The Role of area-yield crop insurance program face to the Mid-term Review of Common Agricultural Policy

and a function for the losses. For the probability weighting function was used the
certainty equivalent method. In this method the procedure for getting the utilities is the
following: in first place, they notice two resulted xH and xL, with xH > xL, such that the
interval includes all the results of interest; in second place, they are attributed two values
arbitrarily to the extreme points, as for instance u(xL) = 0 and u(xH) = 1, soon afterwards
it is requested to the decision maker that establishes the certainty equivalent such that this
is indifferent for ( xL, p; xH, 1-p). Substituting this value in the expected utility function, it
is obtained the following equality:

U(CE) = p U(xl) + (1-p) U(x_h)                                                (12)

Varying the probabilities systematically new games are built in which are obtained new
values of the certainty equivalent, that are going to be substituted in the previous
equation, allowing to determine several points of the utility curve. The use of this method
that varies the probabilities and it maintains the same results in all of the games, allows to
prevent some inconveniences of other variants of this method that determines the
probabilities and vary the results, although it can suffer of the certainty effect, given that
the distortion of the probabilities is more pronounced near the extreme points.

The application of this method to Cumulative Prospect Theory suffers some alterations,
because to determine the value of the decision weights, it is necessary to know the value
function. The obtained certainty equivalent is substituted in the following equality:

V(CE) = h1 v(xH) + h2 v(xL), com xH>xL                                           (13)

As hi = f (pi) and h2 = f (p2+p1) — f (pi) = 1 — f (pi), solving in order f (pi), it is obtained
the following identity:

12

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