To be and to have: a story about language, and art (Picasso, by Cesar Aira)

Cesar Aira, potential friend to all crossword-puzzle composers, has a fine story in the current New Yorker: Picasso. It's the only story I know that's about a verb, or maybe it's about a noun. A man visiting the Picasso Museum stops for a refreshment and is greeted by a genie who emerges from a milk bottle and offers him a choice: Would you rather have a Picasso? Or be a Picasso? That leads to speculation on the difference between "to have" and "to be" - and also on the difference between the two meanings of "a Picasso" - an artist? or a painting? The narrator ponders these differences, eventually determining that "to be a Picasso" would mean obliterating his self, in that one cannot "be" two people at teh same time, so even though, as he notes, a Picasso can create limitless Picassos, and therefore to be a Picasso would also enable him to have a Picasso, he decides that what he would like is a comfortable and pleasant life and to have a Picasso, which he could sell for millions, would enable him to do so -then, bang, right in front of him, he has a Picasso - a very beautiful, cubist 1930s painting (is it based on an actual work?) which he describes in enthralling detail, as he explains that the painting involves a queen who is lame, leading to his recollecting a pun in Spanish that may have inspired this painting. Finally, done with his reverie, he realizes the folly of his choice; as with all "genie" stories, there's always a trick. I won't spoil it - but can you figure out why he can't have his Picasso after all?