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Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher
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Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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Page 1: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Lecture 1

Chulalongkorn University, EBA Program

Monetary Theory and Policy

Professor Eric Fisher

Page 2: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 2Chula, Monetary Theory and Policy

Page 3: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 3Chula, Monetary Theory and Policy

Page 4: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Definition of an Economy

• Demand side

– Agents

– Endowments

– Preferences– Preferences

• Supply side

– Firms

– Production sets

– Pattern of ownership

8/10/2010 Chula, Monetary Theory and Policy 4

Page 5: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 5

Page 6: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Economic environment

Period

Generation 1 2 3 4 5 6 7

0 0

1 y 0

2 y 0

8/10/2010 Chula, Monetary Theory and Policy 6

2 y 0

3 y 0

4 y 0

5 y 0

… … …

Page 7: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

Page 8: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 8

Page 9: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 9

Page 10: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 10

Page 11: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

The initial old

• Never forget generation 0

• They have simple preferences: they want to

eat as much as they can now, before they die

8/10/2010 Chula, Monetary Theory and Policy 11

Page 12: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 12

Page 13: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 13

Page 14: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Feasible allocations, 3

c2

ny

8/10/2010 Chula, Monetary Theory and Policy 14

c1y

ny

Page 15: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Golden rule allocation

c2

ny

8/10/2010 Chula, Monetary Theory and Policy 15

c1y

ny

Page 16: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 16

Page 17: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 17

Page 18: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 18

Page 19: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 19

Page 20: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 20

Page 21: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 21

Page 22: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 22

Page 23: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Budget constraint

c2,t+1

(vt+1/vt) y

8/10/2010 Chula, Monetary Theory and Policy 23

c1,ty

(vt+1/vt) y

Page 24: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

Maximal utility

c2,t+1

(vt+1/vt) y

Now MU1/MU2 = vt+1/vt

8/10/2010 Chula, Monetary Theory and Policy 24

c1,ty

(vt+1/vt) y

Page 25: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 25

Page 26: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 26

Page 27: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 27

Page 28: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 28

Page 29: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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.

8/10/2010 Chula, Monetary Theory and Policy 29

Page 30: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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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Page 31: Lecture 1 - web.calpoly.eduefisher/Lecture 1.pdf · Lecture 1 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher. Three Functions of Money •

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

8/10/2010 Chula, Monetary Theory and Policy 31