Dr Badger thinks that K's little wooden horse is extremely valuable, and yet outside Sapper Morton's house there is an entire tree, which no one remarks on.
It's real wood, so it's rare
In the Blade Runner universe, much of the 'natural' things of the world have been diminished or destroyed, to due various unexplained reasons - including wars, floods and pollution. As such, real things in the world - unreplicated objects - are actually seen to be quite valuable, given their rarity.
We are to assume that the wood used to carve K's horse is in fact real wood. There is no indication that Sapper's tree (get it?) is real so it would become worthless. Besides, even if it was real, the only person who knows about it is Sapper himself and now K.
To add to all of that, remember when Mariette meets K in the market, and she remarks toward the picture of Sapper's tree that she's never seen one? This tells us that in truth - at least in the Megalopolis' - people may not have seen real wood.
When Dr. Badger tells K that he's willing to manufacture a living horse (Replicant version) and trade it for the piece of wood that K has, it tells us that those items are in fact rare, and therefore valuable.
Now juxtapose that with Niander Wallace's living quarters, which is decadently furnished almost entirely with wood. This shows his power and status.