David Gale: Duality and Turnpikes
摘要
This paper presents a review of some of the developments in mathematical economics that were influenced by contributions of David Gale. It begins with the fundamental duality theorems of linear programming and its application to two person zero sum matrix games. Turning to dynamic economics, the multi-sector analysis of a closed model of production by Gale is considered in detail. The applications of von Neumann equilibrium prices to establish the Samuelson conjecture on turnpike properties of a class of optimal programs, to derive Malinvaud prices supporting efficient programs and to throw light on the need for substitution possibilities to sustain a positive level of consumption are elaborated. Finally, Gale’s multi-sector model with a primary factor of production is recalled. The golden rule equilibrium and the use of golden rule prices to establish a turnpike property of programs that are optimal according to the overtaking criterion are presented with an emphasis on the value loss technique.