Extensions of the Le Chatelier-Samuelson Principle and Their Application to Analytical Economics--Constraints and Economic Analysis

The static aspect of the Le Chatelier-Samuelson principle in the local version is fully characterized in an extremum formulation with differing systems of auxiliary constraints. The local characterization results in an interesting finding. With the systems of effective constraints which restrict only as man involved variables as the number of constraints, the variations of an extremum system, as consequences of changes in parametric indices of exogeneous conditions, will be only quantitative. With the systems of effective constraints which restrict more or all the involved variables, however, the consequential variations will be qualitative as well as quantitative. Necessary and sufficient conditions are investigated for constrained saddle points to exhibit a generalized Le Chatelier-Samuelson principle. An economic argument along the lines of demand theory is that the generalized principle among constrained demands is established if and only if the Jacobian of the constrained demands with effective constraints exhibits a dominant complementarity for the new constraint with its coefficients non-negative. The Marshallian conjectures about short run and long run are extensively discussed and rigorously proved with the results.