MONEY (Continuedâ€¦):Three Instruments of Money Supply, Money Demand

<< MONEY:Money Supply, Fractional Reserve Banking,

Macroeconomics ECO 403

LESSON 45

MONEY (Continued...)

How does the Central Bank control the money supply?

1) Open Market Operations

2) Changing the Reserve Requirements

3) Changing Discount rate

Three Instruments of Money Supply

Open market operations are the purchase and sale of government bonds by the central

bank.

When the central bank buys bonds from public, the money it pays for the bonds

increases the monetary base and thus increase the money supply

When the central bank sells the bonds to the public, the money it receives reduces

monetary base and hence reduce money supply

Reserve requirements are central banks regulations that impose on banks a minimum

reserve-deposit ratio.

An increase in reserve requirements raises reserve deposit ratio and thus lowers the

money multiplier and the money supply

The Discount rate is the interest rates that central bank charges when it lends to the banks.

Banks borrow from central bank when they find themselves with too few reserves to meet

reserve requirements. The lower the discount rate, the cheaper are borrowed reserves and

more demands for such loans

Hence a reduction in discount rate raises the monetary base and the money supply.

Although these instrument give central bank substantial power to influence the the money

supply, yet it can't do it perfectly. Bank discretion in conditioning business can cause the

money supply to change the way central bank did not anticipate.

Excessive Reserves

No limit on the amount of bank borrowings from discount window

Money Demand

Classical Theory of Money Demand

The Quantity Theory of Money assumes that the demand for real money balances is

directly proportional to income,

(M/P) d = kY

Where k is a constant measuring how much people want to hold for every dollar of

income.

Keynesian Theory of Money Demand

It presents a more realistic money demand function where the demand for real money

balances depends on i and Y:

(M/P) d = L (i, Y)

Recall, that money serves three functions

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1. Unit of Account

2. A store of value

3. A medium of Exchange

The first function can not by itself generate any demand for money, because we can

quote prices in any currency without holding any amount of it. So we shall focus on the

rest of the two functions as we look at theories of money demand

Portfolio Theories of Money Demand

Theories of money demand that emphasize the role of money as a store of value are called

portfolio theories. According to these theories, people hold money as part of their portfolio

of assets.

The key point is that money offers a different combination of risk and return than other

assets, particularly a safe return (nominal). While other assets may fall in both real and

nominal terms.

These theories predict that demand for money should depend on the risk and return offered

by money and other assets.

Also money demand should depend on total wealth, because wealth measures the size of

portfolio to be allocated among money and other assets.

So we may write the money demand function as

(M/P) d = L (rs, rb, še, W)

Where

rs = expected real return on stock

rb = expected real return on bonds

še = expected inflation rate

W = real wealth

If rs or rb rises, money demand reduces, because other assets become more attractive

A rise in še also reduces the money demand because money becomes less attractive

An increase in W raises money demand because higher wealth means higher portfolio.

Money Demand Function L(i,Y): A useful simplification:

Uses real income Y as proxy for real wealth W

Nominal interest rate i = rb + še

Are these theories useful for studying money demand?

The answer depends on which measure of money are we using.

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Symbol

Assets included

Currency

C + demand deposits, travelers' checks, other checkable deposits

M1 + small time deposits, savings deposits, money market mutual funds, money

market deposit accounts

M2 + large time deposits, repurchase agreements, institutional money market

mutual fund balances

Economists say that M1 is a dominated asset: as a store of value, it exists alongside other

assets that are always better.

Thus it is not optimal for people to hold money as part of their portfolio and portfolio theories

cannot explain the demand for these dominated forms of money

But these theories would be more plausible if we adopt a broader measure of money like

M2.

Transactions Theories of Money Demand

Theories which emphasize the role money as a medium of exchange acknowledge that

money is a dominated assets and stress that people hold money, unlike other assets, to

make purchases.

These theories best explain why people hold narrow measure of money as opposed to

holding assets that dominate them.

These theories take many forms depending on how one models the process of obtaining

money and making transactions assuming

Money has the cost of earning a low rate of return

Money makes transactions more convenient

One prominent model to explain the money demand function is Baumol-Tobin Model

developed in 1950.

Baumol-Tobin Model of Cash Management

This model analyzes the cost and benefits of holding money.

Benefit: Convenience (much less trips to banks)

Costs: foregone interest on money had it been deposited in a savings account

Example:

A person plans to spend Y dollars over the course of an year (assuming constant price

levels and real spending). What should be the optimal size of cash balances for him?

· Possibilities

Withdraw Y dollars at the beginning of the year and gradually spend the money balance

averaging Y/2 over the year

Draw Y/2 at the beginning of year, spend it in six months then draw the rest Y/2 to be

spent in next ½ year. Average balance = Y/4

Generalizing: money holding vary between Y/N and zero, averaging Y/(2N), where N is

the number of trips to bank

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One implication of the Baumol-Tobin model is that any change in the fixed cost of going to

the bank F alters the money demand function-- that is, it changes the quantity of money

demanded for a given interest rate and income.

A Closer Look at Money Creation

Assume each bank maintains a reserve-deposit ratio (rr) of 20% and that the initial deposit is

$1000.

First bank Balance Sheet

Assets

Liabilities

Reserve $200

Deposits $1,000

Loans $800

Second bank Balance Sheet

Assets

Liabilities

Reserve $160

Deposits $800

Loans $640

Third bank Balance Sheet

Assets

Liabilities

Reserve $128

Deposits $640

Loans

$512

Mathematically, the amount of money the original $1000 deposit creates is:

Original Deposit

= $1000

= (1-rr) × $1000

First bank Lending

= (1-rr)2 × $1000

Second bank Lending

= (1-rr)3 × $1000

Third bank Lending

= (1-rr)4 × $1000

Fourth bank Lending

-----------------------------------------------------------------

= [1 + (1-rr) + (1-rr) 2+ (1-rr) 3+...] × $1000

Total Money Supply

= (1/rr) × $1000

= (1/.2) × $1000

= $5000

The banking system's ability to create money is the primary difference between banks and

other financial institutions.

Financial markets have the important function of transferring the economy's resources from

households (who wish to save some of their income for the future) to those households and

firms that wish to borrow to buy investment goods to be used in future production

The process of transferring funds from savers to borrowers is called financial

intermediation.

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A model of Money supply

· Three exogenous variables:

The monetary base B is the total number of dollars held by the public as currency

C and by the banks as reserves R.

The reserve-deposit ratio rr is the fraction of deposits D that banks hold in

reserve R.

The currency-deposit ratio cr is the amount of currency C people hold as a

fraction of their holdings of demand deposits D.

Definitions of money supply and monetary base:

M = C+D

B = C+R

Solving for M as a function of 3 exogenous variables:

M/B = C/D + 1

C/D + R/D

Making substitutions for the fractions above, we obtain:

M= cr + 1

cr + rr

Lets call this money multiplier, m

M=m×B

Because the monetary base has a multiplied effect on the money supply, the monetary base is

sometimes called high-powered money.

An Example

Suppose, monetary base B is $500 billion, the reserve deposit ratio rr is 0.1 and

currency deposit ratio cr is 0.6

The money multiplier is:

0.6 + 1 = 2.3

0.6 + 0.1

And the money supply is:

M = 2.3 x $ 500 billion = $1,150 billion

Let's go back to our three exogenous variables to see how their changes cause the money

supply to change:

1. The money supply M is proportional to the monetary base B. So, an increase in the

monetary base increases the money supply by the same percentage.

2. The lower the reserve-deposit ratio rr (R/D), the more loans banks make, and the more

money banks create from every dollar of reserves.

3. The lower the currency-deposit ratio cr (C/D) , the fewer dollars of the monetary base

the public holds as currency, the more base dollars banks hold in reserves, and the

more money banks can create. Thus a decrease in the currency-deposit ratio raises

the money multiplier and the money supply.

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