The name is absent

It is assumed that n processors and m growers are symmetrically distributed in
the village economy. As is it often employed in empirical research in agriculture,
growers are modelled as risk averse while processors are modelled as neutral risk
landowners² (Allen and Lueck, 1999).

A quality-differentiated input is produced over a crop cycle which is the period of
our analysis. The input depends on the effort levels of the grower, who contributes to its
quantity, q, and quality, s, in terms of production efforts in these variables, x and e
respectively, according to: q = x and 5 = eμ_s where μ_s ~ N(1, σ_s ). Quality uncertainty is
an increasingly important issue in the agricultural sector (Chambers and King, 2002).
Randomness of quality is imputable to risky environment and measurements errors.
Symmetry restriction regarding the quality variance for all growers is also implemented.
Although the quantity is supposed deterministic, the elimination of this uncertainty only
implies under-representing the importance of income risk (Fraser, 2001). However,
since the random variable is multiplicative, grower’s risk premium is also affected by
quantity.

There is a cost associated with effort because it is unpleasant and forgoes the
opportunity to undertake other activities. The standard vertical-product-differentiation
model assumes that the cost is increasing in both quality and quantity, convex in
quality, and the marginal cost of production is independent of quality (McCannon,
2008). To introduce the trade-off between quality and quantity, assume instead that
C(x,e) = c2xe², with c>0; see Champsaur and Rochet (1989) and Giraud-Héraud,
Soler and Tanguy, (1999) for examples that have used this cost function.

Processors transform the raw material (input) into finished product (ouput). We
assume that there are not losses of quantity and quality in the transformation process,
that is, output quantity (Q) and quality (S) are linear functions of the input quantity and

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