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I'm wondering why money is super neutral in Brunnermeier and Sannikov's "I-theory of money", but is not super neutral in their 2016 AER paper "On the optimal inflation rate".

In the I-theory of money, they show the super neutrality of money by arguing that the real return on money is $dp_tK_t/p_tK_t$, so the growth rate of money supply has no effect on the real return on money.

In the AER paper "On the optimal inflation rate", they show that the real return on money is $dpK_t/pK_t-dM_t/M_t$.

My question is, why don't they subtract the growth rate of money in the "I-theory of money"? Or, in other words, why is $dp_t/p_t$ not affected by money growth rate?

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