The name is absent

where β_i (i = 0,1,2, — ,n) are parameters. Because, as has been already mentioned,
functiong(σ) in form (6) must meet the restrictions, g_σ (σ)< 0 and g_σσ (σ)< 0, the parametric
restrictions, β_i ≥ 0 (i = 1,2,3, —, n) and β_i > 0 for at least one i (i = 2,3,4,—, n), are imposed
on form (7). Note also that since the parameter β₀ does not play an important role on the
curvature of function g(σ), β₀ = 0 is assumed a priori for the simplification. Substituting
form (7) and β₀ = 0 for (6) yields the following MS function:

(α > 0, β_i ≥ 0(i = 1,2,3, —,n), β_i > 0 for at least one i (i = 2,3,4,—,n) ).

When α = 1 and β_i = 0 (i = 1,3,4, — , n), form (8) nests the linear mean-variance (LMV)
model, probably one of most frequently applied MS functions in the field of agricultural
economics. This is not, however, a surprising consequence in considering the assumptions
imposed here. As originally demonstrated by Freund (1956), the LMV model is derived
through EU theory assuming that vNM utility is a negative exponential function and random
payoffs follow a normal distribution, and the negative exponential utility represents CARA
preference and the normal distribution belongs to the LS family. Therefore, the specification
procedure, adopted here, of MS function may be an alternative approach that can derive the
LMV model. And undoubtedly, it is feasible to employ the LMV model under the
assumptions of CARA preference and LS condition (an example is the recent study by
Peterson and Ding 2005). On the other hand, form (8), because of the imposed parametric
restrictions, does not nest the linear mean-standard deviation (LMS) model that has been
recently applied by Eggert and Tveteras (2004) in the context of CARA and LS condition.

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