10
Mandatory vs. Voluntary Approaches to Food Safety
unaware of those changes.
To see the relationship between consumer demand and changes in
product safety, consider a simple model of product safety.27 We use the
following notation. Let:
y = the amount of the good bought and sold;
q = probability that a given unit of the product is "not-safe", e.g., that it is
contaminated by microorganisms, or has dangerously high levels of
pesticide residue, where 0≤q≤l;28
B(y) = the gross consumer benefits from consumption of y units of the
good, with B'(y)X), B"(y)>0;
P(q) = the price per unit of the good, with P'(q)≤0;
C(q,y) = tiιe cost of producing y units of the good with the associated
probability of contamination q, where Cq<0, Cy>0 and Cqy<0;29
D = damages from consumption of one unit of the good if it is
contaminated;30
s = the share of the damages borne by the firm, where 0≤s≤l;31
α = scale factor capturing the consumer's under or over-estimation of
damages;32 and
β = scale factor capturing the firm's under or over-estimation of damages.
Clearly, if both consumers and producers correctly perceive the damages
from contamination, then =β=l. We would expect this to be the case
for search goods and in long run equihbrium for experience goods as well.
However, for credence goods, it is possible to have different from one.
27 The development here follows the traditional model of product liability
originally proposed by Landes and Posner (1985). It is essentially a model of
accidents between sellers and consumers. See Shavell (1987) for a general form of
the model.
28 Hence I=l∕(l-q) can be viewed as an index of product safety, where q=0
implies a perfectly safe product (I=I) and q=l implies a perfectly unsafe product
(I=infmity).
29 This specification of the cost function implicitly assumes that output and
safety are joint products for the firm, as suggested by Antle (1998).
30 We assume that per unit damages are fixed, given contamination. An
alternative approach would be to allow the level of contamination (and hence the
level of damages) to vary with investment in product safety. Under risk neutrality,
the qualitative implications of the analysis would not change by relaxing the
assumption in this way.
31 The magnitude of s will be determined by the Iiabihty rule in place, the nature
of the damages (e.g., acute vs. long term chronic), and the characteristics of the firm
(e.g., the firm's asset base). See further discussion below.
32 Alternatively, the consumer (or producer) could over or under-estimate the
probability of contamination. The qualitative results would be similar to those
presented here. For a model of this form of misperceptions, see Spence (1977). For
a discussion of consumer perceptions in the context of pesticide residues, see Ott et
al. (1991).