Lionel W. McKenzie of the University of Rochester, a significant player in Knowledge and the Wealth of Nations and careful reader of the book, has along sent ”a little paper” untangling the highly-compressed description of turnpike theorems that appears in connection with the series of conferences on growth theory that occurred in the early 1960s. [P. 156: “Exciting new theorems about the existence of “turnpikes” were being proved and disproved (routes by which economies might swiftly move to higher levels of industrial development through forced investment in heavy industy).” ] He writes:

I was surprised when I worked on the notion of a turnpike in economics that it was not already explored by mathematicians as a part of the calculus of variations. However I have found many topics in the mathematics of economics which were not dealt with in the mathematical literature not because they were difficult but because they were too special for general mathematical interest. However I have now noticed that some mathematicians have taken an interest in the general problem as a problem in calculus of variations and indeed have even cited my papers.  The general problem of calculus of variations arises when we are presented with a set of functions F and a valuation function v which gives a value to every function in this set and we ask  which function f * in the set F satisfies the condition that v(f*) (> or =)  v(f) for any f in F. I believe the subject arose from considering in what curve a rope of given length suspended between two points would assume. This problem was transformed into the question of what curve would minimize the potential energy of the rope arising from the force of gravitation. The answer is a catenary.

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