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

decision maker reveals indifference between the two games. Soon afterwards, it is asked
to the decision maker that bids the result x2 that turns him indifferent between the pair of
games (x2, p; xr, 1-p) and (x1, p; xR, 1-p). Again the values p, xr, x1 and xR are fixed,
varying x2 until that the decision maker reveals indifference between the two games.
Substituting the values found in the utility function (u) is obtained the following equality
for the first indifference:

p u(x1) + (1-p) u(xr) = p u(x0) + (1-p) u(xR)                                              (8)

Then:

p (u(x1) - u(x0)) = (1-p) (u(xR) - u(xr))                                                      (9)

For the second indifference, it is obtained the following equality:

p (u(x2) - u(x1)) = (1-p) (u(xR) - u(xr))                                                     (10)

Equaling (9) the (10) and making u(x0) = 0 are obtained the following equality:

u(x2) = 2 u(x1)                                                                          (11)

This procedure continues until that an enough number of results is considered. In a
generic way, any xi is defined such that the decision maker is indifferent between game
(xi, p; xr, 1-p) and (xi-1, p; xr, 1-p), that in combination with other indifferences originates
that u(xi) = i * u(x1). It can establish u(xi) = i * α for any parameter positive arbitrary
u(x1) = α (for example: α = 1/n, with n denoting the index of the last result xn) (Wakker
and Deneffe, 1996). The application of this method to the Cumulative Prospect Theory
demands the extraction of two functions, because it is necessary to bid to positive
component and negative component of the value function. Then, it is necessary the
development of two sets of different questions. To estimate the decision weights in the
Cumulative Prospect Theory is also necessary to elicit a function separately for the gains

11

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