Economics 310-1. Professors Hornsten and Braeutigam Page 1 First Midterm Solutions, Winter 2012
SUGGESTED SOLUTIONS FOR THE FIRST MIDTERM (See final page for info on scores)
1) a) An indifference curve illustrates the set of (X, Y) combinations that have a constant level of utility. The 32-util
iso-utility curve passes through (X=4, Y=0), (2, 8), and (1, 24), because 4*8 = 2*16 = 1*32 = 32. The 64-util iso-
utility curve passes through (8, 0), (4, 8), (2, 24), and (1, 56), because 8*8 = 4*16 = 2*32 = 1*64 = 64. It would
also pass through (1/2, 120) because
½
* 128 = 64. Notice that these indifference curves intersect the X-axis
(where Y=0), but never touch the Y-axis.
[Scoring: 5 = 2 pts per IC and 1 for labels on axes & curves; -3 if IC cross; -2 if IC wd hit Y-axis; -1 per math error]
b) If you pay $1 membership fee, leaving $5 of income, you qualify for Club Discount price of P
X
=
½
.
max
X
,
Y
U
[
X
,
Y
]
=
X
(
Y
+
8)
subject to
XP
X
+
YP
X
"
I
#
1
2
X
+
Y
=
5
(because you've paid the $1 fee)
MRS
X
,
Y
=
MU
X
MU
y
=
Y
+
8
X
(which falls as X rises along an iso- U curve, so we cd hv an interior optimum)
MU
X
MU
y
=
P
X
P
y
#
Y
+
8
X
=
1
2
1
#
1
2
X
=
Y
+
8
(Tangency)
Combining : 5 =
1
2
X
+
Y
=
(
Y
+
8)
+
Y
=
2
Y
+
8
#
Y
=
$
3
2
(which is metaphysically troublesome)
#
Y
*
=
0
(a corner solution)
#
X
*
=
10
#
U
[10,0]
=
10(0
+
8)
=
80.
Bang for the Buck verifies we want to max out on X :
MU
X
P
X
>
MU
Y
P
y
%
Y
+
8
1
2
>
X
1
%
8
1
2
>
10
1
.
[Scoring: 10 = 4 graph (proper intercepts, kink & slope) + 1 budget + 3 tangency/bang for buck + 2 answer; -1 for
skipping vertical part of BC]
U=32 utils (black)
(8, 0)
(4, 0)
Good X
Good Y
(1, 56)
(2, 24)
(4, 8)
(1, 24)
(2, 8)
U=64 utils (blue)
BC
DISCOUNT CLUB
Good X
2
4
Good Y
6
4
2
10
IC:80 utils
8
6
5
0