16'The Central Bank and Money Supply

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16. The Central Bank and Money Supply

• The functions of money
• Key aspects of the banking system
• The money multiplier
• Equilibrium in the financial markets

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The Functions of Money

• Medium of exchange it facilitates efficient
  trading
• Unit of account
• Store of value it can be used to make purchases
  in the future

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The Banking System

• In the past, precious metals (e.g. gold or
  silver) were used as a medium of exchange
• Later on, paper currency was issued, but only
  central banks were allowed to issue paper
  currency that was convertible into gold
• Abandonment of the gold standard currencies were
  no longer convertible by law into anything
  valuable
• Today almost all currency is fiat money, which is
  widely accepted because it is declared by
  government to be legal tender

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• Central banks are the ultimate providers of
  high-powered money
• High powered money currency (bank notes and
  coins) in private circulation plus the quantity
  held by the banking system in deposits held with
  the Central Bank
• also referred to as the monetary base or M0
• High powered money is an asset to anyone in the
  private sector who holds it but is a liability of
  the Central Bank
• gtMonetary conditions in an economy can be
  influenced by altering the stock of high powered
  money

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• gtThe Central Bank can increase the amount of
  high powered money in the economy through
  open-market operations (OMO)
• This involves the purchase of securities (usually
  government bonds) undertaken with newly issued
  high-powered money
• The government guarantees to pay a fixed interest
  per year and repay the principal at some future
  date
• Government bonds considered to carry less risk
  than private sector bonds

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The Ratios Approach to the creation of deposit
money

• Two ratios are important in the determination of
  the level of deposit creation
• Commercial banks reserve ratio
• Ratio of currency to deposits held by the public
• Let R cash held in bank reserves
• C cash held by the non-bank public
• H level of high-powered money in the economy
• gt then
• (25) C R H

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• Banks desired reserve ratio (i.e. reserves as a
  proportion of deposits, D) of banks is given by r
  
• (26) R rD
• The public hold a fraction c of its bank deposits
  in cash
• (27) C cD
• Substituting into (25) cD rD H
• Solving for D yields
• (28) D H/(cr)
• if c0, and r0.1, then deposits would be 10 x
  the cash in the economy
• D H/0.1 ? D 10H
• as c ?, the value of D ? e.g suppose c0.2,
  then,
• D H/(0.10.1) ? D H/(0.2) ? D 5H

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• An expression for money supply (M) and H can be
  obtained by noting that the total supply of money
  is the sum of deposits (D) and currency (C).
  Thus
• (29) M C D
• M cD H/(cr)
• M cH/(cr)
  H/(cr)
• (30) M H (c1)/(cr)
• gt (c1)/(cr) is known as the money multiplier
• it tells us how much bigger is the money supply
  (M) with respect to the cash base of the system
  (H)
• gt Money supply money multiplier x monetary
  base
• E.g. In the UK banking system the reserve ratio
  (r) is 0.005 and the cash ratio (c) is 0.033
• gt the value of the money multiplier is just over
  27

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Narrow and Broad Money in the UK(s billion)

• Wide Monetary Base (M0) 24.4
• - Banks Cash Balance at Central Bank
  3.1
• Notes and Coins in Circulation 21.3
• Banks Retail Deposits
  228.2
• Building Societys Deposits Shares 205.0
• Wholesale Deposits
  211.6
• Money Supply (M4) 661.1

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Changing the Money Supply

• If the central bank wants to raise money supply,
  it can use the following instruments
• a) it can lower the required reserve ratio
• b) it can lower its discount rate
• a) and b) affect the money multiplier
• c) it can engage in open market operations (OMO)
• This affects the monetary base (H)

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The Demand for Money

• We assume that individuals can only hold two
  assets money (M) or bonds (B)
• Money does not pay any interest
• Bonds are interest-bearing assets
• gtThere are benefits to holding money, but there
  are also costs the interest foregone by not
  holding an interest bearing asset
• Three motives for holding money
• Transactions motive (related to income)
• Precautionary motive (related to income)
• Asset motive (depends on the risk aversion)

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Figure 16.1 Desired Money Holdings
Marginal cost, marginal benefits
MC
E
MB
L
Real money holdings
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• Is the opportunity cost of holding money the real
  or the nominal interest rate on bonds ?
• Real interest rates measure the real return on
  lending in terms of the increase in purchasing
  power over goods as a result of postponing
  spending
• If ? rate of inflation and r nominal return on
  bonds, then the real return on bonds is r - ?
• Since money is a non interest bearing asset, the
  real return on money is 0 - ?
• gtThe opportunity cost of holding money is the
  differential between the real return on bonds and
  the real return on money
• This is (r - ?) - (0- ?) r (the nominal rate
  of interest)

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• We could thus write an expression for demand for
  real money balances as follows
• (31) M/P f(Y/P, r)
• where M is nominal money demand
• P is the price level
• Y is nominal income
• r is the nominal rate of interest

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Figure 16.2 Money Market Equilibrium
Interest Rate
At r0 there is excess demand for money,
?individuals sell bonds, and the government has
to buy those bonds, thus increasing the supply of
money to restore equilibrium at r0
r
LL demand for real balances
L
Real money holdings