HW_06_Solutions - HW 6 suggested solutions Question 1 In...

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 .