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

22

this model is again a pair of QASs (s₁,s₂) such that s_i^*= b_i(s_-^*_i) , i = 1,2, where b_i (i)
represents the best-response function of player i . Given the complexity of the model, further
analysis requires a bit more specification and the use of numerical simulations. We conduct
such simulations next using linear demands and constant marginal costs to give additional
insight into how the nature of competition and reputations are likely to influence the choice of
QASs.

Numerical Simulations

Assume that consumers’ valuation of the homogenous final product in each period can be
represented by a utility function of the form

(¹²)                U (У1, У2 ) = a (У111 ⁺ У2I2 ) - (^b/²) (У2 ⁺ У2^{2 + 2}У1У2 ) ^,

where a and b are parameters, and (I₁,I₂) are indicator functions denoting the state of the
world. The specific form of the indicators will depend on the structure of the market and the
nature of the reputations. Consumers choose quantities to maximize U(y₁, y₂ ) - p₁ y₁ - p₂y₂.

The link between the stringency of the QAS and the probability of obtaining a product
of good quality is given by the monotonic and concave function λ( s ) = s∣ ( s +1). Therefore,
we assume that if investments in quality are zero, processors will be obtaining a high-quality
product with probability zero. This sort of link is more likely to occur when quality is given by
cost-increasing practices. When the variability is natural and processors just need to select
what input to buy, it may be more reasonable to employ a link that assigns equal probability to
obtaining a good product and incurring a statistical type II error when investments in quality
are zero.¹¹ We begin by specifying the objective functions for each situation studied.

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