"Do you want a pen? Yes, I want"

[snoopya1984]

Is this grammatically correct?

 

[Raymott]

Is this grammatically correct?

The topic line?
No, the second sentence, if it is a response to the first, should be something like, "Yes, I want a pen", or "Yes, I do." or "Yes."
You can't say "Yes, I want".

 

[Rover_KE]

...or 'Yes, please'.

 

[Raymott]

...or 'Yes, please'.

Of course. I'm not sure why I put "must be" there.
The number of acceptable responses could be enormous.

"Do you want a pen?"
"Do you know, now that you mention it, a pen would be much more useful than this hedgehog quill I've been struggling with!"

I will edit out "must".