The name is absent

The optimization problem in equations (9)-(11) can be solved sequentially. First, the
optimal solutions to the grower’s decision on efforts in quantity and quality in equation
(10) are obtained:

Optimizing and substituting the values of Qik and E(Sk), we obtain:

..           (           , _s                 >

^IC                        m           n m           n

(12) ʌ = βi b₁ e_k - b 21 x_k +∑ xi_k I-b₃ ∑∑ x_k - b₃ ∑β_jx_jk — e= - P_kβi_kxi_kb1 skσ_s' = 0
i 1 k 2 ik ik 3            jk 3 j jk k k ik ik 1 k s

^dxik                   к      k=1 J     j=1 k=1           j=1          2

к                                     j≠i         J      j≠i

(13) ^d CE^k =∑(β₁x_kb₁ - cxi_ke_k - ρ_kβi² x²_kb² e_kσ_s² )= 0
i ik 1 ik k k i ik 1 k s

Here, we should substitute equations (12) and (13) into equations (9) and (11) and
maximizing with respect to β, the optimal share for the grower would be obtained⁶.
Finally, substitutingx^*, e^*and β^*into equation (11), we would obtain the optimal fixed
rent α^* . But similarly than in the previous model, these equations can not be solved
analytically and a numerical simulation exercise is obtained instead.

Simulation and discussion

As we mentioned earlier, the mean-variance approach has been used to analyze various
contractual issues. However, it is usually very difficult to explicitly solve the first-order
conditions that define the values of the decision variables in the optimal contract.
Quantitative applications of mean-variance models require numerical simulations
(Robe, 2001).

Theoretically, growers respond to incentives in contracts obtaining greater levels of
quality than in the spot market. And in practice, some authors have obtained conclusive
support empirically (for example, Curtis and McCluskey 2003, Alexander, Goodhue

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