producers are assumed to be equally endowed with an initial acreage allocation a equal to
2,000 acres. This maximum farm size is assumed to be fixed in the short run. I also assume
that for reasons of overall efficiency the government does not wish farmers to produce in the
range of increasing returns to land. Therefore the minimum amount of land cultivated, a,
is 500 acres.8 These restrictions ensure that the profit function satisfies πa > 0, πaa < 0
and πaθ > 0 over the relevant range of a. Consistent with the previous sections, assume
the probability density function of types, f (θ) ≡ dF (θ) /dθ,issuchthatlnθ has a normal
distribution truncated at zero from above.
Assuming all farmland is eligible for participation, the environmental constraint is a
requirement that the average quantity of land idled across all producers be at least A acres:
[a — a (θ)] dF (θ)
≥A
(12)
To ensure that program participation is voluntary, producers must be compensated for the
opportunity cost of idled land:
π (a (θ), θ) + t (θ) ≥ π (a, θ), for all θ.
(13)
Define surplus payments received by a firm in excess of the minimum necessary to
satisfy (13) by:
s (θ) ≡ π (a (θ), θ) + t (θ) — π (a, θ).
(14)
The participation constraint (13) can then be expressed more succinctly by:
s (θ) ≥ 0, for all θ.
(15)
12
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