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Frank Knight's Theorem in Linear Programming Revisited

W. E. Diewert
A. D. Woodland

Abstract

The problem of maximizing the gross national product of a country subject to domestic resource constraints, given exogenous international prices, is studied. The primal problem allows for a general technology, including joint and intermediate products and any number of inputs, outputs, and industries. Dantzig's variable coefficients simplex algorithm in conjunction with the duality between production possibility sets and profit functions is suggested as a method for solving the primal problem. The dual problem is used to prove comparative statics theorems, which generalize several theorems of international trade theory. An appendix characterizes the properties of the inverse of a bordered Hessian matrix.