(2)
Max CEiM =Ε∑
Qik i k=1
ï ï
m n m
- b2∑Q - b3∑∑Q - qkPk
k=1 j=1 k=1
j ≠i J J
Taking the first-order necessary condition for a maximum in (2) yields:
m nm
(3) pk =b1Ε(sk)-2b2∑qik -b3∑∑qjk
k=1 j=1 k=1
j≠i
Aggregation of (3) across the demands for grower k from the processors yields:
(4) Pk = biE( sk ) - 2 b2 + b3 (n 1) ∑ qk
n k=1
The grower k´s problem for the derived demand (4) is to choose his effort in quality and
quantity to maximize his certainty equivalent CEkM :
(5) Max CEM = E\ qkPk - c xkek V pσ2k
xk, ek V 2 J 2 k
Upon expanding the above expression, the following is obtained:
M- ' M Mi'''-' \ ! r! ∖ 2b2 + b3 (n 1) ï C 2 ρ 2-ι2 2 2
(6) MaxCEk = qj b1E(sk)--2---31----∑∑qk I--χkek - —qkb1ekσs
xk, ek V n k=1 J 2 2
Taking into account that qk = xk and maximizing (6) with respect to xk and ek , a
system of two equations with two unknowns is obtained:
(7a)
∂ CEm
dx k
(2b2 +b3(n-1))\ m ï c 2 2 2 2
= b1 ek---I Σ xk + xk I --ek - Pxkb1 ekσs= 0
n V k =1 J 2
∂CEm
(7b) —:---= xkb1 - cxkek - Pxkb1 ekσs = 0
s
∂ek
Since processors and growers face common equations, without loss of generality, in
what follows we omit the subscript i and k in the variables. Analyzing equation (7a), we
see an inverse relation between quantity and quality.
More intriguing information
1. The name is absent2. Cross border cooperation –promoter of tourism development
3. Surveying the welfare state: challenges, policy development and causes of resilience
4. Citizenship
5. Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model
6. Transfer from primary school to secondary school
7. The name is absent
8. The name is absent
9. TOWARDS THE ZERO ACCIDENT GOAL: ASSISTING THE FIRST OFFICER MONITOR AND CHALLENGE CAPTAIN ERRORS
10. The changing face of Chicago: demographic trends in the 1990s