That's simple supply and demand. When supply weakens and the demand stays they same, the price goes up. So the price ends up higher because there are less producers but the same amount of people who want to buy gold. This what you describe creates shortages and shortages produce higher prices.

There is also at least the possibility of demand weakening. Very weak gold demand would be a catastrophe for gold miners.

Very true. It's all supply & demand. That's how markets correct themselves: when the supply is vast but demand non-existent, the prices fall causing supply side (mines in our case) go bankrupt, have financial difficulties, etc. - forcing them to cut cost and improve, be more efficient. On the other hand in the meantime while the supply side isn't really there, the demand starts occurring again because the product becomes very rare. And then the rarity causes the prices to go up again. That's how it usually works not only in gold mining industry but eveywhere.

Let's say iPhone apps. Once they become so plentiful and cheap (free), supply side (developers) start doing other stuff, for example programming web sites, or desktop software. This causes rarity of new iPhone apps, so people start to be willing to pay more for an (let's say) iPhone game because there are less and less game issued every week. The prices going up makes new developers entering the scene, etc.

Another point, I'd like to make is that gold mining cost has been just $800 per ounce 2 years back. This just shows you how inflation works. Gold mining is energy intensive and labor intensive. Once labor cost and energy cost are up, gold price is up too. That's why the Government hates it so much because it just simply shows how big the real inflation is while the Government tries to tell us all we have below 1% inflation per annum.