Homework 8  Solutions
Q1.a
The indi/erence curves will be straight lines, the ones of
S
with a slope of
°
2
and the ones of
G
with a slope
of
°
1
2
:
The picture is (almost) the same as in the notes, p. 54.
Q1.b
The MRS of
G
of
o
vs
b
is
°
1
2
, the one of
S
is
°
2
:
Hence, at each point
(
b; o
)
G
values an additional unit of
o
twice as much as he values an additional unit of
b
and
S
values an additional unit of
b
twice as much as he
values an additional unit of
o:
Therefore the pareto e/cient allocations will be the upper and left edge of the
box, just as in the notes on
p:
55.
Q.1.c
Let
w
G
be the wealth of
G;
i.e.
w
G
=
p
b
±
5 +
p
s
±
5
and
w
S
the wealth of
S:
Appealing to Walras°Law, let
p
b
= 1
for simplicity. Since
G
0
s
preferences are linear, his demand will be
o
g
8
<
:
= 0
if
p
o
>
2
2
[0
;
w
g
p
o
]
if
p
o
= 2
=
w
g
p
o
if
p
o
<
2
; b
g
8
<
:
=
w
g
p
b
if
p
o
>
2
2
[0
;
w
g
p
b
]
if
p
o
= 2
= 0
if
p
o
<
2
where in the case that
p
o
= 2
we need that
p
o
o
g
+
p
b
b
g
=
w
g
;
i.e.
G
exhausts his budget.
S
has the same
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 Spring '08
 Witte
 Macroeconomics, Trigraph, Pareto Optima

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