The name is absent



(2)


Max CEiM

Qik         i k=1


ï ï
m           n m

- b2Q - 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)-2b2qik -b3∑∑qjk

k=1              j=1 k=1

ji

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 2k

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.



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