An Incentive System for Salmonella Control in the Pork Supply Chain

3. Model Description

The model developed for this study is a direct extension of the dynamic principal-agent model
presented in King, Backus, and van der Gaag (2007), and our description here draws heavily on the
description in that paper (pp. 85-92). That model identifies Nash equilibrium farmer incentive system
parameters and associated farm-level Salmonella control policies for a two segment supply chain that
includes producers and a slaughter plant. The model described here adds the possibility of plant
control measures that reduce bacteriological Salmonella prevalence.

Of the two incentive systems described in King , Backus, and van der Gaag (2007), we use the
cumulative experience system in this analysis. The parties in control under IOF and COOP ownership
structures have a uniform preference for the cumulative experience system. That is due largely to lower
testing costs. Consistent with results presented by Starbird (2005), a random testing regime makes it
possible to reduce testing costs without sacrificing product quality.

We assume a homogeneous group of hog producers, each of whom is treated as an independent
agent in the model developed for this study. Each producer delivers a fixed number of hogs once each
month to a slaughter plant that has a Salmonella control program. All producers have identical costs
for inputs not related to Salmonella control, PC, and receive an identical base price, PH, per hog
delivered. They also receive a producer quality premium, α0, per hog delivered that is a reward for
participation in the plant’s Salmonella control program. Each month, the producer chooses one
package from a set of three Salmonella control measure packages, x_t ∈ {x₁, x₂, x₃}, with an associated
cost, c(xt), that increases with the intensity of the control measures. At slaughter, a sample of the
producer’s hogs may be serologically tested for Salmonella prevalence, prev_t ∈ {0, 10, 20, ..., 100}.
The probability distribution of prevalence levels is a function of the current Salmonella control package

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