Tenants, landlords, and soil conservation.

The landlord chooses the cash rental payment so that the participation constraint (7) binds with equality. The landlord's optimal choice of conservation investment under a cash rental contract, [k.sup.c], is then defined by the condition

(8)

[R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e] [partial derivative][e.sup.c]/[partial derivative]k

= [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e] [[R.sub.ek]/[C.sub.ee]-[R.sub.ee]] = 0.

To compare the equilibrium levels of effort and conservation investment under a cash rental contract with the corresponding first-best levels, consider a first-order Taylor series approximation to conditions (3) and (4) that define ([e.sup.*], [k.sup.*]) evaluated at the cash rental contract equilibrium ([e.sup.c], [k.sup.c]), which can be solved to yield

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

by the concavity of the objective function (2) in (e, k). It is evident from equation (9) that [k.sup.*] - [k.sup.c] < 0, so that [k.sup.c] > [k.sup.*]. The sign of the right-hand side of equation (10) is indeterminate, however. The first term in braces({}) is positive by the concavity of the objective function (2) in (e, k). The third term in braces is also positive under our assumptions, but the second term is negative. Thus, [e.sup.*] - [e.sup.c] may be either positive or negative, so that [e.sup.c] may be greater or less than [e.sup.*]. We can summarize this result as

PROPOSITION 1. When both landlord and tenant are risk neutral, under cash rental contracts landlords overinvest in durable conservation measures while tenants" effort may be either greater or less than the first best.

Intuitively and in line with the conventional wisdom, tenants exert too much effort because they have no reason to take into account the deleterious effects of current production on the future productivity--and hence value--of land, as is readily seen by comparing conditions (3) and (5) that define effort levels in the first best and cash rental contracts, respectively. Under cash rental contracts, landlords have no means of influencing tenants' effort levels aside from durable conservation measures. Hence, landlords invest more than is socially optimal in these measures in order to curb tenants' overexploitation of land.

Further insight can be obtained by graphical analysis. Let [L.sup.*](k, e) = {(k, e): [R.sub.k]--[I.sub.k]--[beta]V'[h.sub.k] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for first-best conservation investment and [T.sup.*](k, e) = {(k, e): [R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for first-best effort. The first-best equilibrium ([k.sup.*], [e.sup.*]) is an element of both sets, that is, can be found at the intersection of these two loci.

The slope of [L.sup.*] in (k, e) space is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The numerator is positive while the sign of the denominator is indeterminate, since its first term is negative while the second two are positive. The first term of the denominator is the effect of conservation investment on the marginal productivity of effort in current production. We will refer to it as the current productivity effect of conservation. The second two terms of the denominator combined are the effect of conservation investment on the marginal effect of effort on land degradation, that is, on the value of the land at the end of the lease period. We will refer to it as the land value effect of conservation. When the land value effect is greater (in absolute value) than the current productivity effect, [L.sup.*] is upward sloping, and vice versa.

The slope of [T.sup.*] in (k, e) space is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since the denominator is negative, the slope of [T.sup.*] depends on the relative sizes of the current productivity and land value effects. As with [L.sup.*], when the land value effect is greater (in absolute value) than the current productivity effect, [T.sup.*] is upward sloping, and vice versa. (In other words, [T.sup.*] is upward sloping whenever [L.sup.*] is, and vice versa.) The concavity of the objective function (2) implies that [L.sup.*] is always steeper than [T.sup.*].

Now let [L.sup.c](k, e) = {(k, e): [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e][[R.sub.ek]/([C.sub.ee] - [R.sub.ee])] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for conservation investment under a cash rental contract and [T.sup.c](k, e) = {(k, e): [R.sub.e] - [C.sub.e] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for effort under a cash rental contract. Let (k', e') [member of] [L.sup.c] and consider [L.sup.*](k', e'). By the definition of [L.sup.c], [L.sup.*](k', e') = [beta]V'[h.sub.e][[R.sub.ek]/([C.sub.ee] - [R.sub.ee])] < 0. Since [L.sup.*] is decreasing in k, it must be true for k" such that (k", e') [member of] [L.sup.*] that k" < k', which implies that [L.sup.c] lies to the right [L.sup.*] in (k, e) space. Similarly, consider (k', e') [member of] [T.sup.c]. By the definition of [T.sup.c], [T.sup.*](k', e') = - [beta]V'[h.sub.e] < 0. Since [T.sup.*] is decreasing in e, it must be true for e" such that (k', e") [member of] [T.sup.*] that e" < e', which implies that [T.sup.c] lies above [T.sup.*] in (k, e) space.

Figures 1 and 2 compare the cash rental equilibrium with the first best in the cases where the land value and current productivity effects dominate, respectively. It can be seen from figure 1 that when the land value effect dominates, both conservation investment and effort under a cash rental contract exceed the first best. When the current productivity effect dominates, however, it is possible that effort is less than the first best while conservation investment exceeds the first best, as depicted in figure 2. When the land value effect dominates, durable conservation measures do not constitute much of an impediment to the productivity of effort in current production. As a result, even excessive investment in conservation measures does not induce a reduction in effort to the first-best level or less. In contrast, when the current productivity effect dominates, a larger reduction in the productivity of effort in current production is needed to attain any given reduction in marginal land degradation. Landlords' overinvestment in conservation, undertaken in order to curb tenants' incentives to overexploit land, may reduce the current productivity of effort enough that effort falls below the first best (figure 2).

[FIGURES 1-2 OMITTED]

Share Rental Contract

Share rental contracts can serve as a device for landlords to protect their land against degradation by mitigating tenants' incentives to overexploit soils. The marginal return to effort is lower under a share contract than under a cash rental contract because tenants appropriate only part of the rent generated during the lease period. Formally, let s denote the share of the rent kept by the tenant, so that the tenant's return during the lease period is s[R(e, k, [x.sub.0]) + [epsilon]] - C(e). The tenant's optimal choice of effort is thus defined implicitly by

(11) [R.sub.e]-[C.sub.e] =(1-s)[R.sub.e].

When investment in durable conservation measures is infeasible (so that k = 0), it is evident from a comparison of conditions (5) and (11) that the tenant's optimal choice of effort is lower under a share rental contract than a cash rental contract.

More generally, consider the landlord's choice of contract terms under a share rental system when investment in durable conservation measures is infeasible; this is a two-period version of the case analyzed by Dubois (2002). The landlord's objective is to choose the tenant's share s and fixed payment t to maximize

(12) (1 - s) [E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} + t + [beta] [E.sub.[eta]]{V([x.sub.0] - h(e, 0)) + [eta]}

subject to the tenant's incentive compatibility and participation constraints,

(13) [e.sup.s] = arg max{s [E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} - t - C(e)}

(14) s[E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} - t - C(e) [greater than or equal to] [u.sub.0]

respectively. It follows from condition (11), which characterizes the tenant's optimal choice of effort, that effort is increasing in the tenant's share ([partial derivative][e.sup.s]/[partial derivative][e.sup.s] = [R.sub.e]/[[C.sub.ee] - s[R.sub.ee]] > 0).

The landlord chooses the fixed payment or wage so that the participation constraint binds. The landlord's optimal choice of the tenant's share satisfies

(15) ([R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e]) [partial derivative]e/[partial derivative]s = 0

which implies, after substitution from condition (11), that

(16) [s.sup.s] = 1 [beta]V'[h.sub.e]/[R.sub.e].

The tenant's share of output is adjusted downward in order to make the tenant face the marginal cost of land degradation, i.e., the marginal reduction in the value of the land at the end of the lease period per unit of output during the lease period, [beta]V'[h.sub.e]/[R.sub.e].