The manager of the slaughter plant is treated as the principal in this model. She cannot directly
observe producers’ quality control efforts, but she can influence their behavior through the design of
the compensation/testing system. Specifically, she can choose the structure of the incentive system and
the values of elements in the parameter vector, α, that determine the producer quality premium, testing
probabilities, serological prevalence threshold, penalties, the incidence of testing costs, and the
evolution of production history indicator levels. The plant manager can also choose one package from
a set of three Salmonella plant control measure packages, γt ∈ {γ1, γ2, γ3}, with an associated cost,
c(γt). The slaughter plant receives an exogenously determined quality premium equivalent to QPS per
hog from its downstream customers if the plant level mean bacteriological prevalence of Salmonella
for all hog carcasses produced by the plant on a given day, pprev, is less than or equal to an
exogenously determined bacteriological threshold, BPREV*. The plant’s bacteriological prevalence
level, for a given plant control package, depends on the distribution of bacteriological prevalence levels
for hogs delivered by producers. This, in turn, is related to farm-level serological prevalence levels,
which depend on the farm-level control measures used by producers. Therefore, the bacteriological
prevalence measure for a group of hogs delivered by a producer, bprev, is a random variable with a
probability function, m(bprev|prevt, γt), that is conditional on the producer’s serological prevalence
level and the plant-level Salmonella control package.
The slaughter plant’s bacteriological prevalence level, pprev, is a measure of the mean
bacteriological prevalence level for all hog carcasses produced during a day. As in King, Backus, and
van der Gaag (2007), we assume that there are daily hog deliveries by dhogd homogeneous producers.
Due to past random events, these producers are distributed over production history states and so may
have used a distribution of control packages, though any individual producer will be in a single state
and will have used a single control package. Therefore, the population of producers will deliver hogs
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