1

Money DemandMoney Demand(Handa, Chapter 2)(Handa, Chapter 2)

Monetary Theory and PolicyMonetary Theory and Policy

Graduate Seminar ECON 6411Graduate Seminar ECON 6411

Fall 2008Fall 2008

2

First LessonsFirst Lessons

Hicks (1967), Critical Essays in Monetary Theory, Oxford University Press.    Uses the model of a medieval market fair    Claims to have constructed a system with money

as a medium of exchange, but not as a store of value. Problem: Money is a store of value for the market

period.

3

First and Second PrinciplesFirst and Second Principles

A First Principle of Monetary Theory is: Money is a store of value. There are things that act as stores of value that are not money, but there are no forms of money that are not stores of value.  

A Second Principle of Monetary Theory is:A crucial difference between barter and monetary exchanges is that in a monetary economy exchanges are nonsynchronized—the buying and the selling may occur at different times and in different places.

4

UncertaintyUncertainty

• If the value of money varies over time If the value of money varies over time (inflation), then this nonsynchronization of (inflation), then this nonsynchronization of exchanges amounts to exchanges amounts to riskrisk..

• The need for money occurs because of time The need for money occurs because of time and nonsychronization. Add uncertainty, and nonsychronization. Add uncertainty, and you have potentially costly risk.and you have potentially costly risk.

5

Equations of ExchangeEquations of ExchangeI. Fisher Equation

M=money, T=real number of transactions,=circular velocity of transactions

 

II. Income-type Model/Commodities ApproachM=money, y=real income,

=circular velocity of income 

III. Cambridge Cash-Balances Equationk = cash balances “constant”

TPMV TMT TV

yPMV yMy YV

ykPM y

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Equations of Exchange (2)Equations of Exchange (2)IV. Disaggregation among components

D=demand deposits, Vdy=velocity of demand deposits C=currency in hands of public, Vcy=velocity of currency

=average price of output 

V. Cambridge Cash-Balances EquationB = Monetary Base

k = cash balances “constant”

yPCVDV yCyDy yP

yPBV yBy

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More on Quantity TheoryMore on Quantity Theory

This really results from the system: 

Exogeneity of Money Equilibrium Condition (ex post) Money Demand Relation

 Therefore, the crude quantity theory is a theory of equilibrium absolute price levels. 

Note: Not all quantity theorists assume exogeneity.

0MM s ds MM

kPYM d

8

Neoclassical ModelNeoclassical Modeland the Quantity Theoryand the Quantity Theory

We begin with the “crude”, “old”, or “basic” quantity theory:An exogenous change in the stock of money

eventually results in a proportionate change in the absolute pricelevel.

 

The Quantity Theory operates best in a Marshallian-type neoclassical model.

Marshallian ModelMarshallian Model

w/P

N

Y

P

S

I

r

r*

S*,I*

Ns

LRAS

Y=F(N,K)Nd

S,I

Y*

AD1

AD2

P1

P2

w1

w2

nominalwages

10

)(

Pwdd NN

*)(*,)()( Pw

Pwd

Pws NNN

)(

rII

)(

rSS

**,*,)()( rSIrSrI

**)*,( YKNFY **)(** CrCCSYC

**0 PkY

MP

Marshallian Model in EquationsMarshallian Model in Equations)(

Pwss NN

***)( wPPw

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

11

Fisher (1911)Fisher (1911)

• Fisher used the disaggregated model.Fisher used the disaggregated model.• Argued that the velocities are the “average rate of Argued that the velocities are the “average rate of

turnover” and depends upon:turnover” and depends upon:– Individual agent habitsIndividual agent habits– Population density (demographics)Population density (demographics)– Commercial customsCommercial customs– Rapidity of transportRapidity of transport– Other technical conditionsOther technical conditions– But NOT on the quantity of money or the price level. That But NOT on the quantity of money or the price level. That

is, velocity is EXOGENOUS.is, velocity is EXOGENOUS.

• Fisher does not assume velocity is constant.Fisher does not assume velocity is constant.

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Fisher (1911) -- IIFisher (1911) -- II

• Fisher also argues that the real volume of trade or Fisher also argues that the real volume of trade or transactions is independent of the quantity of money, transactions is independent of the quantity of money, except except during transition periodsduring transition periods..– This has been challenged by Keynesians. This is less likely to be true This has been challenged by Keynesians. This is less likely to be true

if the economy is not continuously at equilibrium.if the economy is not continuously at equilibrium.

• Production is the result of capital, physical capabilities and Production is the result of capital, physical capabilities and technique—none of which depend on the quantity of money.technique—none of which depend on the quantity of money.– This assumes that the labor market always clears and full This assumes that the labor market always clears and full

employment always ensues. It relies on the notion that full employment always ensues. It relies on the notion that full employment is independent of money and prices.employment is independent of money and prices.

• Therefore, if the quantity of money is expanded, prices will Therefore, if the quantity of money is expanded, prices will rise. That is, prices will vary directly as rise. That is, prices will vary directly as MM varies. varies.

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AssumptionsAssumptions

(1)     Money supply is exogenous. (2)     k and Y do not change substantially from one period to the

next. (Are they constant? Stable? Is the velocity function stable?)      Some argue that y is constant, based on the idea that the economy is

always at full employment.      Some argue that y is constant because this is a long run theory and

Say’s Law does not allow for long-run deviations from full employment.

      Some argue that k is relative constant because it is related to the slowly evolving payments system.

      Some argue that k is simply exogenous—it is not related to any of the other variables.

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Fisher’s Direct Transmission Fisher’s Direct Transmission MechanismMechanism

• Fisher assumes that the individual’s money holdings are Fisher assumes that the individual’s money holdings are doubled.doubled.

• ““Prices being unchanged, he now has double the amount of Prices being unchanged, he now has double the amount of money and deposits which his convenience has now taught money and deposits which his convenience has now taught him to keep on hand. He will then try to get rid of the him to keep on hand. He will then try to get rid of the surplus money and deposits by buying goods. But, as surplus money and deposits by buying goods. But, as somebody else must be found to take the money off his somebody else must be found to take the money off his hands, its mere transfer will not diminish the amount in the hands, its mere transfer will not diminish the amount in the community. It will simply increase somebody else’s community. It will simply increase somebody else’s surplus. Everybody will want to exchange this relatively surplus. Everybody will want to exchange this relatively useless extra money for goods, and the desire to do so useless extra money for goods, and the desire to do so must surely drive up the price of goods.” must surely drive up the price of goods.”

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Indirect Transmission MechanismIndirect Transmission Mechanism

• Presented here only for contrast! This is NOT Presented here only for contrast! This is NOT Fisher’s view!Fisher’s view!

• According to the indirect mechanism, money According to the indirect mechanism, money supply increases affect interest rates which then supply increases affect interest rates which then induce changes in investment, which is a induce changes in investment, which is a component of aggregate demand. Aggregate component of aggregate demand. Aggregate demand increases, driving the AD curve to the demand increases, driving the AD curve to the right along an upward-sloping AS curve. Prices right along an upward-sloping AS curve. Prices rise.rise.

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Cash Balances ApproachCash Balances Approach

• This is a theory of money demand.This is a theory of money demand.• Pigou argues that agents choose to allocate Pigou argues that agents choose to allocate

resources to a portfolio of assets, based upon resources to a portfolio of assets, based upon convenience and security.convenience and security.

• The issue is the proportion allocated to money. The issue is the proportion allocated to money. • k = k(r) – k = k(r) – where r refers to the attractiveness of where r refers to the attractiveness of

“rival” uses of resources. As “rival” uses of resources. As rr increases, increases, kk falls. falls.• There is a discussion regarding the provision of There is a discussion regarding the provision of

security against unexpected demands due to security against unexpected demands due to sudden need or rise in prices.sudden need or rise in prices.

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Knut WicksellKnut Wicksell

• Defended the quantity theory as the Defended the quantity theory as the appropriate aggregate theory for the appropriate aggregate theory for the determination of the price level.determination of the price level.– The alternative theory is called the “full cost The alternative theory is called the “full cost

pricing theory” or the “mark-up price theory”. pricing theory” or the “mark-up price theory”. Under this theory, the firms price according to Under this theory, the firms price according to the cost of production plus a normal rate of the cost of production plus a normal rate of profit. In aggregate, this forms the price level.profit. In aggregate, this forms the price level.

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Knut Wicksell (2)Knut Wicksell (2)

• Wicksell analyzed a “pure credit economy” which was short run with a Wicksell analyzed a “pure credit economy” which was short run with a fixed capital stock. fixed capital stock. – The public does not hold currencyThe public does not hold currency– All transactions are paid for by checks drawn on demand accounts in banks.All transactions are paid for by checks drawn on demand accounts in banks.– Banks hold no reserves, so lend all deposits.Banks hold no reserves, so lend all deposits.– Banks can lend without limit without risking insolvency.Banks can lend without limit without risking insolvency.– The market rate of interest is the rate charged by the banks.The market rate of interest is the rate charged by the banks.– Banks are willing to lend any amount that firms want at the market rate of Banks are willing to lend any amount that firms want at the market rate of

interest. interest. – The The normal rate of interestnormal rate of interest is the rate equates saving and investment. is the rate equates saving and investment.– The The natural rate of interestnatural rate of interest is the marginal productivity of investment in firms, is the marginal productivity of investment in firms,

the internal rate of return on firms’ investment.the internal rate of return on firms’ investment.– He presented this in the context of a model of disaggregated output (capital He presented this in the context of a model of disaggregated output (capital

goods industries vs. consumer goods industries). In many ways he was a goods industries vs. consumer goods industries). In many ways he was a precursor of Keynes’ analysis.precursor of Keynes’ analysis.

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KeynesKeynes

• Keynes identifies motives for holding Keynes identifies motives for holding money:money:– Transactions demandTransactions demand– Precautionary demandPrecautionary demand– Speculative demandSpeculative demand– Finance demandFinance demand

• We will discuss Keynesian theory more We will discuss Keynesian theory more fully later in the course.fully later in the course.

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Portfolio ApproachPortfolio Approach

Agents allocate demand wealth across assets, of which money is one: 

 This leads the money demand relations like:  ttt BMW

),...,,,( tA

tB

tM

tdt wrrrfM

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Friedman’s Restatement of Friedman’s Restatement of the Quantity Theorythe Quantity Theory

• Source: Studies in the Quantity Theory of Money, pp. 1-21.Source: Studies in the Quantity Theory of Money, pp. 1-21.

• Quantity theory is a theory of money demand.Quantity theory is a theory of money demand.

• Money is one of a variety of assets, a store of wealth or Money is one of a variety of assets, a store of wealth or value.value.– Money is a factor in the production function; it is a capital good.Money is a factor in the production function; it is a capital good.

• The demand for money, like any other asset, depends upon:The demand for money, like any other asset, depends upon:– Total wealth WTotal wealth W

– Price of and return on this and competing assetsPrice of and return on this and competing assets

– Tastes and preferencesTastes and preferences

– Intertemporal rates of substitutionIntertemporal rates of substitution

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More ElementsMore Elements

• Wealth relates to all sources of income or Wealth relates to all sources of income or consumable services:consumable services:– Y = WrY = Wr

– So thatSo that W = Y/r W = Y/r

– Where Where W W = total wealth, = total wealth, Y Y = total income, = total income, r = r = the rate of interestthe rate of interest

• Agents allocate their wealth across assets so as to Agents allocate their wealth across assets so as to maximize utility subject to costs and returns.maximize utility subject to costs and returns.

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More ElementsMore Elements

• BB = bonds = bonds

• E = E = claims to stated pro-rata shares of firmsclaims to stated pro-rata shares of firms

• G = G = physical non-human goodsphysical non-human goods

• H = H = human capitalhuman capital

• P = P = price levelprice level

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The ModelThe Model

• Assume that the bonds are perpetuities, so that the Assume that the bonds are perpetuities, so that the market price of the bond is:market price of the bond is:

if the price is constant. If capital appreciation can if the price is constant. If capital appreciation can occur, the nominal return is:occur, the nominal return is:

BB r

P1

dttdr

tr

rr

dt

trd

rr b

b

bb

bbb

)(

)(

)0()0(

)(1

)0()0( 2

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The Model (2)The Model (2)

Which is approximated at Which is approximated at t=0t=0

• Rate of return on equitiesRate of return on equities

• Rate of return on physical goodsRate of return on physical goods

dtdr

rr b

bb

1

dtdr

rdtdP

Pr e

ee

11

dtdP

P1

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The Model (3)The Model (3)• Let Let w w be the ratio of nonhuman to human be the ratio of nonhuman to human

wealth. wealth.

• uu is a portmonteau variable, which accounts is a portmonteau variable, which accounts for all the other variables that might affect for all the other variables that might affect tastes and preferences.tastes and preferences.

• Money demand is:Money demand is:

u

rY

wdtdP

Pdtdr

rdtdP

Pr

dtdr

rrPfM e

ee

b

bb ;,;

1,

11,

1,

27

Model (4)Model (4)

• Equivalently, we can write:Equivalently, we can write:

• Arbitrage will lead Arbitrage will lead RRBB= R= REE, or, or

• Assuming the rates move together, Assuming the rates move together,

( (I = r + I = r + ))

urYwRRRPfM KEB ,,,,,,

dtdr

rdtdP

Pr

dtdr

rr e

ee

b

bb

111

dtdP

Prr eb

1

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Model (5)Model (5)

• Assume Assume f(f() ) is homogeneous of degree one in is homogeneous of degree one in P P and and Y.Y.

• Let so that Let so that

);;;,,,(

);;;1

,,,(

);;;1

,,,(

uYwrrPf

uYwdtdP

PrrPf

uYwdtdP

PrrPf

eb

eb

eb

P1 ),,,,,( uY

PwrrfYM

eb

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Model (6)Model (6)

• This implies that:This implies that:

• Note that this moves away from money as a Note that this moves away from money as a transactions medium, and toward money as transactions medium, and toward money as a portfolio asset.a portfolio asset.

MuPY

wrrvY eb ),,,,,(

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ConclusionsConclusions

1.1. Money demand and velocity are highly stable. Money demand and velocity are highly stable. vv is not a constant, but rather a well-defined is not a constant, but rather a well-defined function of a few specific variables.function of a few specific variables.

2.2. Friedman regards money demand as playing the Friedman regards money demand as playing the key role in the determination of the whole key role in the determination of the whole economy.economy.

3.3. This amounts to a defense against the attacks of This amounts to a defense against the attacks of Keynes that money demand and velocity are Keynes that money demand and velocity are unstable.unstable.

4.4. Money supply and demand are independent.Money supply and demand are independent.

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Conclusions (2)Conclusions (2)

5.5. Implies there is not reason to assume that Implies there is not reason to assume that money demand is infinitely elastic at some money demand is infinitely elastic at some small, positive, interest rate, and therefore small, positive, interest rate, and therefore no support for a liquidity trap.no support for a liquidity trap.

6.6. Argues that Argues that YY, as he has defined it, is , as he has defined it, is permanent incomepermanent income, and does not vary as , and does not vary as rapidly as rapidly as measured incomemeasured income. .

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Transmission MechanismsTransmission Mechanisms

• Direct Transmission ChannelDirect Transmission Channel– Increases in the money supply causes undesired money balances Increases in the money supply causes undesired money balances

which are directly spent on commodities, increasing aggregate which are directly spent on commodities, increasing aggregate expenditure and income.expenditure and income.

• Indirect Transmission ChannelIndirect Transmission Channel (Keynes Effect) (Keynes Effect)– Increases in the money supply lowers the interest rate which Increases in the money supply lowers the interest rate which

increases aggregate expenditure (think IS-LM) by increasing increases aggregate expenditure (think IS-LM) by increasing investment and triggering the multiplier.investment and triggering the multiplier.

• The Lending ChannelThe Lending Channel– The availability of money causes banks to change their lending The availability of money causes banks to change their lending

practices, raising or lowering barriers to borrowing that may practices, raising or lowering barriers to borrowing that may involve more than interest rates.involve more than interest rates.

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Walrasian-Type ModelWalrasian-Type Model

There are n goods: In a barter economy, there are n-1 relative prices (exchange ratios) for each good:

.

 

We can consider money as , so that the money prices are:

nxxx ,...,, 21

npp

pp

pp 1

3

1

2

1 ,...,,

1nx

11

2

1

1 ,...,, n

n

nn p

p

pp

pp

34

Numeraire & Absolute Price LevelNumeraire & Absolute Price Level

We define money as the numeraire good, and set so that money prices are: 

. 

The Absolute Price Level is a weighted average of the money prices of the individual goods:

. 

We may define the relative prices as:  

which is essentially the prices in real terms.

11 np

nppp ,...,, 21

n

iii pp

1

p

p

pp

pp n,...,, 21

35

Neoclassical ModelNeoclassical Modeland the Quantity Theoryand the Quantity Theory

 

The Quantity Theory operates best in a Marshallian-type neoclassical model.

    Problem: Link between money and the goods market

    Problem: inconsistencies between the quantity theory and Walrasian General Equilibrium Theory

• Highlighted by Patinkin (1965)

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Walrasian General EquilibriumWalrasian General Equilibrium

Excess Demand

= individualxi = a good, the ith good

 If there are individuals, then in aggregate:

 

Or

is Aggregate Excess Demand.

Si

Di

XDi xxx

111

Si

Di

XDi xxx

Si

Di

XDi xxx

37

Walras’ LawWalras’ LawThe sum of the excess demand and supplies over all markets must identically equal zero. Equivalently, 

Note: If there is an excess demand across the n goods markets, then there must be an off-setting excess supply in the (n+1)th market (for example in the money market). 

.

But if is money, then .

.01

1

n

i

XDii xp

XSnn

XDnn xpxp 1111)(

1nx 11 np

38

Walras’ Law (2)Walras’ Law (2)

Derivation: 

Walras’ Law can be derived from the budget constraint. The budget constraint essentially tells us that no individual can, through market trading, obtain a greater value of goods and money (assets) than the initial endowment. Homogeneity Postulate (typical assumption): 

The demands and excess demands in the n goods markets will not change in response to a change in the absolute price level. Note: A homogeneous function x = f(y,z) is said to be homogeneous of degree with respect to y if and only if it has the property that:

).,( zyfx

39

Walras’ Law (3)Walras’ Law (3)Note that homogeneity of degree one implies: 

, 

which means that changes in y result in proportionate changes in x. Homogeneity of degree zero implies that changes in y result in no change in x.

),( zyfx

Basic Elements of a Basic Walrasian GE Model

1. Walras’ Law2. Excess demand equations

Excess demand equations are homogeneous of degree zero in money prices and the absolute price level; i.e., the excess demand equations obey the homogeneity postulate.

40

Walrasian GE Walrasian GE and the Quantity Theoryand the Quantity Theory

Relative vs. Absolute Price levels     The Quantity Theory determines the absolute price level, but not relative

prices.     The Walrasian GE Model determines relative prices but not the absolute

price level. 

QUESTION: Can we marry the two together?This amounts to integrating microeconomic price theory with

macroeconomic monetary theory. 

Can we add some form of the Equation of Exchange to the Walrasian Model?

 

Answer: No. Patinkin demonstrates that such a model produces an invalid dichotomy.

41

WGE & Quantity Theory (2)WGE & Quantity Theory (2)The model has n goods markets equilibrium equations, which we assume are homogeneous of degree zero.

  

It also has an equation to define the absolute price level:

 

Add money demand: MD = kpy

.0,,...,,...,1

1

Si

n

i

Si

inii

XDi xx

p

p

p

p

p

p

pp

fx

11

p

pin

ii

42

WGE & Quantity Theory (3)WGE & Quantity Theory (3)Subtract MS from both sides: 

(1) at equilibrium.

Link the function with the real sector via Walras’ Law: 

(2) because M is the n+1th good. 

Unfortunately, this gives two excess demand functions for money, and they are mutually inconsistent outside equilibrium: 

(1) is nonhomogeneous to any degree.(2) is homogeneous of degree one in prices.

XDM

n

i

XDii

XD xpM1

)1(

0 SXD MkpyM

43

NotesNotes

• Walras’ Law includes the money market; Say’s Law is real sector only.

• Walras’ Law: If there is a glut of goods, it is accompanied by an excess demand for money.

Say’s LawAs a whole, S=D. Or equivalently,

.01

n

i

XDii xp

44

Patinkin’s SolutionPatinkin’s Solution

Patinkin decides that only reasonable approach is to abandon the homogeneity postulate (and Says’ Law).

Patinkin adds real balances throughout:

thus demands and excess demands depend upon real money balances!

nixp

Mx

p

p

p

p

p

p

pp

fx Si

n

i

SSi

inii

XDi ,...,1,,,...,,...,

1

1

45

Assume:.

Unfortunately, this makes demands and excess demands a function of the absolute price level. To maintain consistency throughout, we write the money demand and money excess demand functions so as to incorporate real balances:

Money does prove neutral in this model.

0

pM

xS

XD

SS

nXD

S

nD

Mp

MypfM

pM

ypfM

,

,

1

1