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AEB 6145 Agricultural Finance
Professor Charles B. Moss
1
Lecture I: Robinson Crusoe Economy and Investment
I.
Setup
A. Robinson Crusoe, a Ph.D.
in Agricultural Economics and survivor of
AEB 6145, is stranded on a desert island after a shipwreck.
He knows that
this group of islands is surveyed every three years and was surveyed last
year.
Thus, he must survive two years.
B. He has
1. 100 lbs of potatoes
2. Sufficient tools and arable land to plant the potatoes such that
they yield future consumption of
( 29
1
2
2
2 10000
yx
=
where
x
is current consumption.
3. The production possibilities frontier for Robinson are thus
[ ] [ ]
2
2
1000
0
;
0,100
,
0,200
4
y
x
xy
=
+
∈∈
4. Robinson’s preferences can be represented as
( 29
.
6
.4
,
U x
y
=
II.
True Robinson Crusoe or economy choice of investment and consumption.
A. Without trade, Robinson chooses
x
and
y
to
( 29
.
6
,
2
2
ma
x,
..10000
4
y
y
s
tx
=
≥+
Thus,
( 29
( 29
2
.
6
.
42
2
2
10000
4
.
.
6
20
.
.
40
2
1000
00
4
y
L x
U
L
x
xx
U
Ly
yy
x
l
l
l
l
=
+

∂
∂
=
=
∂
∂
∂
=
∂
∂
=
=
∂
Taking the ratio of the first two firstorder conditions yields
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View Full DocumentAEB 6145 Agricultural Finance
Professor Charles B. Moss
2
( 29
( 29
22
.
6.
2
.
4.
2
34
2
8
3
U
x
x
U
y
y
yx
xy
l
l
=
=
=
=
Substituting this result into the third firstorder condition yields
2
2
18
1000
00
43
5
1000
3
6000
77.460
xx
x
x
x

=
=
=
Using the result from the ratio of the first two firstorder conditions
( 29 ( 29 ( 29
( 29
.
6
.4
2
8
126.492
3
,
77.4
6
126.49
2
94.248
.
6,
.004712
2
U xy
Uxy
x
l
==
To derive the Marginal Rate of Substitution between
x
and
y
( 29
( 29
( 29
( 29
.
.
2
.
.
3
2 77.460
.4082
3126.492
U
U
yy
MRS
UU
x
x
∂
∂
∂
=
=
=

=
∂
∂
∂
=

B. Robinson Crusoe and the Natives
1. Assume that Robinson finds natives on the neighboring island
who also consume potatoes among other things.
Robinson
decides that he can trade with these natives, but living with them
may result in him becoming the meat in the native’s meat and
potato diet.
The natives decide that they will buy or sell potatoes
at the rate of .925925
x
/1
y
.
Put another way, they will give one
lb of potatoes today for 1.08 lbs of potatoes tomorrow.
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 Spring '11
 Moss
 Robinson Crusoe, Robinson Crusoe, Friday

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