Greg Mankiw has a very good post (and column) on the idea of negative interest rates. I have long found this a good conundrum to tease (these sad days I dare not use the word "torture") graduate students with. Here is one explanatory passage:
If r is the real interest rate, then the relative price of consumption
tomorrow in terms of consumption today is 1/(1+r). Is there anything in
economic theory that requires this relative price to be less than one?
Unless consumption goods are costlessly storable, which they aren't, I
do not think so. Just as the price of apples can be more or less than
the price of pears, the price of consumption tomorrow can be more or
less than the price of consumption today. If people are eager to defer
consumption, then consumption tomorrow could well be more expensive
than consumption today–that is, the equilibrium real interest rate
could well be negative.
Of course there is more than one good in today's economy and no one holds the consumption basket per se. I've been trying to think through the implications of a negative real rate, combined with zero or near-zero storage costs for some goods, and positive or very high storage costs for other goods. What happens to relative prices and relative inventory holdings? Does this situation serve as a tax on the strawberry industry? If there is one good, with zero storage costs, and roughly flat marginal utility across the indicated range, can intertemporal arbitrage, using that good, force us back to a near-zero rate of return? In what way do the falling MU curves for easy-to-store goods enforce limits on the effectiveness of monetary policy in this setting?
These questions make me dizzy.