Unformatted text preview: The total increase in new money (call this “ D ”) can be found by adding up all the successive changes in new money, D = ∆ M 1 + ∆ M 2 + ∆ M 3 + …. Then substituting for ∆ M i , D = E 1 x [1 + (1 – R ) + (1 – R ) 2 + (1 – R ) 3 + …]. Suppose we multiply both sides by the term (1 – R ) and subtract the resulting product from D . D – (1 – R ) x D = E 1 x [1 + (1 – R ) + (1 – R ) 2 + (1 – R ) 3 + …] – E 1 x [ (1 – R ) + (1 – R ) 2 + (1 – R ) 3 + …]. All terms on the righthand side with the exception of the initial E 1 x 1 would cancel out: D x [1 – (1 – R )] = D x R = E 1 . Finally, divide both sides by R to obtain the desired result: D = E 1 x R 1 . That is, an initial amount of excess reserves equal to E 1 creates new money equal to this amount multiplied by the inverse of the reserve requirement, or m = R 1 ....
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 Spring '10
 JONES
 Addition, Multiplication, Fractionalreserve banking, Elementary arithmetic, excess reserves

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