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Table 3. Optimal Portfolios of Oranges, Grapefruit and Oranges, and Strawberries and Oranges for
Various Risk Aversion Levels

Risk Marginal

Aversion Certainty Benefit of

Coefficient Equivalent Expansion

Marginal
Costof
Expansion

Dec.

Acres of Oranges__________

_________.Feb.___________Apr.

Potential

Expansion
Activity

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	—	10^a
0.00002	79,394	1,387	6,574	—	42	108	4^a
0.00005	26,461	0	6,574	—	—	150	0^a
0.0001	-58,364	0	6,574	—	—	150	0^a

________________________________________________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	—	50^a
0.00002	107,030	29,023	31,500	—	16	134	50^a
0.00005	45,685	19,224	31,500	—	—	150	50^a
0.0001	-49,753	8,011	31,500	—	—	150	27^a
			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	50^a
0.00002	88,324	10,317	31,500	—	20	180	50^a
0.00005	26,461	0	31,500	—	—	150	0^a
0.0001	-58,364	0	31,500	—	—	150	0^a

^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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