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

(^{a - s}1 )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 p_i(y₁,y₂) =aI_i-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

(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

<<   20   21   22   23   24   25   26   >>

More intriguing information