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

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function and some tedious rearranging yields sgn I ——■ I = sgn (m2 (s2 )(2 - βm2 (s2 )) -1). The
expression within parentheses is a quadratic equation with negative coefficient -β∈(-1,0) . It
is straightforward to check that the expression is positive if and only if m₂ ∈ [m⁰,1J, where m⁰
is the only root (in the unit interval) of the quadratic equation. This shows that if assurance
systems are complementary, processors will increase their investments in quality only if their
rival’s probability of success is above a certain threshold given by m⁰ . Note also that this
condition is conducive to the property of strategic complementarity. For small values of m₂ ,
processor 1 will find it optimal to reduce investments in quality as consumers become more
knowledgeable.

In summary, when reputations are public, we show that QASs can potentially be
strategic complements or substitutes. However, we argue that the former is more plausible. For
this case, we showed that firms will implement more stringent QASs as the ability of
consumers to perceive quality increases (provided that their rivals’ probability of maintaining
consumers’ approval is high enough).

Duopoly When Reputation Is Private

We now turn to the case in which reputation is a private good. The structure of the
problem is similar to the previous analysis in that firms have to choose the optimal level of
investment in QASs that affects quality stochastically and then compete in quantities for the
random number of periods in which they have consumers’ approval. The key difference with
the previous section is that in this scenario when a processor fails, the rival benefits because it
increases its market share. We still maintain the assumption that firms will be trusted until

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