Empirical Calibration of a Least-Cost Conservation Reserve Program

The expected expenditure of the program is:

Finally, let λ ≥ 0 and μ (θ) ≥ 0 respectively denote the Lagrange multipliers for (12) and
the restriction a (θ) ≤ a.

The first-best program chooses s (θ) and a (θ) to minimize Eq. (16), subject to (12),
(15), and the boundaries of a (θ). The first-best Lagrangian is:

LFB = [ ʃs (θ) - ∏ (a (θ) ,θ) + ∏ (a,θ) - λ [a - a (θ) - A] - μ(^θ)∙ [a - a (θ)]l dF (θ)
_Θ                                                             f (θ)

(17)

At the optimum s (θ) is clearly set equal to zero for all types. In addition to the constraints

already discussed, the optimal land allocation satisfies the following conditions:

Consequently, for an interior solution, the optimal first-best program satisfies the equimarginal
principle. It equates the marginal profit from cultivating an additional acre of land for each
producer to the shadow cost of tightening the environmental constraint for the entire sector.
With full information, the first-best program could be implemented by offering a uniform
price for idled land equal to λ, combined with a type-dependent lump-sum tax that recovers
each producer’s surplus.

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