On second order conditions for equality constrained extremum problems - Mandy, David M. (Economics letters, 2013)
We prove a relationship between the bordered Hessian in an equality constrained extremum problem and the Hessian of the equivalent lower-dimension unconstrained problem. This relationship can be used to derive principal minor conditions for the former from the relatively simple and accessible conditions for the latter. •Establishes a simple relationship between a Hessian and bordered Hessian.•Derives necessary and sufficient second order conditions from this relationship.•The only proof that avoids use of quadratic forms subject to side conditions.•Clarifies Samuelson’s “great loss of symmetry”.