AEB 6533
Assignment 3
I.
Assuming a negative exponential utility function and a normal distribution,
yields a Expected ValueVariance formulation of the expected utility problem.
The objective function for this formulation is
max
2
. .
x
x
x
x
s t
Ax
b
ρ
′
′
μ

Ω
≤
where
μ
is the expected return per acre,
x
is the choice vector containing the
acres planted in each crop,
ρ
is the ArrowPratt risk aversion coefficient,
Ω
is the variance matrix for returns per acre, and
A
is the constraint matrix.
Assuming a risk aversion coefficient of 0.00002, 640 acres of cropland,
$44,000 of capital, and 100 hours of labor, is the crop combination 436.92
acres of corn, 55.38 acres of peanuts, and 147.69 acres of soybeans optimum?
Remember each crop variable must be greater than or equal to zero.
Table 1. Farm Portfolio Problem
Cotton
Corn
Wheat
Peanuts Soybeans
Yield
1500
150
45
1.25
45
Price
0.49
2.23
3.46
678.00
6.20
Variable Cost
450
150
50
500
75
Capital
225.00
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