Lecture 3

The Microfoundations of Money - Part 2

• Dissatisfaction with ad hoc formulation and MIUF approach

• OLG - a theory of monetary exchange under Laissez Faire

• Critical evaluation of OLG - purely a store of value

• Intergenerational contracts

• Legal restrictions

• Another look at MIUF and CIA

Fiat money economy

• Must satisfy two conditions

• 1) Inconvertibility

• 2) Intrinsic uselessness

• According to Wallace if the 2 conditions are taken seriously, then for a monetary theory to develop there are 3 options

Fiat Money Theory

• 1. Abandon the conditions of inconvertibility and intrinsic uselessness

• 2. Impose legal restrictions to give money value

• 3. Model the notion that fiat money facilitates exchange

Overlapping Generations Model (OLG)

The Young have endowment of 1 unit of labour and consumption preferenceof ~ct and ct1

* when old.The old has no endowment but have consumption of ct

*

Output is storable but depreciates at the rate , so

1

1

Let kt = the amount of output stored in period t mt = the quantity of real money held by the young at end period t y = f(n) = f(1)

The young maximise

u ucct t (~, )*1

The old have no endowments but receive a lump sum real value moneytransfer of vt, so that output can be purchased to the amount;

vt + mt-1P

Pt

t

1

per capita consumption of the old at time t is;

ct*= kt-1 + vt + mt-1

P

Pt

t

1

The young chooses, ~ct , ct1* , kt, and mt that maximises;

u u c ct t (~ , )*1

~c k m yt t t t

c k v mP

Pt t t tt

t

1 1

1

*

Let M Mt t ( )1 11

The interior solution for a monetary equilibrium occurs when kt = 0A condition of equilibrium is < which demonstrates the ‘tenuousness ofequilibrium’.

An example

1

1

)~

(

~

),~

(

1

*1

*1

tttt

tt

t

tt

P

MCyC

yP

MC

CCUU

Consumption of the existing old

tttt P

MCyC )~

( 11*

Autarky-no trade (M=0)

C*t+1

CtY

Y

Monetary equilibrium (M0 but no saving)

ttt

ttt

ttt

tttt

t

t

ttt

tttt

t

t

ttt

t

tt

t

yCP

PyC

CyC

yCyP

P

P

PCC

CyCP

P

P

M

CyP

MC

yP

MC

0~

max

0~

max

~~

~

~

~

1

*1

*1

11*1

*1

1

1

*1

Monetary equilibrium (M0)

• Notice that with no inflation Pt+1 = Pt and Y > γY

• If inflation increases Pt+1 > Pt then the upper budget line swings down.

• When Pt/Pt+1 = γ, the young are indifferent between storing their output and receiving money from the old.

C*t+1

Ct Y

Y

Y(P/Pt+1)

Critique

• Ignores medium of exchange function

• does not explain, why store of value function is not dominated by contracts

• But Wallace says that medium of exchange occurs inter-generationally

• McCallum says that an economy with a medium of exchange is more efficient than one without

Store of Value

• Any monetary model must face the following problems

• 1. Possible dominance of money by contracts

• 2. Segniorage

• 3. Terminal value of money

Money in the Indirect Utility Function (MIIUF)

Utility function u = u(ct, lt, ct+1, lt+1)c = consumption, l = leisure

lt = 1-nt-st

nt = amount of labour time expended in workst = amount of labour time expended in search

say st = (mt)‘ < 0

this leads to the composite function u = ~u (ct, nt, mt, ct+1, nt+1,mt+1) which resembles the MIUF approach. Note that unlike the simple MIUF

approach where,

u

m as m 0

In the indirect utility approach if m = 0, this simply implies that the holding costs of money are too high. Similarly it allows satiation to be reached with finite m if 0 . Giving money a framework such as this does not imply that money is ‘intrinsically useless’.

Cash - in - Advance

• The cash in advance constraint is intended as a formal representation of the transactions demand for money. Baumol (1952) for example makes the implicit assumption that money is required for transactions and add a cost of ‘going to the bank’.

C-I-A continued

Households are assumed to maximise a discounted expected utility function;

E tt

t

U c

1

1

( )

where 0 < < 1

subject to cm m

Pb b y r bt

t t

tt t t t t

1

1 1

where {yt}, is an endowment of income, {Pt}is the price of goods in terms ofmoney, {bt} is a vector of the real value of other assets, {rt}is the vector ofreturns paid on the other assets, {ct} is consumption at time t.The cash-in-advance constraint is

cm

Ptt

t

1

C-I-A

• One of the criticisms of this model is that it implies a demand for money that is insensitive to the rate of interest and also has a unit income elasticity of demand for money.

Townsend’s Spatial Separation Model

• There are an infinity of infinitely lived agents

• In each period household ‘i’ has an endowment ‘m’ but because of spatial separation is physically able to contact only adjacent households {i-1} and {i+1}.

• Tastes of household {I} are such that it desires goods from {i} and {i+1}.

Turnpike Model

• Household {i+1} desires goods from itself {i+1} and {i+2}.

• Households cannot make bilateral IOU arrangements because there is nothing that household {i-1} can offer {i} and nothing that {i} can offer {i+1}

• So barter is impossible

Monetary existence

0 1 2M

Goods

Why is it that money and default-free interest bearing

securities co-exist• Suppose government issues risk-free small

denomination bearer bills.

• If the bills co-existed with cash, would they sell at a discount or at par?

• If sold at a discount, consider at a date close to maturity everyone would prefer bills to cash.

• By repeated argument that means no one will ever hold cash.

Co-existence

• If bills co-exist then they must always sell at par - i.e. no interest.

• But since we know that bills sell at a discount, co-existence occurs because:

• bills are non-negotiable

• large denominations

• represents a legal restriction

• The different yields on cash and bills is a LR

Legal Restrictions Theory of Money

• Prediction of legal restrictions theory:

• non-interest bearing paper currency should not co-exist with risk-free small denomination interest-bearing securities in the absence of legal restrictions.

Historical evidence

• Makinen & Woodward - JPE (1986) - provide evidence to show that small denomination French government issued bearer bonds in pre-revolution France, failed to circulate as a medium of exchange

• White JMCB (1987) - free banking period 1716-1844 (Scotland) paper money circulated with interest-bearing promissory notes, redeemable on demand.

Question?

• Economists continue to ask the question:

• A monetary economy clearly works ‘in practice’

• But does it work ‘in theory’

• The answers are not entirely satisfactory