shape thing is what the overall throughput is as you vary the multiplier and you can see that if your only choice was what multiplier to pick and you didn't have any dynamic pricing available the multiplier you would pick is the one where they intersect right that's the peak and so that's that's what we're gonna call that the balance price for the rest of the talk the red curves are just depicting what happens as n increases all right so these are simulations for finite n and the green is the theory in the in the limiting