The minflex Laurent flexible functional form is a special case of a second-order Laurent series expansion. The minflex Laurent, when constructed in square roots, is called the minflex Laurent (ML) generalized Leontief. The minflex Laurent (ML) translog model is the minflex Laurent in logarithms. We find that the regular region of the ML translog is most often even larger than that of the ML generalized Leontief model, except when substitutability is very low. We previously have shown that the regular region of the ML generalized Leontief is substantially larger than that of the usual translog and generalized Leontief models.

Caves and Christensen (1980) have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional forms. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models.

We use the Caves and Christensen procedure to produce the regular regions of three flexible functional forms: generalized Leontief, translog, and Barnett's new minflexLaurent model. We display the regular regions in six cases with three goods using both three-dimensional color graphics and two-dimensional sections. We find that minflex Laurent generally has the largest regular region. In addition, the regular regions of that model are the most stable in shape across the six cases and always expand as real income increases. Consequently that model is especially well suited for use with income-trended time series data.