Infinite Peanut Policy — Reply to Romanchuk

My contentment with the economist’s optimal trade-off did not last. Mathematicians asked: What guarantees the existence of an optimum?

They have learned a lesson in the nineteenth century. Karl Weierstrass demanded existence proofs of minima and maxima. This struck his colleagues as excessively sceptical.

. . . Weierstrass gave memorable illustrations of optimising problems with false existential presuppositions. Suppose a pilot needs to fly from a point directly above A to point B. Which is the shortest path? As the candidate points of descent lose altitude their paths to B shorten. But there is no shortest path.

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