The name is absent

quality as follows: Q=q; S=s. Likewise, we further consider that there are no raw
material processing costs. Although these unrealistic assumptions are made for the
purpose of analytical simplification, they do not take away from the applicability and
implications of the model.

The price function

As we noted earlier, there are a total number of m growers (k:l,,,m) of an input,
each of whom differentiated in quality. We will denote the quantity and quality
produced by grower k by qk and sk, respectively. We denote by qik the quantity of
n

grower k´s input supplied to processor i, where q_k = ∑q_ik . Likewise, there are a total
i=l

of n processors (i: 1...n) who acquire growers´ input. Let Qik and Sk be defined as
processor i´s output quantity and quality derived from grower k´s input. As there is no
loss of yield and quality in input processing, Q_ik = q_ik, S_k = s_k . Likewise, let Qi be

m

defined as the total processor i´s supply, whereQ_i = ∑ Q_ik . Following Lancaster
k=1

(1979), we distinguish between horizontal and vertical differentiation. Let P_ik denote
the price at which each processor sells the output derived from the grower i´s raw
material. An increase in the output quality improves each eonsumer´s utility (see Mussa
and Rosen, 1978). Then, the inverse demand function³ for the processor i´s output
derived from grower i´s input is assumed to be linear in his supply, Q_i, and quality, S_k ,
and symmetrically linear in the supplies of the rest of the competitors as follows:

n

P =bS -b Q -b ∑Q         ∀i=1...n k = 1...m

ik 1 k 2 i 3 j
j≠i
j=1

Where b1, b2 and b3 represent, respectively, the own market specific quality effect
(vertical differentiation) and the own and each rival market specific effects (horizontal
differentiation) with b_h>0 h=1...3.

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