THEORY OF MONEY & MONEY DEMAND

THE OUTLINE

• Meaning of Money• Functions of Money• Evolution of The Payment System• Quantity Theory of Money• Is Velocity a Constant?• Keynes’s Liquidity Preference Theory• Further Developments in the Keynesian Approach• Friedman’s Modern Quantity Theory of Money• Empirical Evidence on the Demand for Money

Meaning of Money• Money (=money supply) define as anything that is

generally accepted in payment for goods or services or in the repayment of debts.

• M1 = Currency+Travelers' checks (issued by non-bank)

+Demand Deposits+Other checkable deposits

• M2 = M1+small denomination time deposits & repurchase agreement+saving deposits & money market deposit accounts

+money market mutual fund shares (non-institutional)

• M3 = M2+ large denomination time deposits & repurchase agreement+ money market mutual fund shares (institutional)+repurchase agreements+Eurodollars

Functions of Money

• Medium of exchange: it is used to pay for goods and services (much more efficient (save the transaction cost) than barter economy (higher transaction cost because people have to satisfy a ‘double coincidence of wants’)

• Unit of account: it is used to measure value in term of money.

• Store of value: it is used to save purchasing power from the time income is received until the time it is spent (during inflation when the price level is increasing rapidly, money loses value rapidly too, people tend to hold wealth)

Evolution of The Payment System

• Commodity money• Fiat money• Checks • Electronic payment• E-money

Quantity Theory of Money

• This theory, developed by the classical economists over 100 years ago, related the amount of money in the economy to nominal income. It begins with an identity known as the equation of exchange: MV = PY Where:

• M is the quantity of money, P is the price level, • Y is aggregate output (and aggregate income). • V is velocity, which serves as the link between money and output. Velocity is

the number of times in a year that a dollar is used to purchased goods and services.

• The equation of exchange is an identity because it must be true that the quantity of money, times how many times it is used to buy goods equals the amount of goods times their price.

The Quantity Theory of Money

• How much money would you need to purchase the economy’s annual output of goods and services?– Suppose GDP (P*Y) was $14 trillion. – Would you need a money supply of $14 trillion to buy all this

output over the course of a year?– No! Each dollar is used multiple times. You would need

considerably less M than P*Y.

• Velocity is defined as the number of times a dollar bill changes hands over the course of a year in an economy.– It tells us the turnover rate for money in the economy.

• Equation of Exchange: M*V ≡ P*Y– The total money supply multiplied by the number of times this

money changes hands must be equal to nominal income (or nominal GDP)

– Total expenditure (M*V) = Total production (P*Y)– Everything produced is consumed

• When the money market is in equilibrium, Md = Ms = M.

• The quantity theory of money can be re-written as:– Md = (1/V)*PY– Md = k*PY (k = 1/V = constant if V is a constant)

• The demand for money is solely a function of nominal GDP

• Money demand is not directly affected by interest rates.

The Quantity Equation

M V P T

Consumers need money to purchase goods and services. The quantity of money is related to the number of

pounds exchanged in transactions. The link between transactions and money is expressed in the quantity equation.

Money•Velocity = Price•Transactions

On the right hand side, “T” is the total number of transactions during some period of time, “P”

is the price of a typical transaction, and “P•T” is the

number of pounds exchanged in a year.

On the left hand side, “M” is the quantity of money, “V” is the

velocity of money, and “V•M” is essentially a measure of how the

money is used to make transactions.

/V PT M

M V P Y

Rearranging the quantity equation yields velocity to be…

Economists usually use GDP “Y” as a proxy for “T” since data on the number

of transactions is difficult to obtain.

( / )dM P kY

It is often useful to express the quantity of money in terms of the quantity of good and services it can buy. This is called the real money balances “M/P”. We can use this

to construct a money demand function.

“k” is a constant that tells us how much money people want to hold for

every unit of income.

This equation states that the quantity of real money balances demanded is proportional to real

income.

Is Velocity a Constant?

Assuming Constant Velocity

( / )dM P kYThe money demand function offers another way to view the quantity

equation. If we set money supply equal to money demand we get…

( / )M P kY

(1/ )M k PYA simple rearrangement of terms changes this equation into…

Which can be written as… MV PYWhere V=1/k

This shows the link between money demand and the velocity of money.

Assuming Constant Velocity

The quantity equation is essentially a definition. If we make the assumption that the velocity of money is constant, then the quantity equation becomes a theory of the effects of money, called

the quantity theory of money.

Because velocity is fixed, a change in the quantity of money (M) must cause a

proportionate change in nominal GDP (PY). So the quantity of money

determines the money value of the economy’s output.

MV PY

Keynes’s Liquidity Preference Theory

• As seen, velocity cannot be accurately treated as a constant.– If velocity can change, then the link between prices and

money is muddled.

• J.M. Keynes postulated that individuals hold money for three reasons:– Transactions Motive You need money to buy things– Precautionary Motive You might need money on hand for

an unexpected purchase– Speculative Motive You hold your wealth as money (as

opposed to bonds) to store value

• The biggest innovation was to identify a link between money and interest rates (an inverse relationship.)

The Liquidity Preference Function

• What people really care about is the purchasing power of their money– If prices rise, then the real value of money falls. – Want to look at the demand for real money balances

• Md/P = f(i,Y)– Real money demand is a decreasing function of nominal

interest rates– Real money demand is an increasing function of real

income.

• Recall that M*V ≡ P*Y– V = P*Y/M– P/Md = 1/f(i,Y)– V = Y/f(i,Y) when the market for money is in equilibrium.

– As i↑, f(i,Y)↓, and V↑ Velocity is not constant!

The Transactions Motive for Holding Money

• Suppose you earn $3000 per month and consume $100 per day.– We’ll assume 30 day months and a constant rate of consumption over this

period.

• Case 1: You hold the entire $3000 in cash to carry out your transactions.– You have $3000 at the beginning of the month and $0 at the end.– Your average cash balance is $1500.– Your annual income (P*Y) $36,000 and your holdings of money (M) average

$1500.– V = PY/M = 36,000/1500 = 24

• Case 2: You hold $1500 in cash and buy $1500 in bonds at the beginning of each month– After 15 days, you sell your bonds and use the principal ($1500) to make

your purchases, keeping any earned interest for yourself.– Your average cash balance is now $750 (1500 at day 1, 0 at day 15, 1500 at

day 16, 0 at day 30: (1500+0+1500+0)/4 = 750.– V = PY/M = 36,000/750 = 48– If i = 1% per month, you also earned (i/2)*1500 = .005*1500 = $7.50

Two Cases

Time

Cash on Hand

Time

Cash on Hand

0 1 2

3000

1500

½

1500

750

0 ½ 1 1.5

2¼

The Transactions Motive for Holding Money

• Case 3: Now suppose you hold $500 in cash and buy $2500 in bonds. – Every 5 days (1/6th month) you run out of cash and have to sell $500 worth

of bonds to make your purchases.– Your average cash holdings over the course of the month is M = $250.– V = 36,000/250 = 144– At 1% monthly interest, you earn (1/6*1%*$2500)+(1/6*1%*$2000)+…

+(1/6*1%*500) = $12.50

• As your average cash balance shrinks, both velocity and the interest earned on bonds increases.

• So why not hold the smallest amount of cash possible?• Transactions costs of bonds!

– Brokerage fees– Time costs

• As interest rates rise, people want to hold smaller average cash balances, causing money demand to fall and velocity to rise.

• As transactions costs of bonds rise, people want to hold more money at any given point, causing money demand to rise and velocity to fall.

The Speculative Motive

• A weakness of Keynes’ original analysis of the speculative motive is that it has a knife edge solution– If the return on bonds is higher, then all speculation is in bonds. If the

return on money is higher, then all speculation is in money.– Only when the two assets have identical returns (an uncommon

occurrence) will people hold money and bonds for speculative purposes.

• James Tobin offered a refinement in 1958 by arguing that people care about both expected returns and risk.– Money has a certain nominal return: zero– Bonds have more volatile returns that may in fact be negative.– Through carrying a diversified portfolio of money and bonds, the

overall risk of the portfolio may be minimized relative to expected returns.

• However, it is not clear that money offers any greater diversification benefits than near risk-free bonds such as U.S. treasury bills.– No speculative motive for holding money?

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Friedman’s Modern Quantity Theory of Money

• Milton Friedman built upon Keynes’ idea and introduced his own model of the demand for money:

• Real money demand is a function of…– Permanent income (YP), expected average income over the

course of one’s life. (+)– The excess return on bonds over money (-)– The excess return on equities over money (-)– The rate at which money loses purchasing power. Can also

be thought of as the excess return on goods over money. (-)

Conclusions of Friedman’s Refinement

• Includes alternative assets to money

• Views money and goods as substitutes

• While the expected return on money is not a constant, the excess return on bonds (rb – rm) is assumed to be a constant.– Thus, interest rates (because they cause the returns on

all assets to rise by the same proportion) will not affect money demand.

• Therefore, the demand for money is predictable a direct function of permanent income.– Thus, Velocity is predictable and stable!– MV = PY Money is the primary determinant of

aggregate spending.

Distinguishing Between The Friedman & Keynesian Theories

Empirical Evidence on the Demand for Money

• Money and Interest Rates– Money demand does appear to be sensitive to interest rates– In the extreme case, money demand is so sensitive to

interest rates that it is a flat curve at the current rate.• Known as a liquidity trap, since monetary policy cannot affect

interest rates in this case.– Very little evidence that money demand hits a liquidity trap

at interest rates above zero.– When nominal interest rates approach zero, we can fall into

such a trap (see Japan).

• The Money Demand function is variable and unpredictable in Keynes’ model, but stable in Friedman’s model– Before 1970, Md was fairly stable.– Since 1970, Md has been much less stable due to the rapid

pace of financial innovation.– Greater instability in Md makes monetary policy harder to

control and less predictable.