Tenants, landlords, and soil conservation.

Further insight can again be obtained by graphical analysis. Let [L.sup.r](e, k) denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for conservation investment (23) and [T.sup.r](k, e) denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for effort (21). Let (k', e') [member of] [L.sup.c] and consider [L.sup.*](k', e'), the set of conservation investment and effort levels that satisfy the necessary condition for first-best effort under risk neutrality. By the definition of [L.sup.c], [L.sup.*](k', e') = [rho]s[R.sub.ek]/[R.sub.e] > 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 left of [L.sup.*] in (k, e) space. Similarly, consider [T.sup.*], the set of conservation investment and effort levels that satisfy the necessary condition for first-best conservation investment under risk neutrality, evaluated at (k', e') [member of] [T.sup.r]. By the definition of [T.sup.r], [T.sup.*](k', e') = [rho](s[R.sub.ee]--[C.sub.ee])/[R.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 below [T.sup.*] in (k, e) space.

Figures 3 and 4 compare the share rental equilibrium with the first best under risk neutrality in the cases where the land value and current productivity effects dominate, respectively. It can be seen from figure 3 that when the land value effect dominates, both conservation investment and effort under a share rental contract with a risk-averse tenant are less than the first best. When the current productivity effect dominates, however, it is possible that conservation investment exceeds the first best while effort is less than the first-best level, as depicted in figure 4.

[FIGURES 3-4 OMITTED]

As before, share rental contracts with risk-averse tenants provide landlords with three instruments to influence land degradation: investment in durable conservation measures k, the output share s, and the fixed payment t. The output share and fixed payment combined influence land degradation indirectly by determining the tenant's level of income risk, which influences effort. The need to use risk sharing to counteract moral hazard results in a level of effort lower than that which maximizes the value of output during the lease period--although it may be higher than the first-best level when land degradation is taken into account. Investment in durable conservation measures lowers the marginal productivity of effort in current production and thus serves to reduce effort further. As a result, effort is always lower than the first best. As with risk-neutral tenants, the optimal output share is adjusted downward by a factor equal to [beta] V'[h.sub.e]/[R.sub.e]. When the land value effect dominates, a change in conservation investment lowers this adjustment factor; when the current productivity effect dominates, a change in conservation investment increases it. Thus, when the land value effect exceeds the current productivity effect, the landlord relies more heavily on output sharing, inducing a risk effect that lowers effort and thus the need for conservation investment. But when the current productivity effect exceeds the land value effect, the landlord relies less heavily on output sharing and may thus need to increase conservation investment above the first-best level in order to limit land degradation.

Production and Conservation Investment with Risk-Averse Landlords

In developed countries like the United States (and in contrast to developing countries), many farm landlords are retired farmers, the spouses of deceased farmers, or absentee landlords, all of whom can be plausibly characterized as risk averse (Huffman and Just 2004). It turns out that the results of the preceding sections carry over qualitatively to situations where landlords are risk averse.

First-Best Effort and Conservation Investment

The first-best levels of effort and conservation ([e.sup.**], [k.sup.**]) in this case maximize [E.sub.[epsilon]]{W(R(e, k, [x.sub.0]) + [epsilon] - C(e) - I(k))} + [beta] [E.sub.[eta]]{W(V([x.sub.0] - h(e, k)) + [eta])} where W(.) is the landlord's utility of income, assumed concave and stationary over time. The necessary conditions characterizing the first-best levels of effort and conservation investment for a risk-averse landlord are

(26) [E.sub.[epsilon]{W'}([R.sub.e] - [C.sub.e])} - [beta][E.sub.[eta]]{W'}}V'[h.sub.e] = 0

(27) [E.sub.[epsilon]{W'}([R.sub.k] - [I.sub.k])} - [beta][E.sub.[eta]]{W'}}V'[h.sub.k] = 0

These conditions differ from those of a risk-neutral landlord only in weighting income during the lease period and land value at the end of the lease period differently. Specifically, one would expect the expected marginal utility of income during the lease period [E.sub.[epsilon]]{W'} to exceed the expected marginal utility of the value of land at the end of the lease period [E.sub.[eta]]{W} because the value of land V(*) likely exceeds income generated during the lease period R(*) - C(*) - I(*), suggesting that risk-averse landlords prefer greater effort and less conservation investment than risk-neutral landlords.

Cash Rental Contract

If tenants are risk neutral, risk-sharing considerations suggest the optimality of cash rental contracts. Under a cash rental contract, the tenant's level of effort [e.sup.ca] is defined by equation (5). The landlord chooses the cash rental payment [t.sup.ca] so that the participation constraint (7) binds with equality. The landlord's optimal choice of conservation investment [k.sup.ca] is then defined by the condition

(28) [E.sub.[epsilon]{W'}([R.sub.k] - [I.sub.k])} - [beta][E.sub.[eta]]{W'}V' ([h.sub.k] + [h.sub.e] [partial derivative][e.sup.ca]/[partial derivative]k) = 0

which is the same as equation (8) except for the differential weighting of income during the lease period compared to land value at the end of the lease period. A first-order Taylor series approximation to the equilibrium conditions (5) and (28) yields expressions for ([k.sup.**] - [k.sup.ca]) and ([e.sup.**] - [e.sup.ca]) equivalent to equations (9) and (10), respectively, with [E.sub.[eta]]{W'V'} replacing V', [[E.sub.[eta]]{W"(V').sup.2] + W'V"} replacing V", and the second-order condition for the first best under risk aversion replacing [OMEGA]. We thus have:

PROPOSITION 5. When the landlords are risk averse and tenants 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.

It follows that the graphical analyses in figures 1 and 2 also illustrate the comparison of the cash rental equilibrium with the first best in the case of risk-averse landlords.

Cash rental contracts achieve optimal risk sharing when landlords are risk averse but do nothing to attenuate tenants' incentives for overexploiting soils. As before, landlords have no means of influencing tenants' effort levels other than installing or requiring durable conservation measures and thus overinvest in these measures in order to limit excessive land degradation.

Share Rental Contract

When landlords are risk averse and tenants are risk neutral, risk-sharing considerations suggest that share rental contracts would be suboptimal. But share rental contracts also attenuate tenants' incentives for exerting effort and hence overexploiting the land. As in the case of risk-neutral landlords, adding rent sharing to the set of instruments at the landlord's disposal permits attainment of the first best. The tenant's optimal level of effort, [e.sup.fa], is characterized by equation (11) as before. The landlord chooses the fixed payment [t.sup.fa] to ensure that the tenant's participation constraint (14') binds with equality. The landlord's respective optimal choices of the tenant's share [s.sup.fa] and conservation investment [k.sup.fa] then satisfy the conditions

(29) [[E.sub.[epsilon]] {W'} ([R.sub.e] - [C.sub.e]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]] [partial derivative]e/[partial derivative]s = 0

(30) [E.sub.[epsilon]] {W'} ([R.sub.k] - [I.sub.k]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.k]] + [[E.sub.[epsilon]] {W'} ([R.sub.e] - [C.sub.e]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]] [partial derivative]e/[partial derivative]k = 0.

As in the risk-neutral case, it is readily apparent that conditions (29) and (30) are equivalent to conditions (26) and (27), respectively. We thus have:

PROPOSITION 6. When the landlords are risk averse and tenants are risk neutral, share rental contracts combined with investment in durable conservation measures are capable of achieving first-best levels of effort and conservation.

The optimal share allocated to the tenant is

(31) [s.sup.fa] = 1 - [E.sub.[eta]]{W'}/[E.sub.[epsilon]]{W'} [beta] V'[h.sub.e]/[R.sub.e]

a close analog of equation (16) with the adjustment for the marginal cost of land degradation [beta] V'[h.sub.e]/[R.sub.e] weighted by the marginal utility of wealth at the end of the lease period relative to the marginal utility of income during the lease period. The arguments above suggest that this ratio is less than one, so that the tenant's share is higher when the landlord is risk averse than when the landlord is risk neutral. Such an outcome is as one would expect, since if overexploitation of soil were not an issue it would be optimal to make the tenant the residual claimant of all income during the lease period.

Risk-Averse Tenants