The short answer is that it really depends on your eCPM and that will dictate the CPI you are able to sustain. However I should mention CPIs rise not because they just magically do, it's because there's no low cost inventory left and you have to increase your bid and hence your CPI to continue to scale.
There's a bit of preface you have to understand in order for this to make sense.
What are you really doing on Facebook?
Think about what you're really doing on Facebook. At the end of the day you're really just paying for the ad space on Facebook to show your ads. Also bear in mind that thousands of other companies are paying to get access to that ad space too. To figure out who gets shown which ads, Facebook turns it into an automated auction for that ad space.
Why your eCPM dictates your CPI
However Facebook has a problem. You might be doing a CPI campaign, but there are other consumer brands that are doing CPC and CPM campaigns. Afterall a chocolate bar brand doesn't care about CPIs. To solve this, Facebook unifies all the types of campaigns into a eCPM and uses the eCPM to auction out their ad space. Remember at the end of the day you're really just paying for ad space and ad space at its most simpliest form is sold for the impressions hence why it uses an eCPM. For a CPI campaign your eCPM is CTRxCVRxBidx1000.
Your eCPM is what you're really using to bid for ad space in Facebook (and really just about any other network). The higher your eCPM the more likely you are to win that ad spot and your ad is shown there.
So lets see how this plays out in your two scenarios:
Scenario 1: $0.50 bid with $200 daily budget to $2000 daily budget
The answer is you will maintain a $0.50 CPI as long as your eCPM stays competitive enough to keep winning the ad auction. However what's likely to happen is that the broader targeting likely means your CTR and CVR will decrease as you scale.
Meaning with CTRxCVRxBidx1000=eCPM your overall eCPM will decrease, and you'll see that your volume does not scale linearly.
If you want to hit your daily budget so that you can continue to scale your options are: increase bid, create better ads (increasing CTR) or create a better appstore page(increases CVR). Then you you'll see eCPM rise and be able to spend to your cap.
Scenario 2: $0.50 bid with $200 daily budget to $2000 daily budget. Also $0.50 bid to $0.30
Same situation as Scenario 1 except you get there faster. This is because CTRxCVRxBidx1000= eCPM with bid going down so does your eCPM. You just win less ad space because your eCPM is no longer as competitive.
So how does this play out in your two scenarios? Well for one thing your CPI's will largely be unchanged but your volume will dry out with time.