Krugman echoes what I told National Journal a while ago on gold prices, but I think he makes it a bit more complicated than it has to be.
What effect should a lower real interest rate have on the Hotelling path? The answer is that it should get flatter: investors need less price appreciation to have an incentive to hold gold.
But if the price path is going to be flatter while still leading to consumption of the existing stock — and no more — by the time it hits the choke price, it’s going to have to start from a higher initial level. So the change in the path should look like this:
And this says that the price of gold should jump in the short run.
A simpler way to tell the story is this: after adjusting for risk the price of any asset has to rise at the long term interest rate.
Because if it rose slower than the long term interest rate then it you can make an easy profit by selling the asset buying bonds, earning interest on the bonds and then buying the exact same asset back later.
On the other hand if it rose faster than the interest rate you could make an easy profit buy borrowing money in the bond market, buying the asset, letting the asset go up in price and the sell it to pay off your bonds plus profit.
So we know all assets rise at the interest rate after accounting for risk.
So what happens when the interest rate goes down? Well we know that long term price appreciation will slow which means one of two possibilities
1) The current price will stay the same but slow price appreciation means the future price is lower
2) The current price will jump and slow price appreciation will get us to the same future price.
How do you know which one will happen? The short answer is that its almost always scenario (2).
The long answer is that declines in the interest rate that reflect declines underlying long run productive capacity will produce scenario (1). Declines that driven by nominal factors will produce scenario (2).