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

processed and sold to downstream customers as possessing the desired trait.

Implementation of different levels of stringency switches the relevant distributions for
quality as follows. For any sⁱ,s^j ∈ S there is an associated conditional distribution for quality,
namely, FQ (q∖s^, ) and FQ (q∣s⁷ ). Increasing the level of stringency involves moving from s'
to s ^j where sⁱ≤ s^j leads to a first-order stochastically dominating shift on the distribution of
quality. Therefore, FQ (q∣s' ) ≥ FQ (q∣s⁷ ) for all q ∈ Q . In particular, this implies that

λ (s¹ ) = 1 - F (qM ∣s⁷ ) ≥ 1 - F (qM ∣s¹ ) = λ (s' ). Increasing s reduces the probability of incurring
both type I errors (rejecting an input that is of good quality) and type II errors (certifying a
product that is of low quality). We assume that FQ (q∣s) is differentiable with respect to s.

Adoption of a QAS by processors incurs a cost, which can include compensation for
sellers’ implementation costs and the costs of monitoring. We capture such costs for firm 1
with a cost function C (s, y_i ), with ∂C (y₁, s)∕∂s > 0 and ∂C (y₁, s)∕∂y > 0, where y₁ is
output.

Participation in the certified market for high-quality goods yields a per-period profit of
∏^{, r} ( y, s ; a ) = R ( y ; a ) - C ( y₁, s ), where the revenue function R ( y ; a ) potentially depends on
the vector of firms’ output, y = (y₁, y_-1) and an indicator of the strength or size of consumer
preference for high-quality goods, a. Clearly, ∂R ( y ; a )∕∂a > 0 . The superscript in the profit
function represents the state of the world, where processor 1 has reputation r.

We could append a term to the profit function, representing the economic loss due to
certifying a product that is of low quality. This would require specification of a damage

function due to the discovery of false certification. We capture punishment to a processor that

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