To illustrate the auction model considered in this study, consider a cattle market
with few packers purchasing cattle through a sequence of first-price sealed-bid auctions
in the context of IPV. Packers’ valuation (Rij) is defined as the price of processed beef
(prj) minus the marginal cost (cij) of processing cattle into beef. That is Rij = prj -cij.
Although competing packers do not know opponents’ valuation, they know that all
valuations R, including their own, come from a common distribution G (•) which is
continuous with density g(∙).
As discussed previously, packer’s valuation depends on the processing technology
employed. Following Sexton (2000), we assume that beef packers use cattle and non-
farm processing inputs to produce beef, y r, using a quasi-fixed proportion processing
technology. Such technology allows no substitution between cattle, y f, and a vector of
non-farm inputs, v, but may allow substitution between non-farm inputs. Processors’
technology is represented as:
(2.1) yr = min{ yf /Y, g( v)},
where γ ≤ yf/yr is the conversion factor between cattle and processed product. Packer’s
profit maximization requires that yr = yf /γ = g (v).
In maximizing expected profits, πi, the ith risk-neutral packer faces the following
maximization problem (Bajari and Hortaçsu, 2005):
(2.2) max πj = yir (Rj - Pf )G(^(Pf ))N'-1,
p
where i (i = 1,..., I) is a subscript for packer, andj (j = 1,..., T) is a subscript representing
the 'th cattle lot, Ri' = pr' -ci' is packer i’s per-unit valuation of processed product yi',
produced at processing cost cij, and sold at price prj ; pif is packer i’s dollar bid for cattle,