The role of money

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Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague

JEM027Monetary Economics

The role of money

Tomáš Holub

Tomas.Holub@cnb.cz

October 5, 2015

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Basic question

Why does moneyexist?

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Three basic roles

Medium of account

Medium of exchange (payments)

Store of value

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Walrasian economy

▪No transaction costs, perfect information, perfect enforcement of contracts

▪Money as a unit of account (numeraire)

▪It can be any type of good

▪Not needed, just convenient

Agent 7

Agent 3

Agent 2

Agent 4

Agent ∞

Agent 6

Agent 1

Agent 5

Divineauctioneer

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▪Transactions are costly (in terms of time andresources)

▪Information asymmetries

▪Imperfect enforcement of contracts

Real world

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Classical approach

▪Why money, rather than barter?

▪Lack of double coincidence of wants (Jevons, 1875)

▪High transaction costs of multilateral barter

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Agent 1

Agent 2

Agent 1

Agent 2

Agent 3

Money helps

Agent 1

Agent 2

Agent 3

Double coincidence of wants

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Advances in transactiontechnology

▪Organized markets

▪Indirect barter

▪Commodity money

▪Fiat money

▪Inside money

▪Electronic money

▪…. (Virtual currencies?)

Resources

Time

Another illustration

Transactiontechnology

Indiference curve

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Storability

Divisibility

Easy manipulation

Acceptability (Menger, 1892)

Minimizing transaction costs

Desirable characteristics

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Divisibility?

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Easy manipulation?

Yap stone money (Micronesia)

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”

According to local legend, two or threegenerations before Furness's arrival a largestone in transit was lost at sea during a storm.The claim to this stone continued to have value,even though the stone itself wasunrecoverable.

“

Yap stone money (Micronesia)

… or acceptability?

Source: http://jpkoning.blogspot.cz/2013/01/yap-stones-and-myth-of-fiat-money.html

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▪Why money, rather than credit?

▪Asymmetric information and imperfect contracts

▪Emphasis on acceptability of money, rather than physicalproperties

Modern approach

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Money helps

Agent 1

Agent 2

Agent 3

Credit may help

Agent 1

Agent 2

Agent 3

... if someone does notrun away

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Money vs. credit

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OLG model of money (e.g. Wallace, 1980) (1/3)

▪Money as a store of value (improves consumption smoothing)

▪Money circulates, only if all future generations will accept it(multiple equilibria)

▪But: rate-of-return-dominance puzzle (money will stopcirculating if there is a store of value with – even marginally –higher return)

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OLG model of money (2/3)

▪Economy exists forever, but people live for two periods (Y,O)only

▪Single non-storable good

▪People get income y only when young, it falls down fromheaven

▪People maximize their lifetime utility ⇒ want to smoothconsumption ⇒ want to trade between young and old

▪With no store of value (money), U=u(y), no consumptionsmoothing is achieved (no double coincidence of wants)

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OLG model of money (3/3)

(Pt/Pt+1)*y

▪If generation 0 getsmoney and if all futuregenerations areexpected to accept it,it can start circulating,thus improving welfare

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▪„Acceptability, Means of Payment and Media of Exchange“

▪Simple theoretical model that determines acceptabilityof money endogenously

▪Money as a means of transactions

▪Economy - assumptions:

–large number of infinitely lived agents, meet bilaterally onceeach period and trade only if it is mutually advantageous

–large number of perfectly storable consumption goods,

–each agent consumes a fraction x of goods

–each good is consumed by a fraction x of agents.

Random matching model (e.g. Kyiotaki, Wright,1991-1992)

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Assumptions – goods and utility

▪All goods produced by an equal number of agents, but agentsdon’t produce goods that they consume themselves .

▪Goods, money - indivisible (units of size 1; no issue of pricedetermination).

▪Consumption of the good provides utility u,

▪Immediately a new good is produced → cost c (disutility)

▪Note: agents cannot produce without first consuming

▪Transaction cost ε (in terms of disutility) carried by thereceiver of the consumption good from the trade (notransaction cost for accepting money)

▪Net utility from consumption: U=u-c-ε > 0

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Assumptions – endownments

▪Initial endowment of some agents (randomly chosen) withconsumption goods and the rest with money (peoplecannot hold both money and goods at the same time).

▪M … fraction of agents endowed with money

(only 1 unit of money per agent, units indivisible)

▪1-M … fraction of agents endowed with their commodity

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Determination of Acceptability of Money (i):

▪π ... own probability of accepting money (by a representativeeconomic agent)

▪Π ... average probability of accepting money by the others

▪V(c) ... value of having a commodity at the end of each period

▪V(m) ... value of having money at the end of each period

▪β ... discount factor between periods

condition for the acceptability of money: V(m)  V(c)

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Determination of Acceptability of Money (ii):

Determination of agent’s payoff (for commodity/money)

agent with a commodity:

V(c) = {(1-M)x2U + MxV(m) + (1-Mx)V(c)}

agent with money:

V(m) = {(1-M)x(U+V(c)) + [1-(1-M)x ] V(m)}

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Determination of Acceptability of Money (iii):

From V(c) and V(m):

if  < x, then V(m) < V(c)

(i.e. when money is less acceptable than the commodity,the payoff from trading with money is less than from barter)

result:  = 0 (never trade commodity for money)

if  > x, then V(m) > V(c)

(i.e. when money is more acceptable than the commodity,the payoff from trading with money is more than from barter)

result:  = 1 (always trade commodity for money)

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Determination of Acceptability of Money (iv):

if  = x, then V(m) = V(c)

(i.e. when money is just as acceptable as the commodity,the payoffs from trading with money and from barter areequal)

result: any  between 0 and 1

 3 equilibria in the model:

 = 0, when money not acceptable

 = 1, money generally acceptable

 = x, money partially acceptable

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Graphical Illustration

▪Multiple equilibria – the system is potentially fragile.

▪Money circulates if acceptability exceeds the critical level x.

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Graphical Illustration – with opportunity cost

▪Opportunity cost ofholding money impliesthat money must be moreacceptable than goods tostart circulating.

▪But it may still circulate,i.e. there is no rate-of-return-dominance puzzle.

▪Only if the OC exceedssome critical level,monetary equilibriumbreaks down (e.g. due tohyperinflation).

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Kyiotaki, Wright: Conclusions

▪Acceptability is key for circulation of money

▪It is determined endogenously in the model

▪Money improves welfare (higher frequency of trade)

▪Money may circulate even with some opportunity costs(no rate-or-return dominance puzzle)

▪But the monetary equilibrium may collapse with too highopportunity costs (e.g. hyperinflation)

▪Multiple equilibria – the monetary system is potentially fragile,based on trust

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Random Matching Model vs. OLG

OLG

Goods

Non-storable

Storable

People

2 periods

Infinitely-lived

Function of money

Store of value

Medium of exchange

May improve welfare

Yes (consumptionsmoothing)

Yes (higher frequencyof trade)

Acceptability crucial

Yes

Endogenous acceptability

Yes

Multiple equilibria

Yes

Rate-of-return dominancepuzzle

Yes

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Money improves welfare by reducing transactioncosts and addressing information asymmetries

The system might be fragile, acceptability(credibility) is key

Policy implications: build credible monetaryinstitutions, avoid hyperinflations

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Conclusions