The gold mining analogy sucks because of the following dynamic:
When the market price for gold is going up, extraction of gold is more attractive and more tons gold will get extracted per day by miners. When market price for gold is going down, mining activity is going down as well, some hard-to-mine source will even be totally unprofitable to mine.
With Bitcoin, it is different. With market price, hashing power is going up and down. But it is always a fixed independent number of BTC that are being mined (right now 150 BTC per hour). The number of Bitcoins is limited, but it is independent from the market price.
the lack of that supply fedback could be engineered into bitcoin somewhat (though bitcoin cant measure price as thats external, it can measure other indicators, like rate of difficulty increase/decrease, and also more slowly and manually adapt supply to community super-majority consensus), see:
https://bitcointalk.org/index.php?topic=907157.msg9969697#msg9969697(I had been meaning to post those two topics and your comment reminded me but I started it in a separate thread).
Adam