those with a Pratt-Arrow absolute risk aversion coef-
ficient of 0.000005 should have diversified into
strawberries. The marginal costs of diversifying
would have to be cut by nearly 50 percent before the
producer with a risk aversion coefficient of0.00001
would have been willing to grow strawberries.
Those producers who were more risk averse would
not have wanted to diversify into strawberries.
Oranges and Grapefruit
The solution for the risk diversification problem
with oranges and grapefruit is given in the third
block of Table 3. The objective function used in the
base model was altered to allow for the addition of
grapefruit production. An additional constraint was
added restricting the number of acres of grapefruit
to less than 50. Before considering the marginal
costs of diversification, for every level of risk aver-
sion except the highest, grapefruit was raised on all
50 acres. However, the marginal benefit for leasing
the grapefruit only exceeded the marginal cost of
$31,500 for Pratt-Arrow risk aversion coefficients
less than or equal to 0.000005. The orange producer
who has a risk aversion coefficient of 0.00001
(0.00002) would have been willing to raise
grapefruit if the annual rent on land were reduced by
5 percent (8 percent). Currently, the more risk averse
managers would not have rented the grapefruit grove
and more risk-neutral managers would have. How-
ever, in the current scenario no one would have
rented the grapefruit grove without planting and
maintaining all 50 acres.
Oranges and Oranges
The solution for the risk diversification into
production of additional oranges is given in the
bottom block of Table 3. The base model objective
was used with the constraint on acreage grown in-
creased from 150 to 200 acres. The marginal benefit
for leasing the extra acreage of oranges exceeded the
marginal cost for the two smallest risk-aversion
coefficients. The producer who had a risk-aversion
coefficient of0.00001 would have rented the 50 acre
grove of oranges, if the rent had been reduced by 33
percent (the marginal cost would have needed to be
less than $21,182).
SUMMARY
The above analysis indicated that only the orange
producer with a risk-aversion coefficient of
0.000005 or less would have expanded his enterprise
after considering the marginal costs of diversifica-
tion. Although producers who were more risk-averse
would want to diversify based on the returns over
variable costs, the marginal benefits did not out-
weigh the marginal costs. However, the more risk-
averse producer might have wanted to consider
grapefruit, because the marginal benefit minus the
marginal cost of diversification would have been
positive, if the marginal costs could have been
reduced by between 5 and 10 percent. It should be
noted that the above analysis was based upon
statewide information and that the individual
producer is likely to have faced yields that were
more variable.
CONCLUSION
This study used the certainty equivalent of a risky
investment derived from the objective function to
evaluate the marginal benefits and costs of diver-
sification opportunities. Specifically, this paper
recognized that the objective value from a popular
form of a quadratic risk (mean-variance) program-
ming problem is equal to the certainty equivalent
under Freund’s assumptions. The change in certainty
equivalent between two mean-variance solutions,
one without and one with an additional diversifica-
tion opportunity, was shown to be the marginal
benefit of the diversification opportunity. This mar-
ginal benefit can be compared with the marginal
cost of the opportunity to determine the economic
efficiency of additional diversification.
Using this framework, three investment oppor-
tunities available to Florida orange producers were
evaluated: strawberry, grapefruit, and additional
orange production. The results indicated that the
marginal benefit of diversification into any of the
enterprises was exceeded by the cost for moderate
and high levels of risk aversion. The marginal
benefit to additional investment was greater than the
marginal cost of diversification for all three
enterprises for the profit maximizer and the in-
dividual with a Pratt-Arrow risk-aversion coeffi-
cient less than 0.00001. For the moderately
risk-averse producer, the marginal benefit of
grapefruit production would have been greater than
the marginal cost, if the costs had been reduced by
as little as 10 percent.
REFERENCES
Adams, R.M., DJ. Menkhaus, and B.A. Wbolery. “Alternative Parameter Specification in EV Analysis:
Implications for Farm Level Decision Making.” West. J. Agr. Econ. 5(1980): 13-20.
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