, Volume 41, Issue 1, pp 115-120

Note on an alternative solution of Kamien-Schwartz's limit pricing problem

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Abstract

The present authors found Kamien-Schwartz's (Ref. 1) theory of limit pricing with infinite planning horizon interesting mainly because of a certain disproportion between the rather simplelooking result, viz., constancy of the optimal price strategy, and its comparatively difficult proof, viz., use of Pontryagin's Maximum Principle (PMP) which in the infinite horizon case is encumbered by the additional difficulty of not leading to a uniquely solvable system of necessary conditions. Quite in consonance with Arrow's opinion referred to in Takayama (Ref. 2, p. 446) that sometimes “the infinite horizon formulation is more convenient and revealing” than the finite one, it turned out that in this special case the original optimization problem could be replaced by a much simpler one and, therefore, the use of PMP avoided.