I am facing this situation where description of the personality of a character is quite important. Is it good to describe the personality traits or shall I let the readers deduce it based on the action. Is this description worth, compared to the amount of content it would take?
Well, if you don't have time or space in your story to show some aspect of a character's personality, why bother with it? Does it matter if your character refuses to shop at Walmart because of their abusive business practices if the story is about how he hates strawberries?
If the characteristic is that important to the story, then yes, you need to spend the time and content showing us.
The other problem is that you may run into what's called an "informed characteristic," which is when the writer tells us that the character is X (for example, brave and daring), and the other characters treat him like he's brave and daring, but we only see the character being nervous and risk-averse.
Picture a few people that you have formed opinions of.....friends, family, coworkers, celebrities, strangers. Reflect on how you formed those opinions.
Most likely they came from your own experiences interacting with and observing these people, and maybe from hearing other people characterize them. Almost certainly little to none of your opinions are based on how these people describe themselves.
Now picture how you want your reader to view your character. Act accordingly.
Use your own psychology as a sounding board for your writing.