volves a fraction of an activity. However, the costs
of obtaining fixed facilities are often not proportion-
al. For example, if an investment requires special-
ized equipment, the average costs of obtaining the
equipment for the first acre may be different from
the cost for multiple acres. Extrapolating the results
may yield incoσect diversification recommenda-
tions. Thus, whether or not the investment is con-
sidered divisible helps to determine whether or not
fixed costs can be subtracted from variable costs.
APPLICATIONS
In the late 1980s, orange juice production in
Florida appeared profitable in comparison with
many other agricultural enterprises. However,
memories of devastating freezes and increased im-
ports from Brazil indicated that significant risk ex-
isted in orange production. Several alternatives were
available for Florida orange producers considering
expansion. This application assumed that a Florida
orange producer currently had 150 acres of oranges
and that three expansion opportunities were avail-
able: producing 10 acres of strawberries, 50 acres of
grapefruit, or another 50 acres of oranges.1 Each
expansion opportunity required roughly the same
managerial ability to operate.2
The income information for orange production
was derived from state seasonal yields and cash
prices for oranges marketed as frozen concentrated
orange juice (FCOJ) for the period 1973-1987.
Three orange harvesting periods were chosen:
December, February, and April. The Horida Depart-
ment of Citrus provided FCOJ prices in dollars per
pound solid. The yield, in pounds of solids per acre,
for each marketing period was derived from the state
average, measured in boxes of oranges per acre, for
early and midseason oranges in the December and
February marketing periods, and Valencia oranges
in the April marketing period (Horida Agricultural
Statistics, 1988a). The yield variability of FCOJ
depends not only on tree yields, but also on the
quality of the oranges. Quality of oranges is
measured by the gallons of juice that can be obtained
from a box. The variety of the orange and weather
are primary factors in determining this quality.
Average yields for white grapefruit and on-tree
PricesforHoridawhitegrapefruitbetween 1973 and
1987 WereobtainedfromHorida Agricultural Statis-
tics (1988a). The variable cost of producing one acre
of oranges or grapefruit was assumed to be $748.15
(Murraro), and all returns were deflated using the
personal consumption expenditure component of the
implicit GNP deflator. Tlie marginal cost of diver-
sification, which is the rental rate for an acre of
oranges or grapefruit, was $630 (Hunt).
The returns to strawberries were computed based
on state average prices and yields (Horida Agricul-
tural Statistics, 1988b). The variable cost of produc-
tion for strawberries was assumed to be $11,710.54
per acre (Taylor and Smith). The marginal cost of
diversification into strawberries included $260 per
year per acre for land rental and a one-time cost of
$22,000 for additional equipment investment
(Hewit). The $22,000 of additional equipment was
amortized into equal annual payments for 10 acres
assuming a 10-year equipment life and a 12.5 per-
cent interest rate. Amortization resulted in an annual
charge of $3,974 for the additional investment in
equipment Thus, the total annual cost of diversifica-
tion into 10 acres of strawberries was $6,574.
Gross revenues less variable costs expressed in
1987 dollars, mean returns, and standard deviation
of returns for strawberries, grapefruit and each
marketing period for oranges are reported in Table 1
on a per acre basis. Strawberries had the highest
mean return per acre. December-produced oranges
had the lowest mean return from 1973-1987. Straw-
berries also had the highest standard deviation.
April-produced Valencia oranges had the lowest
standard deviation per acre. The correlation matrix
of returns for oranges, strawberries, and grapefruit
is reported in Table 2. The returns from oranges
harvested during different periods were highly cor-
related. Grapefruit and strawberry returns were less
correlated with oranges.
A mean-variance model was constructed using the
means, variances, and covariances. The objective of
the mean-variance model was to maximize (3) sub-
ject to the constraint that total acres of oranges raised
were less than or equal to 150. Six Pratt-Arrow
coefficients of absolute risk aversion ranging from
zero to 0.0001 were used. Individuals with a zero
ɪ This study assumed that the average variable cost curve was flat for the additional expansion opportunities considered. Also, if
an individual producer was interested in more than one of the expansion activities these could be put into one programming model.
However, given the large increase in managerial expertise required (roughly one-third), it is unlikely that more than one addition
would be considered at a time.
2It is unlikely that some additional education may be required for a producer to manage the expansion. The return for this
additional education could be determined by comparing the marginal benefit with the marginal cost of expansion. The difference
∞uld be considered as the return to education. The producer could determine whether the return was high enough to warant
additional education followed by the expansion.
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