On flat production surfaces associated with Cobb-Douglas-type production models exhibiting variable returns to scale

We prove that the flatness of the production surface associated with a Cobb–Douglas-type production model exhibiting variable returns to scale forces the local return-to-scale index to be constant, thereby establishing a rigidity result for this class of production functions. Consequently, every flat production model in this class is homogeneous, and its local classification follows directly from the classification theorem established in [8] . This demonstrates a remarkable phenomenon: the flatness condition completely suppresses the variability of the local return-to-scale index.