2. Producer Decisions and Welfare
Before examining the innovation and pricing decisions in the pure and mixed oligopsonies, we need to
analyze the way farmers make their selling decisions at the pre- and post-innovation stages. By doing so,
we can derive the supplies faced by each firm and obtain measurements of producer (farmer) welfare
before and after the cost-reducing process innovation activity.
In both the pre- and post-innovation stages of the game, farmers have to decide whether to sell
their product to Firm I or Firm C. Due to differences in their location, commitment to the two firms
(Fulton and Giannakas, 2001), and/or the prices offered by the two firms, their net returns depend on the
firm they will deliver their product to. Let α∈ [0,1] be the attribute that differentiates agricultural
producers. The farmer with attribute α has the following net returns function at the pre- and post-
innovation stages of the game:
(1) ΠIf(k)=wI(k)-cf-tα If a unit of product is sold to Firm I
ΠCf(k)=wC(k)-cf-t(1-α) If a unit of product is sold to Firm C
where k denotes the stage of the game; ΠIf(k) and ΠCf (k) are the per unit net returns when the farm output is
delivered to Firm I and Firm C, respectively; wI(k) and wC(k) are the per unit prices paid by Firm I and Firm
C, respectively; and c f is the farmers’ cost of producing the agricultural product. The parameter t is non-
negative and captures the degree of producer heterogeneity (when producers differ in their physical location,
t denotes the transportation cost they face). Ceteris paribus, producers with large values of α prefer to sell
their product to Firm C, while producers with low values of α prefer selling to Firm I. The greater is t , the
greater the difference in the net returns associated with selling the farm product to the two firms.
To ensure positive market shares for the two firms, it is assumed that t exceeds the difference in
the prices of the two firms (see equations (3) and (4)), while, to retain tractability, the analysis assumes
that producers are uniformly distributed between the polar values of α. Each farmer produces a unit of the
agricultural product and their selling decision is determined by the relationship between ΠIf(k) and ΠCf (k).