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Assuming ceterus paribas in each case:

(i)The bank expands its operations in the field of financial derivatives.

(ii) Increasing competition leads to a fall in the transaction costs incurred by banks in adjusting their balance sheets.

(iii) The non-bank public fears a banking crisis and a bank 'panic' occurs

I know that Money Multiplier formula is as follows: $m$ = $(1+c)$/$(r+e+c)$, so that's just a question of how each case impacts $c$ - cash - to - deposit ratio and $e$ - excess reserve ratio.

in case (iii) I believe as there is an uncertainty in the economy people will be less willing to take loans and deposit into banks, so $c$ should increase and probably $e$ should decrease.

(ii) fall in transaction costs should create more money for banks to give out as loans, so that creates more deposits and more reserves. thus $c$ will fall and $e$ will increase

Regarding (i) I have no idea how to proceed. As far as I got financial derivatives are the contracts which enable more credit in the sector and thus there is an increase in loans, deposits, and reserves but I am not sure if its right way of thinking.

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