I am looking at the following paper. Glenn Ellison & Sara Fisher Ellison, 2009. "Search, Obfuscation, and Price Elasticities on the Internet," Econometrica, Econometric Society, vol. 77(2), pages 427-452, 03. Link: https://www.nber.org/papers/w10570
The model did not include price but did include rank ie. the position of a product on a comparison website sorted by price. They then used the model results to calculate price elasticity.
To summarise, the way they did this was: they treat log(1 + Rank) as a continuous variable and compute estimated elasticity when all variables are at their means by setting the derivative of Rank with respect to a change in Price equal to the inverse of the average distance between the twelve lowest prices. They concluded "the low-quality 128MB PC100 demand equation corresponds to an own-price elasticity of -25.0".
I can't understand this explanation, how is this price elasticity calculated?