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EEP101/ECON125 Spring 99
Prof D. Zilberman
TA's: Malick/Marceau
Suggested Solutions to Problem Set 5
*
1.
The rule for a single rotation is to choose the cropping age T when
)
(
)
(
'
T
rQ
T
Q
=
.
(a) In this exercise, the change in growth is :
T
T
T
T
e
e
e
e
T
Q
87
.
0
2
87
.
0
87
.
0
2
87
.
0
)
8
.
0
1
(
264
.
6
)
87
.
0
)(
8
.
0
(
)
8
.
0
1
(
9
)
(
'





=



=
The right hand side of the optimal condition is:
3
87
.
0
3
87
.
0
)
8
.
0
1
(
3
.
0
)
8
.
0
1
(
3
1
.
0
)
(
T
T
e
e
T
rQ



=

×
=
Our condition becomes:
)
(
)
8
.
0
1
(
3
.
0
)
8
.
0
1
(
264
.
6
)
(
'
3
87
.
0
87
.
0
2
87
.
0
T
rQ
e
e
e
T
Q
T
T
T
=

=

=



Dividing both sides by 0.3 and by
2
87
.
0
)
8
.
0
1
(
T
e


gives:
T
T
e
e
87
.
0
87
.
0
8
.
0
1
88
.
20



=
Collecting terms in
e
gives
0461
.
0
68
.
21
1
87
.
0
=
=

T
e
.
Taking the natural logarithm of each
side yields:
years
T
T
536
.
3
87
.
0
0764
.
3
)
0461
.
0
ln(
=
⇒

=

=
and the conclusion that a
rhino’s horn should be cut off after three and half years of growth.
(b.i) Factors that can reduce the rotation period include
•
Higher interest rates
•
Cropping more than once, i.e., regrowth
•
Anticipated future sales restrictions (Why let something grow until nest year if you
won’t have a market in which to sell it.)
•
Note: There is a possibility that the animal dies while under anesthetic during the
hornremoval operation.
This will lengthen the optimal rotation time. (That is,
uncertainty will affect when something is cut.)
*
Solutions provided by S. Marceau.
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View Full DocumentEEP101/ECON125 Spring 99
Prof D. Zilberman
TA's: Malick/Marceau
(b.ii) Factors that may explain more frequent dehorning in reality include
•
Real higher interest rates (e.g., 30% rather than 10%)
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 Spring '09

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