. On one sketch, draw indifference curves through the points (1
,
1) and
(2
,
2) corresponding to the following CobbDouglas utility functions.
Show all the points where these indifference curves intersect (if any).
Be careful about what happens near the coordinate axes.
(a)
u
(
x, y
) =
x
1
/
2
y
1
/
2
(b)
u
(
x, y
) =
x
2
/
3
y
1
/
3
(c)
u
(
x, y
) =
x
3
/
4
y
1
/
4
3. On one sketch, show indifference curves through the points (1
,
1) and
(2
,
2) corresponding to the following quasilinear utility functions. Show
all points where these indifference curves intersect (if any). Be careful
about what happens near the coordinate axes.
(a)
u
(
x, y
) =
x

1
y
(b)
v
(
x, y
) =
x
+
4
√
y
(c)
w
(
x, y
) =
x
+ log
y
1
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4. Many people care about others: siblings, parents, humanity in general;
this is not hard to model. To make life simple, let’s think about ONE
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 Fall '07
 McDevitt
 Utility, indifference curves, Utility Functions

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