  A new method of deriving comparative statics information using generalized
compensated derivatives is presented which yields constraint-free
semidefiniteness results for any differentiable, constrained optimization
problem. More generally, it applies to any differentiable system governed by an
extremum principle, be it a physical system subject to the minimum action
principle, the equilibrium point of a game theoretical problem expressible as
an extremum, or a problem of decision theory with incomplete information
treated by the maximum entropy principle. The method of generalized compensated
derivatives is natural and powerful, and its underlying structure has a simple
and intuitively appealing geometric interpretation. Several extensions of the
main theorem such as envelope relations, symmetry properties and invariance
conditions, transformations of decision variables and parameters, degrees of
arbitrariness in the choice of comparative statics results, and rank relations
and inequalities are developed. The relationship of the new method to existing
formulations is established, thereby providing a unification of the main
differential comparative statics methods currently in use. A second theorem is
also established which yields exhaustive, constraint-free comparative statics
results for a general, constrained optimization problem. This theorem subsumes
all other comparative statics formulations. The method is illustrated with a
variety of models, some well known, such as profit and utility maximization,
where several novel extensions and results are derived, and some new, such as
the principal-agent problem, the efficient portfolio problem, a model of a
consumer with market power, and a cost-constrained profit maximization model.
