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yield, is .667, and that it will be 600, or 1.20 of a normal yield,
is .333. The expected yield in a good year (Y ) is
E[Y ] = 500 [.667 (1.1) + .33 (1.2)]
= 500 [1.13]
= 565.
The probability of having a good year is .15 (i.e. S/kO). Thus, the
expected yield at the beginning of each crop period is calculated as
follows:
E[Y] = P(Yg) (E[Yg]) + P(Yn) (E[Yn]) + P(Yb) (E[Yb])
= (.15) (565) + (.65) (500) + (.20) (375)
= **85.
The above procedures can be repeated for lower and higher than normal
prices. At the farm level the probability of occurrence of any price
(P ) is considered independent of yield, thus the probability of a
combination of yield and price is the product of the separate proba
bilities. However, if the farm yield is correlated with the area
yield and the area production is sufficient to affect price, then there
may be an inverse correlation between farm yield and farm price. In
this three-level (low, normal, and high) model, when price is indepen
dent of yield, there are nine possible combinations of price and yield
(i.e., of gross income) and nine corresponding probabilities of the
occurrence of each combination (Table 3).
In a continuation of the above example, let the probability of
a normal price be .75. Then, the probabilities of the various combina
tions are: a low yield with a normal price .15 (i.e., .20 x .75), a
high yield with a normal price .11 (i.e., .15 x .75), etc.