Profit/Cost/Expenditure Function

Verifying Curvature of Profit and Cost/Expenditure Functions

Convexity or concavity of optimal value functions is sometimes checked by evaluating leading principal minors of the Hessian matrix. This practice is not justified by extant theorems
about semidefinite matrices. A theorem is presented that justifies the practice and provides a relatively easy method of proving the relationship between semidefiniteness and principal minors.

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