Derivation and Solution of Karadi-Nakov (2020) value function

Hi. I’m trying to replicate the Karadi-Nakov 2020 ( for a university project. I’m stuck in the bank’s problem since I can’t quite graps how the authors have solved the Value function in the paper. For example I can’t understand the usage of two different value functions one into the other.

I know that @Max1 has tried to derive those conditions. Maybe he can provide some insights.

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Hi FerrettiC,

maybe I can help you out.
I have some old notes about the bank’s problem on my PC.

I hope these notes are helpful.
Karadi & Nakov (2021) - Banking Sector FOCs.pdf (141.8 KB)


Thank you very much for your help. I really appreciate.