Reputations, Market Structure, and the Choice of Quality Assurance Systems in the Food Industry

where m(s,ω) denotes the probability that a processor with a QAS s in place will stay in the
value-added market for a trait with discoverability ω. In particular, note that the probability of
staying in the market for two successive periods, m(s,ω) = λ(s) + (1-λ(s))(1-ω), combines
the probability that the resulting quality is high with the probability of type II error weighted
by the consumers’ level of awareness.⁴ A processor will face a zero demand in the second
period with probability1- m(s,ω).

We now need an expression for E (β ∣m (s, ω )). Note that Tis just counting the
number of periods until the first notorious (discovered) failure. Since the outcome in a given
period is independent of the outcome of other periods, T is the number of Bernoulli trials
required to get the first failure. This is just the description of a geometric random variable with
“success” probability 1-m(s,ω). The previous observation allows us to obtain the required

expression:

∞∞

E (β^τ m (s, ω )) = ∑ β Pr (T = t) = ∑ βm (s, ω )'“' (1 - m (s, ω )) =

t=1                               t=1

π( У, s ; a )

1- βm ( s,ω)

Antle (2001) classifies quality-control technologies for producing quality-differentiated
goods as process control, inspection, testing, and identity preservation. He argues that all these
technologies except testing affect the variable costs of production. However, the costs of the
testing technologies are not independent of the rate of output, since testing typically involves
sampling a small proportion of the product. This discussion reveals that the choices of

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