That was to show the absurdity of your ideas (i.e. deflation being the mirror of inflation).
It nevertheless is. If you ask for an example where the nominal interest comes out negative, then it is your assumptions in the example that are wrong, that's all.
If you ask me to assume that the earth has a negative mass, and then using Newton's gravity, I have to conclude that the moon will not remain in orbit around the earth, you will say that my explanation is confused. But that crazy example doesn't prove Newton's theory wrong of course.
Of course nominal interest cannot get negative. It won't. That doesn't mean that the real interest doesn't exist, and that there is no compensation for deflation or inflation.
It just means that in deflation debt will most likely be more burdensome (the higher the deflation), since nominal interest rate will always be over 0 (whatever deflation rates might be). You are still arguing your primarily point?
Yes. I don't see how you cannot see that elementary point.
We only have to assume that in the example, all nominal interests remain positive (simply because it doesn't make sense to have them negative).
So let us consider, again, a symmetric situation of 2% inflation, 0% inflation, and 2% deflation.
Let us start with the deflation case. Consider a positive nominal interest rate of, say, 1%. We have to assume this. But as I showed, this is also normal, because the mechanism that generates long term steady state deflation (namely, economic growth) also generates
real interest rate (the increase in real buying power of capital). If the nominal interest rate is 1%, then the real interest rate is 3% in our case.
Now, this is a genuine economic factor. It gives you the genuine return in the loan market. This is not something monetary. The real interest rate is the real price of borrowing VALUE which is the essence of the loan market.
So if we assume all else equal in the economy, except for monetary inflation or deflation, we have to keep this REAL interest rate constant, which is 3%.
So in 2% deflation (say, because there is fixed supply money, gold or something) environment, the nominal interest rate will be 1%.
In a 0% inflation environment (say, the "ideal reserve" of our friend chicagoschooler) the real and the nominal interest rate coincide, so the nominal interest rate will be 3%.
And finally, in a 2% inflation environment (say, a Keynesian inspired monetary policy) the nominal interest rate will be 3% (real) + 2% (inflation) = 5%.
So we have, all else equal:
a loan at 1% in a 2% deflation environment
a loan at 3% in a 0% inflation environment
a loan at 5% in a 2% inflation environment.
These 3 give identical burdens.