where δ and η are parameters that are restricted to 1 ≤δ≤η. Apparently, if 1 <δ<η, form
(15) corresponds to form (12) that displays the combination of DARA and IRRA under LS
condition, and when 1 <δ=η, it corresponds to form (10) that displays CRRA under LS
condition. Furthermore, when 1 =δ<η, it is a member of form (6) that displays CARA
under LS condition. These types of risk aversion expressed by form (15) are shown in table 5.
Here, it is observed that there is a relationship between the NLMS model and form (15).
Specifically, form (15) is derived from transforming the NLMS model by the concave
function, W = {V (σ, μ)} 1, and imposing the restrictions, 1 ≤ θ ≤ γ and μs - σγ > 0 . In the
following section, we consider the meaning of this mathematical relationship from economic
point of view, and then discuss the implications for an empirical approach called “joint
analysis of risk preference structure and technology” that has been recently employed in the
field of production economics under uncertainty.
Discussion
It is well known that a positive monotonous transformation of utility function has no essential
meaning in the case of consumer choice without uncertainty. Since the traditional consumer
theory relies upon ordinal utility theory, the utility function may be transformed by a positive
monotone function and then the transformed utility function is considered to be essentially
identical to the original one. However, the situation is different in the case of
decision-making problems under uncertainty, especially those based on EU theory such as
the MS approach established by Sinn (1983) and Meyer (1987). EU theory belongs to
cardinal utility theory in which vNM utility function is transformable only by positive linear
function. If MS approach is interpreted within EU theory, the transformation of the MS
function also needs to be linear (Proposition 1). Nonlinear transformation of the MS function
contradicts the assumption of interpreting MS approach within EU theory. Therefore, the
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