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I like this analysis, but I don't think that a 1 second increase in M would impact nominal GDP even if the interest elasticity of the demand for money were zero.

I am willing to go out on a limb and say the same for a one month increase in M.

I think you need to fit in Krugman (and Sumner's) argument about what is happening to the real interest rate earned on money.

And remember that behind the "real interest rate" on money, we are talking about people waiting out a temporary price spike for durable goods.

Bill: agreed. It would be hard to make the case that a one-month increase in the money supply would make any difference, even if the money demand were perfectly inelastic. It takes time to increase production, or prices. But might not durable goods prices increase, just a bit?

I think durable priced goods would increase just a bit. To a point that their prices would fall at a rate equal to the real interest rate.

In other words, it is something like your formula.

The assumed lower nominal interest rate because nominal GDP is shrinking offsets the deflation, so that real interest rates on things other than hand-to-hand currency don't rise. But the real interest rate on currency does rise with the deflation.

If we hit the zero bound on other financial assets, then their real return is the same as currency.

So, you can hold them until prices are back down to the initial level.

Now, if all money has a nominal interest rate, and it can be negative, which is a world where the interest rate elasticity of the demand for money is zero, then I think maybe your formula works.

Still, I can't imagine that NGDP would change second by second, hour by hour, week by week, in proportion to the quantity of money.

Like I said, I like your formula.

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