lOMoAR cPSD| 45211451
CHAP 2 Modeling Monetary Economies
4th Edition
MONEY AND BANKING
, lOMoAR cPSD| 45211451
Chapter 2
A Simple Model of Money
1 Roadmap
Now that we know how people execute trades in a pair
of one-time meetings without money, we add a friction into
the model that can account for valued fiat money. The
key friction is that record keeping is costly. Suppose, for
example, that the cost of maintaining such a record-keeping
device is prohibitively high. Now young people can fake
trading with an old person in order to get goods when they
are old. Faking means that there is no way to punish non-
participating young people. What should people do in
the economy with such a friction?
There are three goals for this chapter. First, we want to
demonstrate that the only equilibrium in the decentralized
economy results in no trade between the young and the
old. We call this non-participating equilibrium autarky. In other
words, old people want to use the credit they earned by
trading when they were young. If there is no way to verify
that an old person did indeed trade when young, such
credit arrangements will not be granted. Not surprisingly, autarky
is not the efficient equilibrium. Second, we propose valued fiat
money as a governmentpolicy that can attempt to deal with
the friction. Third, it important to show that the stationary
equilibrium is efficient in an economywith a constant money
stock over time.
Thus, the chief purpose of this chapter is to create
a friction and incorporate that into the overlapping generations
economy. As we did in the previous chapter, we compare
the equilibrium quantities with what a planner would choose
for the current and future generations. Even with perfect
social memory absent, and the externality associated with this
, lOMoAR cPSD| 45211451
friction, the equilibrium quantities are efficient in an economy
with valued fiat money. Because the equilibrium in the monetary
eco- nomy and in the perfect recordkeeping economy is
identical, we use this equivalence to say that money is
memory.1
2 The Environment
To arrive at the simplest possible model of money, we
must ask ourselves which features are essential to monetary
economies. The demand for money is distinct from the
demand for the goods studied elsewhere in economics. People
want goods for the utility received from their consumption. In
contrast, people do not want money in order to consume
it; they want money because money helps them get the
thingsthey want to consume. In this way, money is a
medium of exchange – something acquired to make it easier
to trade for the goods whose consumption is desired.
A model of this distinction in the demand for money
therefore requires two special features. First, there must be some
“friction” to trade that inhibits people from directly acquiring the
goods they desirein the absence of money. One of the main
messages from Chapter 1 is that people want to smooth
their consumption over lifetime. If there are no frictions, they can
accomplish this feat through the discipline imposed by social
memory; that is, if, when young, Andy participates by giving
goods to an old person, then next period, a young
person will redeem that memory by giving goods to Andy.
Moreover, the level of giving is part of that memory and
determines how much is given when young and received when old.
Social memory is necessary because trading partners only meet once
2
in their lifetime. So what happens if there is no social
memory. To make this point more concrete, let represent the
cost of keeping societal records at any date . We assume
that so that keeping perfect memory is not feasible in
this economy. With the desireto trade, but without memory, the
, lOMoAR cPSD| 45211451
question is whether some other means can be developed that
can support trade.
Second, we propose a model in which fiat money is
used to deal with social amnesia. Someone must be willing to
hold money from one period to the next for this to be even
possible. This is necessary because money is an asset held
over some period of time, however short, before it is spent.
The overlapping generations model makes it possible for people
to acquire money when young and use when they are old.
Themodel economy has the same physical environment as
the model we studied in Chapter 1 with the addition of
no record keeping. Each period there are young people
born. Each person lives for two periods, except for a
group that is alive in the first period of the economy, whom
we refer to as the initial old. There is a single, perishable
consumption good. And each young person receives an
amount of that good. Each young person wants to consume
when young and when old.
3 The Economic Problem
The problem facing future generations of this economy is very
simple. They want to acquire goods they do not have. Each has
access to the nonstorable consumption good only when young
but wants to consume in both periods of life. They must
therefore find a way to acquire consumption in the second
period of life and then decide how much they will consume
in each period of life.
We examine, in turn, two solutions to this economic problem.
The first, a centralized solution, proposes that an all-knowing,
benevolent planner will allocate the economy’s resources between
consumption by the young and by the old. In the
second, decentralized solution, we allow people to use money
to trade for what they want. We then compare the two solutions
CHAP 2 Modeling Monetary Economies
4th Edition
MONEY AND BANKING
, lOMoAR cPSD| 45211451
Chapter 2
A Simple Model of Money
1 Roadmap
Now that we know how people execute trades in a pair
of one-time meetings without money, we add a friction into
the model that can account for valued fiat money. The
key friction is that record keeping is costly. Suppose, for
example, that the cost of maintaining such a record-keeping
device is prohibitively high. Now young people can fake
trading with an old person in order to get goods when they
are old. Faking means that there is no way to punish non-
participating young people. What should people do in
the economy with such a friction?
There are three goals for this chapter. First, we want to
demonstrate that the only equilibrium in the decentralized
economy results in no trade between the young and the
old. We call this non-participating equilibrium autarky. In other
words, old people want to use the credit they earned by
trading when they were young. If there is no way to verify
that an old person did indeed trade when young, such
credit arrangements will not be granted. Not surprisingly, autarky
is not the efficient equilibrium. Second, we propose valued fiat
money as a governmentpolicy that can attempt to deal with
the friction. Third, it important to show that the stationary
equilibrium is efficient in an economywith a constant money
stock over time.
Thus, the chief purpose of this chapter is to create
a friction and incorporate that into the overlapping generations
economy. As we did in the previous chapter, we compare
the equilibrium quantities with what a planner would choose
for the current and future generations. Even with perfect
social memory absent, and the externality associated with this
, lOMoAR cPSD| 45211451
friction, the equilibrium quantities are efficient in an economy
with valued fiat money. Because the equilibrium in the monetary
eco- nomy and in the perfect recordkeeping economy is
identical, we use this equivalence to say that money is
memory.1
2 The Environment
To arrive at the simplest possible model of money, we
must ask ourselves which features are essential to monetary
economies. The demand for money is distinct from the
demand for the goods studied elsewhere in economics. People
want goods for the utility received from their consumption. In
contrast, people do not want money in order to consume
it; they want money because money helps them get the
thingsthey want to consume. In this way, money is a
medium of exchange – something acquired to make it easier
to trade for the goods whose consumption is desired.
A model of this distinction in the demand for money
therefore requires two special features. First, there must be some
“friction” to trade that inhibits people from directly acquiring the
goods they desirein the absence of money. One of the main
messages from Chapter 1 is that people want to smooth
their consumption over lifetime. If there are no frictions, they can
accomplish this feat through the discipline imposed by social
memory; that is, if, when young, Andy participates by giving
goods to an old person, then next period, a young
person will redeem that memory by giving goods to Andy.
Moreover, the level of giving is part of that memory and
determines how much is given when young and received when old.
Social memory is necessary because trading partners only meet once
2
in their lifetime. So what happens if there is no social
memory. To make this point more concrete, let represent the
cost of keeping societal records at any date . We assume
that so that keeping perfect memory is not feasible in
this economy. With the desireto trade, but without memory, the
, lOMoAR cPSD| 45211451
question is whether some other means can be developed that
can support trade.
Second, we propose a model in which fiat money is
used to deal with social amnesia. Someone must be willing to
hold money from one period to the next for this to be even
possible. This is necessary because money is an asset held
over some period of time, however short, before it is spent.
The overlapping generations model makes it possible for people
to acquire money when young and use when they are old.
Themodel economy has the same physical environment as
the model we studied in Chapter 1 with the addition of
no record keeping. Each period there are young people
born. Each person lives for two periods, except for a
group that is alive in the first period of the economy, whom
we refer to as the initial old. There is a single, perishable
consumption good. And each young person receives an
amount of that good. Each young person wants to consume
when young and when old.
3 The Economic Problem
The problem facing future generations of this economy is very
simple. They want to acquire goods they do not have. Each has
access to the nonstorable consumption good only when young
but wants to consume in both periods of life. They must
therefore find a way to acquire consumption in the second
period of life and then decide how much they will consume
in each period of life.
We examine, in turn, two solutions to this economic problem.
The first, a centralized solution, proposes that an all-knowing,
benevolent planner will allocate the economy’s resources between
consumption by the young and by the old. In the
second, decentralized solution, we allow people to use money
to trade for what they want. We then compare the two solutions
