53
(6)
Lo,B,n,Agfg ≥0. (7)
Equation (3) states that expenditures on nonlabor input, n , for farm production plus
(variable) transaction costs incurred if household members work off-farm or borrow are
limited to the sum of the value of the household’s liquidity, which is the sum of liquidity asset,
amount borrowed and compensation from land retirement. Equation (4) states that the
household’s time endowment is divided among working on-farm, working off-farm and
leisure. Equation (5) limits the amount of cultivated land that can be used for agricultural
production and for conservation to the household’s land endowment. Equation (6) is a full
income constraint that limits consumption to income from off-farm labor, profits from
production of agricultural commodities, compensation from the set-aside program and
liquidity asset minus fixed transaction costs associated with participation in off-farm labor
and/or credit markets.
The first-order necessary conditions for an interior solution with respect to on-farm
and off-farm labor (after rearranging the terms) can be written as
(8)
According to equation (8), at the optimum the household allocates time to on-farm and
off-farm labor so that the marginal value product of farm labor multiplied by marginal utility
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