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Introduction to the Money Supply Process z Fundamental Property -- Money supply expands when banks make loans (or more generally, expand loans or buy bonds) Deposit Expansion: The Individual Bank Consider the following example. (rD = 0.10, rT = 0.05) Chase R $20000 D $70000 L $90000 T $80000 Bonds $50000 E $10000 Computing Required and Excess Reserves Chase rD = 0.10 R $20000 D $70000 rT = 0.05 L $90000 T $80000 Bonds $50000 E $10000 RR = rDD + rTT = (0.10)($70000) + (0.05)($80000) = $11000 ER = R - RR = $20000 - $11000 = $9000 Loan of $9000 Step #1 -- Loan is Approved Chase R $20000 D $79000 L $99000 T $80000 Bonds $50000 E $10000 Borrower signs loan contract, receives check from bank. Step #2 -- Loan is Spent Chase R $11000 D $70000 L $99000 T $80000 Bonds $50000 E $10000 Seller deposits check in her bank. HSBC DR + $9000 DD + $9000 Bank Loaning and Money Supply Expansion Consider: M2 = C + D + T + MMMF Þ DM2 = DC + DD + DT + DMMMF Our example: DM2 = $0 + $9000 + $0 + $0 = $9000 (Chase’s loan leads to new deposits for HSBC.) Key Concepts: Money Supply Expansion z Key is step #1, Chase expands its deposit commitments without changing its reserves. z Note -- Process is symmetric. Repayment or liquidation of loan leads to decrease in M2 (by the amount of the loan). Deposit Expansion: The Banking System z Multiple Expansion -- An initial change in bank reserves prompted by the Federal Reserve leads to an eventual increase in the money supply which is a multiple of that initial change. Developing a Formula for Multiple Expansion z Define -- The Monetary Base, or High Powered Money (H) H=C+R Key Properties: The Monetary Base z The monetary base (H) is unaffected by changes in public asset holdings. z The monetary base (H) is also unaffected by bank loaning. z Important factors that change H: Open Market Operations and Discount Loans (DL). Discount Loans and the Monetary Base z Example 1 -- Chase borrows $100 from the Federal Reserve. Chase DR + $100 DDL + $100 DH = DC + DR = $0 + $100 = $100 Open Market Operations and the Monetary Base z Example 2 -- The Federal Reserve buys a $100 bond from Chase. Chase DBonds - $100 DR + $100 DH = DC + DR = $0 + $100 = $100 The Nonborrowed Base z The Nonborrowed Base (HNON) HNON = H - DL z Key property -- The nonborrowed base is only affected by open market operations. A Formula for Money Supply Determination z Define the following variables. k = C/D t = T/D e = ER/D Money Supply Determination: The Formula M2 = (1 + k + t) (HNON + DL) + MMMF (k + rD + rTt + e) The money multiplier (m2) Computing the Money Multiplier: An Example Suppose that: C = 550 rD = 0.10 D = 600 rT = 0.03 T = 3000 ER = 10. Compute the money multiplier (m2). Computing the Ratios k = C/D = 550/600 = 0.917 t = T/D = 3000/600 = 5.000 e = ER/D = 10/600 = 0.0167 Plugging Into The Multiplier Formula m2 = 1+k+t k + rD + rT t + e m2 = 1 + 0.917 + 5.0 0.917 + 0.10 + (0.03)(5.0) + 0.0167 m2 = 5.84 Effects of HNON and DL on M2 Determination z Since M2 = (m2)(HNON + DL), DM2 = (m2)(D HNON), DM2 = (m2)(DDL). z In other words, HNONÞ M2 DL Þ M2 z Changes in HNON or DL give banks reserves, greater ability to loan. Effects of Reserve Ratios on M2 Determination z Increases in reserve ratios hinder bank loaning, thereby decreasing the multiplier and M2. m2 = 1+k+t k + r D + r Tt + e rD Þ m2¯ Þ M2¯ rT Þ m2¯ Þ M2¯ Effects of k (C/D) and t (T/D) on M2 Determination z Changes in k and t (public’s desire to reallocate assets) have different effects on bank loaning, the multiplier, and M2. m2 = 1+k+t k + r D + r Tt + e k Þ m2¯ Þ M2¯ t Þ m2 Þ M2 Effects of e (ER/D) on M2 z Changes in e (banks desire to hold more excess reserves) affect the multiplier, which affects M2. m2 = 1+k+t k + r D + r Tt + e e Þ m2¯ Þ M2¯ M2 Determination: Summary First, the formula again. M2 = (1 + k + t) (HNON + DL) + MMMF (k + rD + rTt + e) A Summary Table HNON Þ M2 DL Þ M2 r D Þ M2¯ r T Þ M2¯ k Þ M2¯ t Þ M2 e Þ M2¯ The Multiplier -- Trying to Control the Money Supply M2 = (1 + k + t) (HNON + DL) + MMMF (k + rD + rTt + e) z Federal Reserve controls HNON, rD, and rT and uses them as policy tools. z But M2 is also determined by public asset holding (k, t, MMMF) and bank behavior (e, DL). Can the Federal Reserve Control the Money Supply? z Practical Solution -- The Federal Reserve tries to control money supply growth within a given target range. If actual M2 growth falls within the range, M2 is considered controlled. The Multiplier Effect and Controlling M2 z Consider formula for M2 determination (apart from MMMF), written as follows (recall that H = HNON + DL). M2 = (m2)(H) M2 Determination in Growth Rates z Since the levels are multiplicative, the growth rates are additive z Growth in M2 @ (Growth in m2) + (Growth in H) Implications for M2 Control z Growth in M2 @ (Growth in m2) + (Growth in H) z If the multiplier is roughly constant over time (growth in m2 » 0), then the growth rate of M2 will approximate closely the growth rate of the monetary base. Difficulties in M2 Control z Growth in M2 @ (Growth in m2) + (Growth in H) z But if the multiplier changes over time (growth rate either positive or negative), then the growth rate of M2 will deviate from the growth rate of the monetary base. Non-Federal Reserve Changes in M2 z Best solution: constant multiplier, zero DL. Unfortunately, not true. z Second best solution: predictable multiplier and DL. z How to predict non-Fed controlled changes in M2? What determines movements in the components (k, t, e, DL, MMMF)?
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