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

31

⁹ For strategic substitutes, the optimal adjustment will depend not only on the sign of the cross
partial studied below, but also on the relative magnitude of a_1,1 and a_1,2 . To see this, impose

ds1^*   1              ∂²E ∏¹

symmetry and rewrite —- = —( - a 2 2 + α₁2 )------

dω _Ω2,2   1,2 _∂s_1∂ω

¹⁰ Note that the case where reputations is a public good, is also a Markov process, but with
only two possible states (corresponding to the first and fourth states of the current setting).

11                                              e^s

¹ An example would be λ( s ) = —;—^

¹² However, as Hennessy, Roosen, and Jensen note, branding also provides a target to
consumers in the marketplace when a problem occurs (more on this to follow).

¹³ A figure illustrating this point is available from the authors upon request.

¹⁴ Though not presented, as the demand for high quality products, (parameterized by a ) rises,
the stringency of the QAS under all scenarios increases.

¹⁵ A necessary condition for consumers to weakly prefer the monopoly situation over the
duopoly with public reputations is β(16m_M - 9m_D² ) ≥ 7 , where m_j , j= M,D represents the
equilibrium probabilities that reputations are maintained in two successive periods by the
monopolist and a duopolist respectively. A sufficient (not necessary) condition, is given by
βm_D(16-9m_D)≥7 , which is much harder to satisfy.

¹⁶ Note that if consumers value the future more than producers, or beta is close to 1 (higher
than 0.98), the expected utility from the monopoly scenario exceeds that of the duopoly with
public reputations for all ω . In those cases, the monopoly scenario would also Pareto
dominate the duopoly with public reputations.

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