The name is absent

We have chosen these specific functional forms for the price and cost functions so
that the impact of the quality-quantity can be readily observed. On the one hand, the
price of a product is greater when a higher quality product is made, but it is more costly,
in total cost and marginal cost. On the other hand, the marginal cost of production is
assumed to be constant for a given level of quality, but for larger values of the supply
the price decreases.

Our formulation of the models⁴ implicitly recognizes the law of supply and demand
for both raw material and finished product, that is, the volume demanded will be
equivalent to the volume supplied in the regional area.

The Spot Market

To model the spot market, we consider that n processors (indexed by i:1...n) compete
on the market for processed products by setting quantities. It is assumed that each
processor i takes as given the qualities (sk) and prices (pk) of raw materials supplied by
the m growers (indexed by k:1.m). Moreover, each grower competes on the market for
raw materials by setting quantities and qualities.

The model is solved by backward induction. The objective function of the i-th
processor, assuming that he takes pk and sk as given, is defined in equation 1. The
processor maximizes his certainty equivalent, CE_i^M , which is equivalent to his expected
profit, π , by choosing quantity for each level of quality produced, q_ik. A processors
profit is the revenue generated minus the total cost paid:
m

(1) Max CEi^M =Ε∑(QikPik-qikpk)

^Qik                  k=1

Upon expanding the above expression, the following is obtained:

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