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paradox that emerged when Cagan used his estimates of x to calculate the sustained rates of inflation associated with the maximum flow of real resources that the creators of money could command by printing money. This optimal rate of inflation turns out to be -l/oc. For each of the seven hyperinflations, the reciprocal of Cagan's estimate of -a turned out to be less, and often very much less, than the actual average rate of inflation. The data are shown in
Thomas J. Sargent (Tue,) studied this question.