The name is absent

As is seen in the specification process of form (6), if the MS function is specified as being
additively separable and linear in μ, then it has to be decreasing and strictly concave in σ.
While the LMV model fully meets those properties, the LMS model fails to meet the strict
concavity condition. Therefore, the LMS model is not a relevant form at least in this context.
This arises because attention is not paid to the relationship between Arrow-Pratt’s risk
aversion measures in interpreting the LMS model under LS condition. As shown in table 1,
CARA indicates IRRA that imposes condition (5-iii’). The condition in conjunction with
condition (1) does not allow MS function to be linear in σ as long as it is additively
separable.

Despite that the LMS model may not display CARA under LS condition, there is no
doubt that additive separability is, if applicable, a useful property because it considerably
simplifies the specification of MS function. The remaining part of this section considers
whether the property applies to the case that an individual displays non-CARA preference. If
an individual is risk averter of IARA under LS condition, then the MS function has to entirely
fulfill conditions (1), (2), (3-i), (3-ii), (3-iii), (4-iii) and (5-iii). They also allow the MS
function to be specified as being additively separable when it is increasing and strictly
concave in μ and decreasing and concave in σ . This is easily shown through the following
three-step procedure. Firstly, an outline of MS function is drawn using conditions (1), (2),
(3-ii) and the signs of the derivatives, V_μμ (σ, μ) < 0, V_μσ (σ, μ) = 0 , which fulfill conditions
(3-i), (3-iii), (4-iii) and (5-iii). Since V (σ, μ) = 0 indicates that the MS function is additively
separable and V_μμ (σ, μ) < 0 in conjunction with condition (1) indicates that it is increasing
and strictly concave inμ , these together imply the expression, V(σ,μ) =h(μ) +k(σ), where
h (μ) denotes a function that is restricted to being h_μ (μ) > 0 and h_μμ (μ) < 0 . Secondly, the
remaining conditions (2) and (3-ii) restricts function k (σ) to being k_σ (σ)< 0 and k_σσ (σ)≤ 0 .
Thus, the additive separable MS function with the restrictions discussed here,

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