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

The Credit Expansion Process 215If we keep in mind that d represents the 1,000,000 m.u.originally deposited, and that r=1-c; that is, r=1-0.1=0.9, thenclearly the sum of all the bank’s deposits (original and secondary)would be:[14] d=d1 – (1 – c) cThus, the total volume of deposits in a monopolistic bank(or in a bank where all those who receive money from thebank’s borrowers also ultimately have their accounts) wouldbe equal to the value of the original deposits, d, divided by thereserve ratio, c.Formula [14] is the simplest version of the so-called bankmultiplier, and it is identical to formula [27], which yields thesame result for a banking system of multiple small banks andappears to have been worked out for the first time by AlfredMarshall in 1887. 28We could use the following formula to calculate the netcredit expansion the bank brings about ex nihilo (in other28 This is how Marshall describes the procedure which led him to thisformula:I should consider what part of its deposits a bank could lend,and then I should consider what part of its loans would beredeposited with it and with other banks and, vice versa,what part of the loans made by other banks would bereceived by it as deposits. Thus I should get a geometricalprogression; the effect being that if each bank could lend twothirdsof its deposits, the total amount of loaning power gotby the banks would amount to three times what it otherwisewould be. If it could lend four-fifths, it will then be five times;and so on. The question how large a part of its deposits abank can lend depends in a great measure on the extent onwhich the different banks directly or indirectly pool theirreserves. But this reasoning, I think, has never been workedout in public, and it is very complex. (Alfred Marshall, “Memorandaand Evidence before the Gold and Silver Commission,”December 19, 1887, in Official Papers by Alfred Marshall[London: Royal Economic Society, Macmillan, 1926], p. 37)