used and so really the result is saying here is feel free to pick the threshold and the two prices however you want and you're never gonna do better than what what static pricing gets you yeah okay now B I should be done before that already okay so this is the limit and what it basically says is let our n star be the rate of completed rides in the n system using the optimal static price and let our n double star be the rate of completed rise in the n system using the optimal threshold pricing strategy then if the valuation distribution has a