HW 6  suggested solutions
February 12, 2010
Question 1
In figure 1 we see the two indifference curves through the endowment point.
Question 2
In figure 2 we see the two indifference curves through the endowment point.
All bundles to
the northeast of
IC
1
are preferred by agent 1. All bundles to the southwest of
IC
2
are preferred
by agent 2. All bundles between the indifference curves are preferred by both and hence allow
mutual gains from trade.
Question 3
In figure 3 we see the set of efficient allocations (red line). In particular it is the set of bundles for
which
MRS
1
=
MRS
2
, or
x
1
y
2
=
2
y
2
x
2
y
2
2
=
2
x
2
y
2
=
2
10

x
1
10

y
1
.
We can solve this for
y
1
to get
y
1
=
10
x
1
20

x
1
and hence the set of efficient allocations is
[(
x
,
y
)
,
(
10

x
, 10

y
)]
:
y
=
10
x
20

x
,
x
∈
[
0, 10
]
.
The set of efficient allocations that make each consumer better off relative to his/her endowment
is the piece of the red line between the indifference curves, or
[(
x
,
y
)
,
(
10

x
, 10

y
)]
:
y
=
10
x
20

x
,
x
∈
[
0, 10
]
,
u
1
(
x
,
y
)
≥
18,
u
2
(
10

x
, 10

y
)
≥
7
·
16
.
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 Winter '09
 McDevitt
 Utility, red line, Francis Ysidro Edgeworth, consumer endowment economy

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