An Incentive System for Salmonella Control in the Pork Supply Chain

does not allow for saving. Producers consider the plant’s investments in Salmonella control measures
and the incentive system to be exogenously determined and fixed. Each period, the producer chooses a
Salmonella control package and realizes a net gain from participation in the Salmonella control
program that is equal to the quality premium minus costs for quality control measures and Salmonella
testing and, possibly, a penalty for a Salmonella prevalence level that exceeds thresholds set by the
slaughter plant.²

The producer’s dynamic programming problem can be formally stated as:

∞

max E[∑ δ^t (-e ʌ' (^x-R^t))]

{^xt }t=0      t=o

(4) s.t.

∫mm(( Rt + ɪ), ɑɪ)

Rt + ɪ = <

0

where E is the expectations operator, δ is a monthly discount factor and λ is the producer’s constant
level of absolute risk aversion. The optimal solution to this problem yields a steady state Salmonella
control package for each production history indicator state. The solution also yields probabilities that
the producer will be in each state, expected control and testing costs, and expected penalties assessed to
the producer. If the certainty equivalent of the net gain from participation in the Salmonella control
program falls below zero, the producer will terminate his relationship with the slaughter plant and will
deliver his hogs to another plant that does not offer a producer quality premium because it sells its
product in markets that do not restrict Salmonella prevalence.

² Production costs not related to Salmonella control, PC, and the base price per hog, PH, are treated as deterministic in this
analysis. Therefore, the base net return for hog production can be treated as a fixed component of overall returns that
include gains from participation in the Salmonella control program. With a CARA utility function, this fixed component
does not affect the optimal choice of a control package and so can be disregarded.

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