distribution of quality. The former has an analog to a discrete attribute (the good was produced
using a desired process or it was not), whereas quality in the latter case is a continuous random
variable whose distribution is altered by the process followed. In the continuous case, let qM
be the minimum quality standard. Hence, FQ (qM ) is the unconditional probability that the
product is inferior or unacceptable.
In the discrete case, the input has or fails to have a particular attribute or was or was
not produced following a value-adding (cost-increasing) production process. For example,
eggs can be produced using animal welfare enhancing techniques (such as free-range
production) or by conventional means. The processor buys from producers who have the
capabilities needed to produce, and are believed to produce, following the desired processes.
Having the capabilities does not necessarily mean that the process will be strictly followed
under conditions of imperfect information. Because production of the high-quality input is
costlier than production for a commodity market, and there is a strictly positive probability
that deviant behavior will not be discovered and penalized, suppliers will find it rational to
deviate from perfect compliance.1,2 Hence, there is a strictly positive fraction of the output
that will not be produced under the desired cost-increasing conditions. This fraction is again
represented by FQ (qM).
Let S = {5 ^ : s ≤ s ≤ su} be the set of alternative QASs where s = so represents the
absence of quality verification and s= su represents perfect revelation of quality. The
processor that procures raw materials from certified suppliers using the QAS indexed by s
expects to certify a fraction of good-quality input, denoted by λ(s) = 1 - F (qM ∣s) and a
fraction 1 - λ (s) = FQ (qM ∣s) of the inferior input. All certified input purchased will be
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