Agricultural Policy as a Social Engineering Tool

decision. The random component comes from maximization errors, and other
unobserved characteristics of choices or measurement errors in the exogenous variables.

Let the profit function of farm operator i, making thej-th choice be,

∏j = Uj + E                                         ɑ)

where U_ij = (lnX _i1, InX _i2 , ....., InX _ik ) with InX _im representing the set of m observable

characteristics of the i-th farm operator, and ε_ij is a random variable. If the i-th farm
operator maximizes profit s/he will choose decision j rather than k according to the
expression,

∏ > ∏ik, ∀k, k ≠ j.                                             (2)

Note that the profit function has a random component. Then the probability that choice j
is made by the i-th farm operator can be defined as,

P = P^r ob ⁽ⁿ„ > π_ik ), ∀^{k, k} ≠ j.

^{lt can be shown that i}f^{the error term ε has standard τ}yp^e 1 ^{eχtreme distributions with}

density

f (ε ) = exp{-ε - exp{-ε}}
then (see Maddala, 1983, pp60-61)

_p = e^χpU. ^}
j = ∑ exp{Uik}^,

which is the basic equation defining the multinomial logit model. In the case where j =

2, the i-th farm operator will choose the first alternative if π_{i 1} - π_i2 > 0 . If the random

^{π have inde}p^{endent extreme value distributions, their di}f^{ference can be shown to have a}

11

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