Dual ‘prices’ in plan and market

(JEL classification: 020) The solution to the dual programming problem is traditionally conceived as a vector of unit values for the constraints of the primal problem, which in much economic-theoretic exposition employs dollar-denominated output (revenue; gross output) as the maximand, and in some applied literature, contribution to profit. This interpretation of the dual is unreasonable and we argue that the dual values either are the unit Premiums over market prices, for those inputs whose acquisition costs are deducted from selling price (and only for those units which are incremental to the amounts represented by the current constraints) or, for ‘common’ or ‘overhead’ capacity constraints whose costs are not deducted to calculate the maximand, the potential profit contribution per unit activity/per unit time. The latter application requires estimation of facility life and consumption rates in the first place, which is abjured in the standard microeconomic cost model. The paper reviews other uses of duality, including that of the planned/semiplanned economy and the evolution of Kantorovich's treatment.