Structural Conservation Practices in U.S. Corn Production: Evidence on Environmental Stewardship by Program Participants and Non-Participants

infield or perimeter-field conservation structures are correlated with the field acreage allocation
decision for corn production.

The theoretical approach, based on prior work by Kim, et al. (CJAE 2005), compares cost
functions across alternative conservation technologies by conservation program participants and
non-participants. First, letting ci,p(yi,p) and cj,p(yj,p) be per acre cost functions (where y is per acre
yields) for the i^th and j^th technologies for the p^th program participation class (p = 1, 2 for
conservation program participants and non-participants, respectively), there exists for the p^th
participation class an acreage supply function Aj(yj) for the j^th conservation or production practice
such that:

(1)      a^ρi,j(p) = Aj,p(yj,p),

where a = yi / yj and a conservation or production technology cost relationship such that:
(2)       ci,p(yi,p(x1, x2, .., xn))  = a^{ρi, j(p)} cj,p(yj,p(x1, x2, .., xn))  = Aj,p(yj,p) cj,p(yj,p(x1, x2, .., xn)),

where ρi,,j(p) is the relative cost elasticity of relative output for the i^th and j^th technology and p^th
participation class, a is constant, and xk is the kth input per acre. If the production function, yj,p(x1,
x2, .., xn), is linearly homogeneous, then the cost relationship holds. (However, the cost relationship
does not imply that production is linearly homogeneous.)

With minor mathematical application, and applying Shephard’s lemma, we obtain an
equation for acreage shares for the j^th technology and p^th participation class relative to the k^th input
cost shares, for example, [∂ln Aj,p(yj,p) / ∂lnPk] = [px-(yi,p) / ci,p(yi,p)] - [pχ₁(yj,p) / cj,p(yj,p)]
where pk is the k^th per unit input price (k = 1, 2, . . . , n). The associated derived acreage function for
the j^th conservation or production technology and P^th participation class has the following
exponential form:

⁷ Structural practices may include field (and/or conservation tract) acres devoted to terraces, infield vegetative buffers,
stream-side forest buffers, windbreaks, field borders, grassed waterways, hedgerow plantings, stream-side herbaceous
buffers, infield contour buffers, filter strips, critical area plantings, and grade stabilization structures.

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