Front Page Titles (by Subject) 1.: THE NOTE–ISSUING CASE - The Rationale of Central Banking and the Free Banking Alternative
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1.: THE NOTE–ISSUING CASE - Vera C. Smith, The Rationale of Central Banking and the Free Banking Alternative 
The Rationale of Central Banking and the Free Banking Alternative, Foreword by Leland Yeager (Indianapolis: Liberty Fund, 1990).
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THE NOTE–ISSUING CASE
Assume that there are two banks (or groups of banks), A and B. Both carry on the same volume of business in the first instance. Each lends 10,000 and has 10,000 loans falling due on each settlement day.
A now increases its lending on a given day by 10,000 and all these extra loans fall due for repayment four clearing periods later, so that there are three clearings in between. Assume further (a) that if B draws gold from A, B does not immediately increase its note issue to the extent that would bring its reserve ratio back to its former level, but only to the extent necessary to replace the notes that have not come in as usual, but have stayed out in the circulation (this merely makes it possible for it to lend currently the same amount as before); (b) that A correspondingly reduces its outstanding note issue by the amount of the loss of gold, that is, by the amount of extra notes it has returned to it by B through the clearings. Then the total note issue outstanding of A and B together remains the same throughout the period under consideration.
A receives 5,000 of its own notes and 5,000 of B’s.
B receives 5,000 of its own notes and 5,000 of A’s.
Notes are therefore cleared without any transfer of gold.
A receives 5,555 of its own notes and 4,444 of B’s.
B receives 4,444 of its own notes and 5,555 of A’s.
B draws 1,111 gold from A.
A receives 5,433 of its own notes and 4,567 of B’s.
B receives 4,567 of its own notes and 5,433 of A’s.
B draws 826 gold from A.
A receives 5,341 of its own notes and 4,659 of B’s.
B receives 4,659 of its own notes and 5,341 of A’s.
B draws 682 gold from A.
A receives 10,530 of its own notes and 9,470 of B’s.
B receives 4,735 of its own notes and 5,265 of A’s.
B loses 4,205 gold to A.