and Rausser, 2007). However, given the trade off, often present, between the quality of
a good and the quality produced, it can not be assumed that a greater level of quality
always lead to a greater level of expected profit.
In this section we undertake some comparative statics in order to see how changes
in the number of operators, uncertainty and/or grower´s risk aversion can explain that
the processor could be not acting optimally with an incentive contract. Our models
allow two sets of results. First, there are implications about the consequences of
contractual choice in grower´s decision variables. Second, the models developed above
are used to show the optimality of these contractual mechanisms.
We carry out a simulation exercise with a wide range of scenarios, and selected the
examples below as being representative of the behaviour we found. We use
Mathematica7 to solve the model, and use Excel to draw the graphs using the data
produced by Mathematica. We initially choose the following parameters: b1 = 1,
b2 = 0.00001, b3 = 0.0001 and c = 0.4 . It should be noted that these initial values are
used for convenience and has no special significance here and that simulation results do
not change substantially if different values for b1, b2, b3 and c are used.
It will be seen below that this exercise is able to provide a consistent explanation for
many issues relating to governance mechanisms. However, before proceeding, we
should note the caveat that this simulation exercise uses restrictive assumptions about
the shapes of price and cost functions. Although these seem highly plausible to us for
most situations, there may be situations which are not covered by our simulations.
Then, we have three free parameters in our model: the number of growers, n, the
number of processors, m, the primary producer’s coefficient of absolute risk
aversion, ρ, and the variance of input quality,σs2 . It may be worth noting here that the
risk premium can be higher for a grower than for another either because he is more risk