How do the prices of an app’s IAPs impact the CPI paid for installs of that app?

Eric is right for a CPI campaign, but for a campaign with a Value optimization (means that facebook is looking for the best ROAS and target only high-value buyers) your in-app purchases price will impact your result. 

Since you are asking facebook to separate low value and high-value customers, if you have small and high in-app purchases, (3$ VS 100$) facebook will easily target high-value buyers by taking in account users that buy the "100$" in-app purchase. 

If you have only low price in-app purchases, it will be harder for facebook to find high-value buyers. 

In conclusion, for that particular optimization, your result might be less good if you don't have high and low in-app purchases. 

You can find more details here: https://www.facebook.com/fbgaminghome/marketers/mobile-all-stars

If you're running campaigns on a CPI basis, nothing in the app -- content, IAP prices, ad placements, etc. -- will impact the CPI price you pay. Campaigns that are optimizing for installs are only impacted by 1) performance of ad creatives (CTR) and 2) performance of app store page assets (install rate).

This isn't to say that in-app IAP prices won't impact your ROAS, which they absolutely will: the price you charge for in-app items will define your overall user economics. But CPI-optimized campaigns don't use any in-app behavior to define targeting, so your IAP prices won't impact the prices you pay for installs.