Flexible functional forms and tests of homogeneous separability

The paper addresses functional form issues that arise when testing for the existence of homogeneously weakly separable aggregates in producer or consumer theory. Blackorby, Primont and Russell showed that the commonly used flexible functional forms became inflexible when separability restrictions were imposed. The paper proposes functional forms that are: (i) flexible, (ii) parsimonious, and (iii) have the correct curvature, both before and after separability restrictions are imposed. Two functional forms are proposed that are based on the normalized quadratic functional form, and the appropriate tests for the existence of separable aggregates are derived. The second test is a modification of Woodlandʹs separability test.