Money, Bank Credit, and Economic Cycles - The Ludwig von Mises ...

The Credit Expansion Process 201d 1 :the money or reserves which leave the bank as a resultof loans it grants;x: the bank’s maximum possible credit expansion startingfrom d;c: the cash or reserves ratio maintained by the bank,in keeping with the banker’s experience and his carefuljudgment on how much money he needs to honorhis commitments; andk: the proportion of loans granted which, on average,remain unused by borrowers at any given time.From the above definitions it is clear that the reserveswhich leave the bank, d 1 , will be equal to the loans grantedmultiplied by the percentage of these loans which is used byborrowers; that is:[1] d 1 = (1 – k)xIn addition, if we consider that the money which leavesthe bank, d 1 , is equal to the amount originally deposited, d,minus the minimum amount kept on reserve, cd, in relation tothe money originally deposited, plus ckx, in relation to thepercentage of loans which on average remains unused, thenwe have:[2] d 1 = d – (cd + ckx)If we now replace d 1 in formula [2] with the value of d 1 in[1], we have:(1 – k)x = d – (cd + ckx)Next we work to solve the equation, factor out commonfactors and isolate x:(1 – k)x = d – cd – ckx