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

Authors

Karl-Walter Küpper

Johann Walter

Institut für MathematikRWTH Aachen

Articles

Received:

DOI:
10.1007/BF01415069

Cite this article as:

Küpper, K. & Walter, J. ZOR - Methods and Models of Operations Research (1995) 41: 115. doi:10.1007/BF01415069

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.

Key words

Pontryagin's maximum principleinfinite planning horizontransversality conditions