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,sj ∈ 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≤ sj 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, yi ), 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