Clipboard$$s marketplace users $$book a transaction in the future,$$ as is true for other apps with which you may be familiar. So we use the analogy below to leverage that familiarity.

Pretend you$$re the pricing product manager for Lyft$$s ride$-$scheduling feature, and you$$re launching a new city like Toledo, Ohio.

The prevailing rate that people are used to paying for rides from the airport to downtown $($either direction, one way$)$ is $$25.$ The prevailing wage that drivers are used to earning for this trip is $$19.$

You launch with exactly this price: $$25$ per ride charged to the rider, $$19$ per ride paid to the driver. It turns out only $60$ or so of every $100$ rides requested are finding a driver at this price.

$($While there is more than one route to think about in Toledo, for the sake of this exercise you can focus on this one route.$)$

Here$$s your current unit economics for each side:

Drivers:

Customer acquisition cost $($CAC$)$ of a new driver is between $$400-$ $$600.$ CAC is sensitive to the rate of acquisition since channels are only so deep.

At the prevailing wage, drivers have a $5\%$ monthly churn rate and complete $100$ rides $/$ month

Riders:

CAC of a new rider is $$10$ to $$20($similar to driver CAC it$$s sensitive to the rate of acquisition, since existing marketing channels are only so deep$)$

Each rider requests $1$ ride $/$ month on average

Churn is interesting: riders who don$$t experience a $$failed to find driver$$ event churn at $10\%$ monthly, but riders who experience one or more $$failed to find driver$$ events churn at $33\%$ monthly

You$$ve run one pricing experiment so far: when you reduced Lyft$$s take from $$6/$ride to $$3/$ride across the board for a few weeks, match rates rose nearly instantly from $60\%$ to roughly $93\%.$

Your task is to maximize the company$$s net revenue $($the difference between the amount riders pay and the amount Lyft pays out to drivers$)$ for this route in Toledo for the next $12$ months. Let$$s assume that you cannot charge riders more than the prevailing rate.

The core question is: how much more or less do you pay drivers per trip $($by changing Lyft$$s take$)?$ Your goal is to maximize net revenue for the next $12$ months on this route. Include the rider and driver churn rate for this calculation