yields the following Lagrangian for the government’s second-best problem:
LSB
= F (F^(θ)[∏θ (a, θ) - ∏θ (a (θ), θ)] - ∏ (a (θ), θ) + ∏ (a, θ) T dF (θ) + (25)
Θ f (θ)
—λ ʃ [a — a (θ) — A] dF (θ) — y μ (θ) [a — a (θ)] dθ.
Consequently, an optimal second-best land allocation satisfies the following conditions:
λ _ F (θ) πaθ (a (θ) ,θ>+ μ (θ) — ∏a (a ,θ) ≥ 0;
f (θ)
Jx F (θ) ∏aθ (a (θ) ,θ)+ μ (θ) umJ ∩
[a (θ) — a] ∣ λ--f(θ)--∏a (a (θ), θ)J = 0;
μ (θ) [a — a (θ)] = 0;
λ { {[a — a (θ)]
Θ
— A} dF (θ) = 0;
(26)
(27)
(28)
The properties of F (θ) and π (a (θ) ,θ) ensure that this solution satisfies (22) (see Guesnerie
and Laffont, 1984). The impact of asymmetric information can be easily seen for interior
solutions. Unlike the first-best case, rather than having the marginal profit of land be
equated for all farms, there is a distortion created by the term F (θ) παθ/f (θ). As a result,
the equimarginal principal is never satisfied. This program could be implemented by the
government requesting that producers choose a land allocation and total transfer payment
from a menu of possible choices. For an interior solution, such a scheme would not result in
a linear price per acre of land idled.
The Pigouvian subsidy program can be thought of as a hybrid of the first and second
best programs. With this program, the transfer is ta (θ) rather than t (θ). The first order
condition of incentive compatibility condition (21) requires that an interior solution satisfy:
πα (a (θ) ,θ)=t.
(29)
15