They all have the same basic costs for the materials. Those material costs are relatively fixed and if anything I would think these costs will increase with demand.
The actual materials costs are a small proportion of the price of LI battery cells. This is easy to look up, lots of articles on this.
As for why Tesla has cheaper cells, just look at the magnitude of the Panasonic production, which was almost 100% devoted to the hundreds of millions of laptop computers sold per year around the time of the Model S initial design in 2010. Those laptops turned into tablets and smaller form factors by 2012, and there was a huge amount of capacity of 18650 cells (that powered laptops) available for Tesla, who made a shrewd deal with Panasonic.