Integrating the Structural Auction Approach and Traditional Measures of Market Power

As was with the auction model, packers’ processing technology is assumed to be
of Generalized Leontief form. For simplification, the conversion factor to convert cattle
into boxed beef is assumed to be one. Thus, y ^f = y ^r = y.

The profit maximization problem for packer i is represented as:

(2.6)                    ^{max π}i = [P^{r -} P^f (Y^{f )]}yr ^- C(yr^{, v)}.

y_i

where πi is packer i’s profit, p^r is the retail price of beef, and C(y_i^r) is the processing cost
function for a representative packer. The first order condition for maximizing equation

(2.6) is:

Rearranging and re-writing the first order condition yields:

Pr = p^f [1 + ^{(1 +} θ')s' ] + c( yr ),
εs^f

where c(y_i^r) =dC(y_i^r,v)/dy_i^r is packer i’s marginal cost of processing beef,

εs^f = (dY^f /dp^f )(p^f /Y^f ) is elasticity of cattle supply, s_i = yr∣Y^r processor i’s market

share, and θ = d∑ⁿ y^f /dy^r is packer i’s conjecture about rivals’ responses to its
ⁱ                i≠j ^{j i}

change in purchases of cattle.

Customary with the NEIO model, an industry pricing equation is obtained from
equation (2.7) after multiplying every term of (2.7) by each firm’s market share si, and
summing across all processors in the industry as:

(2.8)              ∑'^p^r =∑,SiP-' +∑nf(^{1 +} θfs-s` P^f + c(yr).

V ^ε s         )

Re-arranging (2.8) equation yields the industry pricing equation:

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