Fiat Money Economy - Banking - Lecture Slides, Slides of Banking and Finance

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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 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 preference

of

ct and c t + 1

when old.

The old has no endowment but have consumption of c t

Output is storable but depreciates at the rate δ, so γ

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 chooses,

~ c t

, c t + 1

, kt, and mt that maximises;

u u c c t t

=

(

~ , )

1

~ c k m y t t t t

• • =

c k v m

P

P

t t t t

t

t

= + +











1 1 

1

γ

Let M M t t = + − ( 1 ) 1 μ

μ ≥ − 1

The interior solution for a monetary equilibrium occurs when kt = 0

A condition of equilibrium is μ < δ which demonstrates the ‘tenuousness of

equilibrium’.

Consumption of the existing old

t

t t t P

M

C = y− −C−)+

Autarky-no trade (M=0)

C*t+

Y Ct

γY

Monetary equilibrium (M≠0)

C*t+

Y Ct

γY

• Notice that with no

inflation P t+

= P t

and Y >

γY

• If inflation increases P t+

P t

then the upper budget

line swings down.

• When P t

/P t+

= γ, the

young are indifferent

between storing their

output and receiving

money from the old.

Y(P/P t+

)

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

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 work

st = amount of labour time expended in search

say st = ϕ(mt)

ϕ‘ < 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 ϕ (^) ′′ > 0. Giving money a framework such as this

does not imply that money is ‘intrinsically useless’.

C-I-A continued

Households are assumed to maximise a discounted expected utility function;

E β

t t t

U c

−

=

∞

∑

1

1

where 0 < β < 1

subject to c

m m

P

t b^ b^ y^ r b

t t

t

• (^) t t t t t

 +^ −^ =^ +

− − −

1 1 1

where {yt}, is an endowment of income, {Pt}is the price of goods in terms of

money, {bt} is a vector of the real value of other assets, {rt}is the vector of

returns paid on the other assets, {ct} is consumption at time t.

The cash-in-advance constraint is

c

m

P

t

t

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.