Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher
Lecture 1
Chulalongkorn University, EBA Program
Monetary Theory and Policy
Professor Eric Fisher
Three Functions of Money
• Medium of exchange
• Unit of account
• Store of value
• We will largely focus on the third role of • We will largely focus on the third role of
money
• We will use the model of overlapping
generations extensively
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Key Elements of this Model
• In the model of overlapping generations,
there are two key aspects
– There are infinitely many agents
– There are infinitely many commodities– There are infinitely many commodities
• It is perhaps better to think of a dated
commodity as a service
• You cannot eat phad thai one week after it is
cooked. It becomes poison by then.
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Definition of an Economy
• Demand side
– Agents
– Endowments
– Preferences– Preferences
• Supply side
– Firms
– Production sets
– Pattern of ownership
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Exchange economy
• We concentrate only on the demand side, the
first three elements of the abstract definition
• The pattern of production is fixed
• Production across time necessarily involves • Production across time necessarily involves
elements of capital theory
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Economic environment
Period
Generation 1 2 3 4 5 6 7
0 0
1 y 0
2 y 0
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2 y 0
3 y 0
4 y 0
5 y 0
… … …
Notation
• Each generation born at time 1 or after will
have a consumption profile (c1,t, c2,t+1)
• You should read this as:
– Consumption when young at time t– Consumption when young at time t
– Consumption when old at time t+1
• The original old who were born at time 0 only
have (c2,1).
• You should read this as old-age consumption
at time 18/10/2010 Chula, Monetary Theory and Policy 7
Preferences
• The utility function an agent born at time 1 or
after is u(c1,t, c2,t+1)
– It is increasing in each argument
– If either argument is 0, then the agent dies– If either argument is 0, then the agent dies
– The agent enjoys diversity
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An important aside
• Do you care about consumption after you are
dead, or before you are born?
• The assumption of only one good in each
period is very stark. It means that there are period is very stark. It means that there are
no gains from trade among members of the
same generation
• The assumptions are designed to force agents
to save
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Meaning of the assumptions
• The first assumption means that no agent is
ever satisfied. He or she always wants more
• The second assumption means that a little bit
of consumption gives infinite marginal utility of consumption gives infinite marginal utility
when you are stuck at a corner, consuming
some in one period and nothing in another
period
• The third assumption means that you will
always smooth your consumption stream
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The initial old
• Never forget generation 0
• They have simple preferences: they want to
eat as much as they can now, before they die
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Feasible allocations, 1
• You are the social welfare planner. Can you
maximize the utility of all future generations
in a stationary environment?
• Stationary means that consumption of the • Stationary means that consumption of the
typical agent is not changing through time.
• There are Nt agents born at time t. Hence
aggregate supply is Nty.
• The total population is Nt-1 + Nt
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Feasible allocations, 2
• Nt-1 c2,t + Nt c1,t ≤ Nt y
• We will assume that the gross rate of
population growth is n = Nt/Nt-1
• For example, if population growth is 2% per • For example, if population growth is 2% per
generation, then n = 1.02
• (1/n)c2,t + c1,t ≤ y
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Feasible allocations, 3
c2
ny
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c1y
ny
Golden rule allocation
c2
ny
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c1y
ny
Economic interpretation
• MU1/MU2 = r, the gross real interest rate
• The golden rule sets r = n
• So if the population is growing are 2%, then n
= 1.02= 1.02
• The gross real interest rate should be 1.02,
and you would see 2% real interest rates on
net
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Decentralized solution
• Each individual takes prices as given
• Chooses consumption plans to maximize
utility
• Demand and supply for goods balance in • Demand and supply for goods balance in
every period
• The demand and supply for money balance in
every period.
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Aspects of equilibrium
• Agents must form expectations about the
future.
• If you think about it, you must understand
how people born after you will look towards how people born after you will look towards
the far future
• This is called a perfect foresight equilibrium
• It is a special case of a rational expectations
equilibrium
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Budget constraint
• Consider a generation born at time 1 or later
• c1,t + vt mt ≤ y
• vt is the price of money at time t
• m is the demand for money by the young at • mt is the demand for money by the young at
time t
• c2,t+1 ≤ vt+1 mt
• We have written these budget constraints as
though they are two separate ones.
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When will fiat money have value?
• If there are only finitely many agents, then
there will be no value for money in the final
period (in most typical cases).
• Hence money will never have value• Hence money will never have value
• Even if there are infinitely many agents, there
is always an equilibrium in which no one
believes in money
• This is an autarkic equilibrium.
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The price of money
• We have said vt is the price of money This is a
strange concept.
• What is the price of a 100 baht note? It is 4
phad thai in front of the EBA building.phad thai in front of the EBA building.
• So if the price of money increases, it becomes
easier to buy food
• The price of money is opposite of inflation
• Let pt be the price level. Then pt = 1/vt
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Lifetime budget constraint
• Consider a generation born at time 1 or later
• c1,t + (vt / vt+1) c2,t+1 ≤ y
• vt+1 / vt is a very important concept. It is the
real return from holding money. real return from holding money.
– It costs you vt to buy money when you are young
– But you can sell money for vt+1 when you are old.
• The present value of your consumption profile
is equal to your lifetime wealth.
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Budget constraint
c2,t+1
(vt+1/vt) y
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c1,ty
(vt+1/vt) y
Maximal utility
c2,t+1
(vt+1/vt) y
Now MU1/MU2 = vt+1/vt
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c1,ty
(vt+1/vt) y
Rate of return on fiat money
• The supply of money is Mt
• The demand for money is mt = Nt (y-c1,t)
• Hence vt Mt = Nt (y-c1,t), and
• v = N (y-c )/ M• vt = Nt (y-c1,t)/ Mt
• This expression says that money is valuable if:
– Many people want it
– Savings are high
– Its supply is low
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The price level
• pt = 1/vt = Mt /Nt (y-c1,t)
• This expression says that prices are high if:
– There is a big supply of money
– Few people are in the economy– Few people are in the economy
– No one is saving much
• This is the foundation of the quantity theory
of money.
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The rate of return on fiat money, 2
• vt+1 /vt = [Nt+1 (y-c1,t+1)/ Mt+1]/ [Nt (y-c1,t)/ Mt ]
• Write the gross rate of growth of the money
supply is z = Mt+1 / Mt
• Then v /v = [n/z][(y-c )/(y-c )]• Then vt+1 /vt = [n/z][(y-c1,t+1)/(y-c1,t)]
• The real interest rate will be high if:
– The population growth rate is high
– The rate of monetary expansion is low
– Future generations really want to save
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Stationary equilibria
• Assume that c1,t+1 = c1,t = c1
• Then vt+1 /vt = n/z
• The gross real interest rate is decreasing in the
rate of money growth creationrate of money growth creation
• The net real interest rate can be negative if z >
n
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Implementing the golden rule
• If z = 1, then the money supply is not growing
• Then the individual’s budget constraint has
slope n, which is the same as the feasible set
for the social welfare planner.for the social welfare planner.
• This rate of money growth will implement the
golden rule.
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Details about the gold rule
• Generation 0 gets v1m0 = v1M/N = c2
• This formula pins down the initial price level.
• The price level declines at the rate n
• Hence the rate of return on fiat money is n• Hence the rate of return on fiat money is n
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Summary
• Monetary economics is the study of the most
ubiquitous phenomenon in economic life
• We will concentrate on the model of
overlapping generationsoverlapping generations
• Monetary equilibria require us to think about
dynamic aspects of the economy
• The golden rule is implemented by a constant
money stock, with the right initial price level
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