(5.3) This exercise deals with deriving the money multiplier - relating high-powered money (the monetary base)...

  

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(5.3) This exercise deals with deriving the money multiplier - relating high-powered money (the monetary base) to M1 (ignoring traveler's checks). Money demand for M1, Md, can be decomposed into the sum of demand for currency CUd cMd and demand for checkable deposits Dd = (1 - c) Md, where 0 ≤ c ≤ 1. The demand for checkable deposits generates demand for reserves by commercial banks, given by Rd = 0Dd, with 0 ≤ 0 ≤ 1. The demand for central bank money is therefore given by Hd = CUd + Rª. The equilibrium nominal interest rate equates the supply of central bank money and the demand for central bank money, i. e.: H = Hd = CU + Rd = (c +0(1-c)) Mª, where Md = PYL(i), with PY nominal income and L(.) a decreasing function in the interest rate i20, i. e., dL(i) < 0. di = Assume that 80% of money demand falls on checkable deposits and let total money demand be given by Mª - PY (0.7-3√0.5i), where nominal income equals 3,000 bil- lion euros. Moreover, assume that the supply of central bank money equals 150 billion euros and 0 = 0.01. (a) Calculate the money multiplier in this example and briefly explain its economic interpretation. (b) How does the money multiplier change in the event of a (small) change in the reserve requirement ratio or in the share c of the demand for cash in money demand? Calculate the partial derivatives of the money multiplier with respect to and c. (c) Calculate the equilibrium nominal interest rate, i. e., the nominal interest rate such that demand and supply of central bank money are equal. (d) Which effects does an increase in the supply of central bank money have on the equilibrium nominal interest rate? Explain your answer using an appropriate graph. (e) Determine the new equilibrium nominal interest rate when the supply of central bank money increases by 50 billion euros. (5.3) This exercise deals with deriving the money multiplier - relating high-powered money (the monetary base) to M1 (ignoring traveler's checks). Money demand for M1, Md, can be decomposed into the sum of demand for currency CUd cMd and demand for checkable deposits Dd = (1 - c) Md, where 0 ≤ c ≤ 1. The demand for checkable deposits generates demand for reserves by commercial banks, given by Rd = 0Dd, with 0 ≤ 0 ≤ 1. The demand for central bank money is therefore given by Hd = CUd + Rª. The equilibrium nominal interest rate equates the supply of central bank money and the demand for central bank money, i. e.: H = Hd = CU + Rd = (c +0(1-c)) Mª, where Md = PYL(i), with PY nominal income and L(.) a decreasing function in the interest rate i20, i. e., dL(i) < 0. di = Assume that 80% of money demand falls on checkable deposits and let total money demand be given by Mª - PY (0.7-3√0.5i), where nominal income equals 3,000 bil- lion euros. Moreover, assume that the supply of central bank money equals 150 billion euros and 0 = 0.01. (a) Calculate the money multiplier in this example and briefly explain its economic interpretation. (b) How does the money multiplier change in the event of a (small) change in the reserve requirement ratio or in the share c of the demand for cash in money demand? Calculate the partial derivatives of the money multiplier with respect to and c. (c) Calculate the equilibrium nominal interest rate, i. e., the nominal interest rate such that demand and supply of central bank money are equal. (d) Which effects does an increase in the supply of central bank money have on the equilibrium nominal interest rate? Explain your answer using an appropriate graph. (e) Determine the new equilibrium nominal interest rate when the supply of central bank money increases by 50 billion euros.

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a To calculate the money multiplier in this example we need to use the equation H c 1 c 1 001 M2 Given that c 08 and the supply of central bank money ... View the full answer