Lecture 27: Money multiplier Mishkin Ch14 – part A page 351-359

Review A simple model of multiple deposit creation. The bank creates deposits by lending. Initial $100 increase in reserves will result in $1000 in deposit. The increase is tenfold, the reciprocal of reserve ratio 10%.

Introduction Fed’s control over checkable deposits is affected by two factors: holdings of currency; holdings of excess reserves. a more advanced model: the money supply model monetary base  money multiplier  money supply

The money supply model Define money as currency plus checkable deposits: M = C + D M1 definition of money The Fed can control the monetary base better than it can control reserves Link the money supply (M) to the monetary base (MB) and let m be the money multiplier

Deriving the money multiplier

Deriving the money multiplier II

Deriving the money multiplier III An increase in the monetary base that goes into currency is NOT multiplied, whereas an increase that goes into supporting deposits is multiplied. Also, an additional dollar of monetary base that goes into excess reserve does not support any additional deposits or currency.

Deriving the money multiplier IV

Example If the required reserve ratio is 10 percent, currency in circulation is $400 billion, checkable deposits are $800 billion, and excess reserves total $0.8 billion, What’s the money supply, monetary base and money multiplier? c = C/D = 400/800 = 0.5; e = E/D = 0.8/800 = 0.001; r = 0.1; m =(1+c)/(r+e+c) = 1.5/0.601 = 2.49584 M = C + D = 400+800 = $1200 billion Can check: M = m * MB = m * (C+R) = 2.49584*(400+0.8+0.1*800) = $1200 billion

Intuition

Factors that determine the money multiplier Required reserve ratio r: the money multiplier and the money supply are negatively related to r Currency ratio c: the money multiplier and the money supply are negatively related to c. Excess reserves ratio e: the money multiplier and the money supply are negatively related to the excess reserves ratio e.

Factors that determine the money multiplier – cont’d The excess reserves ratio e is negatively related to the market interest rate Opportunity cost of holding excess reserves Relative expected return on excess reserves relative to loans and securities The excess reserves ratio e is positively related to expected deposit outflows Excess reserves provide insurance against losses due to deposit outflows.

Recap Money multiplier Currency and excessive reserves are NOT multiplied. changes in c, e, r are negatively related to changes in m. e is negatively related to market interest rate but positively related to expected deposit outflow.