Table 3. Optimal Portfolios of Oranges, Grapefruit and Oranges, and Strawberries and Oranges for | ||||
Risk Marginal Aversion Certainty Benefit of Coefficient Equivalent Expansion |
Marginal |
Dec. |
Acres of Oranges__________ _________.Feb.___________Apr. |
Potential Expansion |
Base Plan
0.0 |
137,036 |
— |
— |
— |
150 |
— |
— |
0.000005 |
120,933 |
— |
— |
— |
150 |
— |
— |
0.00001 |
104,830 |
— |
— |
— |
150 |
— |
— |
0.00002 |
78,007 |
— |
— |
— |
50 |
100 |
— |
0.00005 |
26,461 |
— |
— |
— |
— |
150 |
— |
0.0001 |
-58,364 |
— |
— |
— |
0 |
150 |
— |
Diversification into Strawberries | |||||||
0.0 |
148,029 |
10,993 |
6,574 |
— |
150 |
— |
10 |
0.000005 |
128,163 |
7,230 |
6,574 |
— |
150 |
— |
10 |
0.00001 |
108,297 |
3,467 |
6,574 |
— |
150 |
— |
10a |
0.00002 |
79,394 |
1,387 |
6,574 |
— |
42 |
108 |
4a |
0.00005 |
26,461 |
0 |
6,574 |
— |
— |
150 |
0a |
0.0001 |
-58,364 |
0 |
6,574 |
— |
— |
150 |
0a |
________________________________________________Diversification into Grapefruit__ | |||||||
0.0 |
173,401 |
36,365 |
31,500 |
— |
150 |
— |
50 |
0.000005 |
154,018 |
33,085 |
31,500 |
— |
150 |
— |
50 |
0.00001 |
134,635 |
29,815 |
31,5∞ |
— |
150 |
— |
50a |
0.00002 |
107,030 |
29,023 |
31,500 |
— |
16 |
134 |
50a |
0.00005 |
45,685 |
19,224 |
31,500 |
— |
— |
150 |
50a |
0.0001 |
-49,753 |
8,011 |
31,500 |
— |
— |
150 |
27a |
Diversification into Oranges | |||||||
0.0 |
182,714 |
45,678 |
31,500 |
— |
200 |
— |
50 |
0.000005 |
154,087 |
33,154 |
31,500 |
— |
200 |
— |
50 |
0.00001 |
126,012 |
21,182 |
31,500 |
— |
158 |
42 |
50a |
0.00002 |
88,324 |
10,317 |
31,500 |
— |
20 |
180 |
50a |
0.00005 |
26,461 |
0 |
31,500 |
— |
— |
150 |
0a |
0.0001 |
-58,364 |
0 |
31,500 |
— |
— |
150 |
0a |
a Expansion would not occur because the marginal ∞st of expansion exceeds the marginal benefit of expansion. The
marginal ∞st and the marginal benefit of expansion are zero in these cases in actuality because diversification does
not take place.
Farmers who had a risk aversion coefficient greater
than 0.00005 should have grown only Valencia
oranges.
Oranges and Strawberries
The results from the risk programming model for
diversification into strawberries are presented in the
second block of Table 3. The objective function was
altered to allow for the addition of strawberry
production. An additional constraint was added,
restricting the number of acres of strawberries to less
than 10. Strawberries offered potential for increas-
ing the expected utility of the farmer if the farmer’s
risk aversion coefficient was less than or equal to
0.00002. The marginal benefit of diversification (the
difference in certainty equivalents between the base
plan and augmented plan) into strawberries was
$10,993 for the zero risk aversion coefficient,
$7,230 for 0.000005, $3,467 for 0.00001, and
$1,387 for 0.00002. The annual amortized fixed cost
of diversifying into strawberries was $6,574. There-
fore, only those producers who were risk-neutral or
195
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