Eco11, Fall 2008
Simon Board
Economics 11: Solutions to Practice Problems 3 (Week 4)
October 23, 2008
1. Budget Sets
There are two goods:
x
1
and
x
2
with prices
p
1
= 2 and
p
2
= 2. Suppose the government
subsidises the ﬁrst 10 units of
x
1
by $1. Draw the budget curves for
m
= 8,
m
= 12 and
m
= 16
Solution
When
m
= 8, it is as if
p
1
= 1 and
p
2
= 2.
When
m
= 12 or
m
= 16, there is a kink at
x
1
= 10. The slope is

1
/
2 to the left and

1
to the right. The vertical intercept is
x
2
= 6 when
m
= 12 and
x
2
= 8 when
m
= 16. The
horizontal intercept is
x
1
= 11 when
m
= 12 and
x
1
= 13 when
m
= 16.
2. Income Eﬀects and Quasilinear Utility
Suppose utility has the form
u
(
x
1
,x
2
) =
x
1
/
2
1
+
x
2
. Let
p
1
= 1 and
p
2
= 2. Derive the
consumer’s income oﬀer curve.
Solution
Note: Here I use the MRS argument (which is identical to the Lagrange method). We could
also use the substitution method.
The consumer’s MRS is
MU
1
MU
2
=
1
2
x

1
/
2
1
The price ratio is
p
1
/p
2
=
1
2
. The solution is
x
*
1
= 1, which is feasible if
m
≥
1. If
m <
1 then
MRS > p
1
/p
2
, so the consumer will spend all her money on good 1.
1
1
Equivalently, the bang–for–the–back from good 2 is
MU
2
/p
2
= 1
/
2. This is less than the bang–for–the–back
from good 1 if
x
1
<
1.
1
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Simon Board
We thus ﬁnd that
x
*
1
=
m
for
m <
1 and
x
*
1
= 1 for
m
≥
1. More concisely,
x
*
1
= min
{
m,
1
}
.
3. Price Changes
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 Fall '08
 cunningham
 Economics, X1, p1, Simon Board

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