Equation (3) is typically estimated with some kind of error specification to account for the lagged dependent variable specification. Technology variables could be incorporated in Zt provided they were exogenous. Adoption of MVs is typically a choice variable and thus endogenous, although some features of MVs, e.g. the availability of traits, may be considered the product of research programmes and thus not a choice variable to farmers.
In the older supply response literature a yield equation is sometimes estimated to achieve a full supply model.
The older duality-based supply model has also typically ignored technology, and the adjustment cost dynamics have typically also been ignored in earlier works. Equations (4)-(6) set out the fundamentals of the standard duality model.
Equation (4) describes a multiple output transformation function where two products (Y1, Y2) are produced using variable inputs (X1, X2, X3), fixed factors, F, infrastructure, I, and technology, T:
Variable profits are defined as:
Maximized variable profits are defined as:
where Y* and Y* are profit-maximizing levels determined by maximizing equation (5) subject to equation (4). Since these levels are functions of output prices, input prices, F, I and T, the maximized profits function can be written as:
The Shephard-Hotelling Lemma applied to Equations (6) and (7) yields a system of output supply and factor demand equations:
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