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

240 Money, Bank Credit, and Economic CyclesIf we substitute into this equation the value of D N in formula[29] and the value of F in [30], we obtain:[32] d = (D G – F) . c + fD GIf we replace F in the equation with fD G , we obtain:[33] d = (D G – fD G )c + fD GThen we factor out D G :[34] d = D G (c – cf + f)And therefore:[35] D G = dc – cf + fAs D N = D G (1-f),[36] D N = D G (1 – f) = d(1 – f) = d(1 – f)=dc – cf + f c(1 – f) + f fc+1 – fThis would be the formula for the net deposits created bythe banking system. The credit expansion brought about by abanking system out of which some money filters would beequal to:[37] x = c + D N – d = dfc+1 – f– d1 – fIf we substitute a value of zero for f in the preceding formulas,we are left with the same equations we have used until