While your points are certainly true, I'm not sure that state is characterized by shortage. Shortage occurs when price does not rise. When price does rise, demand wanes.

Hypothetically, if there was only one programmer in the world, the price would rise to the point where that programmer is no longer willing to change jobs with the offers being given. At that point, the additional demand goes away. Those businesses are no longer in the market for a programmer. It really doesn't matter if it takes time to retool, as far as shortages go, because the demand has met the supply. A shortage does not mean not being able to get what you want at a price you are willing to pay.

On the other hand, where I come from the government sets the price that doctors must charge. We really can run into the issue of doctor shortages. I can't go to my doctor and say, "I know you are completely booked and can't see me, but here is $100,000 above your regular rate to cancel those appointments and take care of me instead". The doctor is required, by law, to reject my offer.

If price was able to rise, the doctor would be able to take my offer, allowing me to get what I want as indicated by price, and those who aren't willing to pay $100K more to have the doctor look at their common cold exit the market. Equilibrium is reached. That scenario certainly comes with its own set of issues – and why our government defines the price to not allow market-based preferential treatment – the issue would not be that of a shortage.

I'm not arguing that government action can prevent prices from rising and that such activity can cause shortages. I agree with your arguments about the doctors.

What I'm arguing is that, because many goods (in particular labor) aren't fungible and liquid, that an increasing price doesn't (in the short term) solve shortages with these types of goods.