have a prevalence test result above the allowable threshold and zero otherwise. Therefore, Rt+1 is a
random variable that depends not only on the control package used by the producer but also on the
probability of testing determined by the current production history indicator. The probability that the
prevalence test result will be below the plant’s Salmonella threshold level, s(xt), is calculated for each
control package by summing values of the prevalence probability function, h(prevt|xt), over prevalence
levels less than or equal to the Salmonella threshold, α7. This incentive system has two additional
parameters: α5 is the share of the expected testing cost paid by the producer , and α6 ∈ [0,1] is the size
of the producer penalty per hog for a prevalence test result that exceeds the plant’s Salmonella
threshold level. The single period return for the producer, f(xt,Rt), is defined by the following
expression:
(3) f (xt, Rt) = a0 - c(χt ) - a5t(Rt )TC - a6TesttFail(xt )
The producer pays the expected testing cost, regardless of whether his hogs are actually tested. The
producer’s choice of a Salmonella control package, xt, influences the distribution of current returns not
only through control costs but also through its effect on the probability of paying a penalty for a
prevalence test above the allowable threshold. The current control package also influences future
returns through its effect on the production history indicator level, which affects testing costs and the
probability of having one’s hogs tested.
The producer’s problem is solved by dynamic programming, with the Salmonella control
package as the control variable and the production history indicator level as the state variable.
Producers are assumed to be risk averse with an infinite planning horizon. Preferences are represented
by an additively time separable constant absolute risk aversion (CARA) utility function, and the model
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