Integrating the Structural Auction Approach and Traditional Measures of Market Power

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
(p^r_j) minus the marginal cost (c_ij) of processing cattle into beef. That is R_ij = p^r_j -c_ij.
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)                              y^r = ^min{ y^f /Y^, g( v)}^,

where γ ≤ y^f/y^r is the conversion factor between cattle and processed product. Packer’s
profit maximization requires that y^r = y^f /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 π}j = yir (Rj ^- Pf )G(^(P^f ))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' = p^r_' -c_i' is packer i’s per-unit valuation of processed product yi',
produced at processing cost cij, and sold at price p^r_j ; p_i^f is packer i’s dollar bid for cattle,

<<   6   7   8   9   10   11   12   >>

More intriguing information