Conservation Payments, Liquidity Constraints and Off-Farm Labor: Impact of the Grain for Green Program on Rural Households in China

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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 (L^f ) and a composite consumption good (C) and is conditional on household
characteristics that define consumption preferences (z^c) . 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 (L^O), or leisure (L^l) . For work off the farm, the household incurs variable
transaction costs, τ^vo (e.g., transportation costs), and fixed transaction costs, τ^O (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, z^o , 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 ( A^gfg ) or to production of agricultural
goods (A^f ) . 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: A^f ≤ A -Ag^g . When the
government compensation rate for conservation set-aside is designated by δ, the income
from participating in the program is δA^gfg .

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