During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.

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