# WTP and take-rate of level in ACBC piecewise price

Dear Sawtooth Support-Team,

I'd like to conduct a project to study the WTP of vehicle features, such as sunroof, LED headlamps etc. The design is like following
- The attributes are the feature on the vehicles , with level 1 " without the  feature" level 2"with the feature".
- A large number of features(about 40) will be test by the ACBC
- Maxdiff on-the-fly importance and constructed list in ACBC are design to reduce the attributes number for each respondent.
- Each respondent may see less than 12 features in their screen.
- Summed price are applied. Each feature has a price increament and there is a basic price for the vehicle itself.

By this study, i'd like to know the WTP of each feature, as well as the "take-rate" of each feature, such as \$ 1000 may be accept by 50% of the customers and \$500 may be accept by 80% of the costomers.

And the first question is, that the piecewise price utility(hypothesis 6 cutpoint), has several different gradient, and the gradient between the 1st and 2nd cutpoint usually is positve based on experience. When I use simulator to calculate, which of the price point should I use? Is there any mathematically reasonable method to get a linear utility?

Secondly, the shown price is the total price of the vehicle, while the price sensitive is relatively low comparing with the feature's price. When I use simulator, the feature will get a low price sensitivity.
For example, I use simulator to simulator product A: without LED headlamp and product B: with LED headlamp + price X.
When X=\$1000, the share of product A and B are the same, and \$1000 will be the WTP.
But when price X raises up to \$2000, which seldomly accepted by the customers, product B also will have a share of about 40%.
So if there is any reasonable method to get the price-share curve of each level(based on level 1, without the features)