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



23

Monopolist processor

The monopoly situation can be obtained by setting I2 = 0. I1 = 1 if the processor is trusted and

zero otherwise. This yields an inverse demand function for good 1 given by p1(y1)=aI1-by1,
and hence per-period profits (after substitution of the equilibrium output levels) are

π11* = (a - s1 )2/4b . Plugging this back into the monopolist problem, we obtain

max

s1S 4b


(a - s1 )2___________

(1 - β (1 - ω + ωλ( s1 )))

Duopoly situation when reputation is a public good

This case is obtained by letting I1 and I2 equal one if no failure has been detected and zero
otherwise. The inverse demand for processor
i is given by pi(y1,y2) =aIi-b(y1+y2). Then,
equilibrium quantities for the second stage and per-period profits are easily found to be

y* =( a - 2 si + s- i )/3 b and π2 * ( si, s - i ) = ( a - 2 si + s - i )2/9 b, i = 1,2. Plugging this into the
first-stage problem, we find that processor’s 1 objective is given by

max
s1S


(a-2 s1+s2)

9 b (1 - β (1 - ω + ωλ( s1 ))(1 - ω + ωλ( s 2 )))

Duopoly situation when reputation is a private good

For this case, I1 equals one in states 1 and 2 and zero otherwise. Also, I2 equals one in states

1 and 3, and zero otherwise. As long as the stochastic process stays in the initial state (both
processors have good reputations), per-period profits are as in the duopoly situation previously
presented. When the system reaches states 2 or 3, the monopolist’s per-period profit (also
previously presented) becomes relevant. Here, the problem of processor 1 is



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