It's a tricky spot. Letting the prices rise keeps the folks who don't need one, but merely want one, from buying one, thus leaving some supply for those who actually need one.
On the other hand, prices quickly get out of control if left to their own devices. Some say that's natural, and perhaps it is, but that doesn't mean it's good all the time.
As for increasing production, this is one thing where raising prices can actually decrease the incentive to increase production. For literally the same money that I was using to create 100 units per month, I'm now getting the same profit that 10000 units per month would have given me. Why would I spend money to increase production, thus increasing supply which reduces demand, which lowers prices, which lowers profits?