51
Appendix 1. Household model with liquidity, labor, land and full income
constraints and derivation of its first-order conditions.
We consider a farm household that maximizes utility, which is defined by consumption of
leisure (Lf ) and a composite consumption good (C) and is conditional on household
characteristics that define consumption preferences (zc) . The household derives income by
working off-farm in a wage-earning activity, producing agricultural goods on-farm and
receiving compensation for participating in the conservation set-aside. Each household is
endowed with a fixed amount of time, (L ), that it can allocate to on-farm activity (L ),
off-farm work (LO), or leisure (Ll) . For work off the farm, the household incurs variable
transaction costs, τvo (e.g., transportation costs), and fixed transaction costs, τO (e.g.,
job-search costs or start-up costs for a family-owned business). Participation in off-farm
employment is a function of the individual’s human capital, zo , which includes
characteristics such as level of education.
The household also is endowed with a total holding of land, A . The household can
allocate land to the conservation set-aside program ( Agfg ) or to production of agricultural
goods (Af ) . We assume that land rental markets function poorly, which is consistent with the
environment in the areas of rural China in which Grain for Green has been implemented.
Therefore, there is a constraint on land available to the household: Af ≤ A -Agg . When the
government compensation rate for conservation set-aside is designated by δ, the income
from participating in the program is δAgfg .
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