be fully compatible with conditions (4-i), (4-ii), (4-iii), (5-i), (5-ii) and (5-iii) (see table 2).
The compatibility with conditions (4-i), (4-ii), (4-iii), (5-i), (5-ii) and (5-iii) is maintained
under the parameter restrictions, θ > 0 and γ > 0 , as discussed by Saha (1997). Besides, the
conditions (1) and (2) are satisfied since Vμ (σ, μ) = θμe-1 and Vσ (σ, μ) = -γσγ-1. However,
conditions (3-i), (3-ii) and (3-iii) are not always fulfilled under the initial parametric range,
because Vμμ (σ, μ) =θ(θ-1)μθ-2, Vσσ(σ,μ) =-γ(γ-1)σγ-2, and
Vμμ (σ, μ)Vσσ (σ, μ) -Vμ2σ (σ, μ) =-θ(θ-1)γ(γ-1)μθ-2σγ-2. In order to satisfy them, a stronger
parametric restriction, 0<θ ≤1 and γ ≥ 1 , is necessary. Although conditions (1) and (2) as
well as conditions (3-i), (3-ii) and (3-iii) are fully met under the new parametric range, the
full compatibility with conditions (4-i), (4-ii), (4-iii), (5-i), (5-ii) and (5-iii) is lost, as
conditions (4-i) and (5-i) are not satisfied. It means that the NLMS model is reduced to a
model that is capable of displaying the two types of risk aversion, CARA and IARA, under
LS condition. Actually, if θ = 1 and γ > 1 , then the NLMS model is categorized into form
(6) that displays CARA under LS condition, and when 0<θ <1 and γ ≥ 1 , it is a member of
form (9) that displays IARA under LS condition. The reconsideration of the NLMS model
alters the interpretation from table 3 to table 4, implying the difficulty in explaining Saha’s
empirical result that the production agents are risk averter of DARA by means of the NLMS
model. To incorporate this type of risk aversion, some modification would be needed.
In fact, the NLMS model can be easily modified so that it explains Saha’s (1997)
empirical result. It is carried out by combining the MS functions proposed in the previous
sections. The MS function is derived as follows,
(15)
(1 ≤ δ ≤ η; μs -
ση>0),
23
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