I am following the textbook of Freixas and Rochet (p.249 and 253) and cannot understand where their condition for bank runs comes from:

They say that bank runs occur iff $$C_1 > \pi_1C_1 +(1-\pi_1 )L$$

The way I thought this worked was: (i) the bank saves $\pi_1C_1^*$ (mirroring the social planner optimum) such that in a no-run scenario, it has enough to fulfil the claims of the early depositors; (ii) it therefore has $1-\pi_1C_1^*$ to invest, which will return L if a bank run occurs and the bank needs to monetize its investments.

Why then does the bank-run condition have $(1-\pi_1 )L$ instead of $(1-\pi_1C_1 ^* )L$?





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