Economics 101, Problem Set 1
Alan C. Marco
Solutions.
1.
Bill’s preferences for goods
x
and
y
are given by the following table that lists combinations of goods that make
Bill equally well oF.
Units of
x
Units of
y
16
6
12
8
8
12
4
24
(a)
Graph Bill’s indiFerence curve, with
x
on the horizontal axis. Assuming that the price of
x
is $1.00 and
the price of
y
is $1.50, and that Bill has $24 to spend, add a budget line to the graph.
0
5
10
15
20
y
5
10
15
20
x
(b)
What combination of
x
and
y
will maximize Bill’s utility?
•
12 units of
x
and
8
units of
y
, because that combination yields the same utility as the other points,
but is the only one that is aFordable.
(c)
Show that your answer meets the
MRS
=
P
x
P
y
rule. [This may not be exact, so explain why if it’s not.]
•
Well, the curves are tangent at that point on the graph, so we know it’s true. However, we want to
show it formally:
•
Starting at
(12
,
8)
should we sell some
x
and buy some
y
?
(No.)
—
MRS
=
P
x
P
y
is the same thing as
MU
x
MU
y
=
P
x
P
y
.
—
Moving from
(12
,
8)
to
(8
,
12)
,
the slope of the
IC
is
4

4
=

1
.
The slope of the budget line is

2
3
.
—
This means that
MU
x
MU
y
= 1
>
P
x
P
y
=
2
3
.
Put another way,
MU
x
P
x
>
MU
y
P
y
which means we should buy
more
x
and less
y.
•
Starting at
(12
,
8)
should we sell some
y
and buy some
x
?
(No.)
—
Moving from
(12
,
8)
to
(16
,
6)
,
the slope of the
IC
is

2
4
=

1
2
.
The slope of the budget line is

2
3
.
—
This means that
MU
x
MU
y
=
1
2
<
P
x
P
y
=
2
3
.
Put another way,
MU
x
P
x
<
MU
y
P
y
which means we should buy
more
y
and less
x.
•
Seen another way, the
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 Spring '08
 Staff
 Economics, Microeconomics, Supply And Demand, Price point, Economics curves

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