I would say that telling stories is an art and is already a type of social currency – people gravitate towards those who can tell a good story. Storytellers who write books, host podcasts, sell goods, and more can also make a good living.
However, for this idea, I was thinking more about daily life. What if I had to tell a story to the cashier in order to buy my groceries for the week. And if the story wasn’t “expensive” enough, I had to tell additional stories. Or what if I needed to tell a story to rent an apartment? In this world, maybe the more interesting and unique stories are worth a lot. Imagination or strong memories in addition to strong speaking abilities would be highly valued. Perhaps there would be a story trading system or perhaps people would be secretive with their ideas, similar to a great startup idea. The value of the story would depend on the person though – I might find a story about superheroes to be worth a lot, but someone else may value the same story to be worthless.
I don’t think I have enough stories to survive in this type of world, so there might need to be a fallback to the existing regions’ currency, like the US Dollar, Euro, etc.
Jeffrey's Thoughts 