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

all	a1,2	1	d^s1
_ a2,1	a2,2 _	(1-βm₁(s₁)m₂(s₂))²	_ds2_

~∂² E ∏¹	∂² E ∏¹ ^			~∂² E ∏¹ ' -----dω ∂s₁∂ω
^ds²	∂s₁∂s ₂	^ds1		~∂² E ∏¹ ' -----dω ∂s₁∂ω
∂² E ∏²	∂² E ∏²	_ds2_	_	∂² E ∏² ——z—dω [_ ∂s₂∂ω J
∂s ₂∂s₁	∂s ₂²			∂² E ∏² ——z—dω [_ ∂s₂∂ω J

where a_i_,_i and a_i_,_-_i, for i = 1,2 are as previously defined. The system can in principle be

solved to obtain

(8)	^ ds₁* ^ dω	1	- a 2,2	a1,2	~∂² E ∏¹
	^ ds₁* ^ dω	1	- a 2,2	a1,2	∂s₁∂ω
		=	^,	^,	∂² E ∏²
	ds *	Ω	_ a2,1	^-a1,1 _	∂² E ∏²
	_ dω _				∂s ₂∂ω

where again the stability conditions are Ω =(a_1,1a_2,2 - a_1,2a_2,1) >0 and a_i_,_i < 0 for i = 1,2 .

The decisions of both processors are equal, so it suffices to analyze the responses of
processor 1. From equation (8), the change in the optimal stringency of assurance for firm 1 is
given by

(9)

ds 1 ( ∂² E ∏¹ ∂² E ∏²

^^= = _ I ^- a 2 2 Z ⁺⁺ al 2 Z Z

dω Ω₄ ^, ∂s₁∂ω ^, ∂s ₂∂ω

The sign of expression (9) is ambiguous in general. However, we can further analyze
some cases. From the stability conditions, we know that Ω is positive and a_2,2 is negative.

Nothing more can be ascertained without imposing further structure. If symmetry is assumed
(as it is here) the cross-partial terms are equal and hence we need to sign only one of them.

We study the case in which QASs are strategic complements.⁹ From the previous

analysis we know that this case arises when a_1,2 > 0 . Using the stability conditions, we

• ʃɪ, ɪ, ɪ (ds* I (∂²E∏¹

immediately see that sgn ∣ —- I = sgn ∣------

У dω ) ∂s₁∂ω

Cross-partial differentiation of the objective

More intriguing information

1. EXECUTIVE SUMMARY
2. The name is absent
3. National curriculum assessment: how to make it better
4. Ex post analysis of the regional impacts of major infrastructure: the Channel Tunnel 10 years on.
5. The name is absent
6. Tax Increment Financing for Optimal Open Space Preservation: an Economic Inquiry
7. The name is absent
8. Standards behaviours face to innovation of the entrepreneurships of Beira Interior
9. Social Balance Theory
10. Educational Inequalities Among School Leavers in Ireland 1979-1994