Gold Prices Determined By Real Interest Rates

Krugman says that gold can be understood as a stock of an exhaustible resource. 

Here’s how it works. Imagine that there’s a fixed stock of gold available right now, and that over time this stock gradually disappears into real-world uses like dentistry. (Yes, gold gets mined, and there’s a more or less perpetual demand for gold that just sits there; never mind for now). The rate at which gold disappears into teeth — the flow demand for gold, in tons per year — depends on its real price:
Crucially, at least for tractability, there is a “choke price” — a price at which flow demand goes to zero. As we’ll see next, this price helps tie down the price path.
So what determines the price of gold at any given point in time? Hotelling models say that people are willing to hold onto an exhaustible resources because they are rewarded with a rising price. Abstracting from storage costs, this says that the real price must rise at a rate equal to the real rate of interest, so you get a price path that looks like this:

Obviously there are many such paths. Which one is correct? Given rational expectations (I know, I know) the answer is, the path under which cumulative flow demand on that path, up to the point at which you hit the choke price, is just equal to the initial stock of gold.
Now ask the question, what has changed recently that should affect this equilibrium path? And the answer is obvious: there has been a dramatic plunge in real interest rates, as investors have come to perceive that the Lesser Depression will depress returns on investment for a long time to come:

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.
The logic, if you think about it, is pretty intuitive: with lower interest rates, it makes more sense to hoard gold now and push its actual use further into the future, which means higher prices in the short run and the near future.
 

Larry Summers has a similar theory.  Karl Smith agrees and adds that:

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.
Why?
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).

Housing prices also go up when the nominal interest rate declines for much the same reason.  In this case you can think of it as being that the cost of borrowing money declines which allows people to borrow more money for a home and spend more.  The main expense for homebuyers is not the house, but the interest and when the interest goes down, the ability to pay goes up which is the same thing as an increase in demand which raises prices.  This is a nominal interest story, and real interest rates should also have an effect on house prices, but I would wager that the nominal interest rate is almost always more important for driving house price changes.