Variation in the monetary basis ΔM ΔM = ΔD + ΔFc Fc/D = ΔFc/ΔD ΔFc = (Fc/D) × ΔD ΔM = ΔD + ΔD × (Fc/D) if I divide ΔD ΔM/ΔD = Fc/D + 1 ΔM = ΔD × (Fc/D + 1) ΔD = ΔM/(1 + (Fc/D))
ΔD = ΔRn + ΔP ΔRn = ΔD × Rn / D ΔD = ΔD × Rn/D + ΔP /ΔD ΔM = ΔRn + ΔFc ΔD = ΔRn + ΔP ΔRn = ΔD × Rn / D ΔD = ΔD × Rn/D + ΔP /ΔD 1 = Rn/D + ΔP/ΔD’ ΔP = ΔD × (1 – Rn/D)
FINAL QUANTITIES RESULTING Δ D = ΔM / (1 + Fc/D) Δ P = ΔM / (1 + Fc/D) × (1 – Rn/D). Δ D' = ΔM / (1 + Fc/D)2 × (1 – Rn/D) Δ P' = ΔM / (1 + Fc/D)2 × (1 – Rn/D) 2 ΣD = Σ n = 1 ΔM/(Fc/D + 1)n × (1 – Rn/D) (n – 1) ΣP = Σ n = 1 ΔM/(Fc/D + 1)n × (1 – Rn/D) n ΣFc = Σ n = 1 ΔM/(Fc/D + 1)n × (1 – Rn/D) (n – 1) × Fc/D ΣRn = Σ n = 1 ΔM/(Fc/D + 1)n × (1 – Rn/D) (n – 1) × Rn/D