According to standard economic theory, shortages only happen when pricing mechanisms fail.
If prices rise, then demand would lower and shortage will be resolved (?)..
No, not it isn't. That assertion is fundamentally wrong at many levels. It seems you're confusing the intro to economics definition of equilibrium between supply and demand with your own definition of shortage. However, in the process you're making the mistake of believing somehow that pricing out demand from the market and being unable to scale up production to meet demand does not involve any shortages of any kind.
Think about it for a second: I'd suddenly food prices skyrocketed to the point a single 1kg bag of rice sold for over €100, and most of the world was thus unable to buy food for being priced out of the market, would that represent a shortage even if some people could still afford it?
For microchips, it's likely the prices have not increased enough to kickstart this increase in supply.
And the time scale to establish new capacity from scratch is many years to a decade or more. Look at the capacity build up in China. It has taken decades, and that is with all the power of the nation, and in some cases loose on regulations regarding IP rights.
It simply isn't worth it to manufacture these chips without selling billions of units. Not to mention the development, even the small chips today are extremely advanced from a technical perspective.
Opening a lemonade stand is a far more solid business plan. Since owning know how is somehow not worth anything despite heavy handed patent laws, I think the business case is just bad. China seems to work against this with specifically funding establishment of fabs.
You gave a right example, to prove the current problem... the prices are high now... go build a nuclear energy heater to grow rice, I'll wait.
The prices for chips are high now, the process of building a production facility is very very expensive, and takes a lot of time, and the people building them (and quite a few are being built right now), are still unsure if the high prices will hold, to make it worthwhile.