Recitation IX

1
Recitation IX

• Money and Prices

2
Goals

• Understand what money and prices are
• Distinguish between nominal and real concepts
• Determine how much money an average person (or
  the economy) whishes to hold and relate this
  Money Demand to
• Interest rate
• Income

3
Money

• Defined by its functions
• Unit of Account
• Store of Value
• Medium of Exchange

4
Money

• Defined by its functions
• Unit of Account
• Store of Value
• Medium of Exchange
• We expand on this by looking at what Prices are

5
Prices

• What are prices?
• Do they have to be in dollars?
• Consider the intertemporal (real) consumption
  decision
• Two periods choose consumption level in each,
  for a given real interest rate
• WITHOUT MONEY, are there something like prices
  here?
• Do we know what the relative value is of one unit
  of consumption today relative to one tomorrow?

6
Prices

• My understanding (NOT OFFICIAL DEFINITION)
• Prices are simply the value of a unit of one
  thing in terms of units of another

7
Prices

• My understanding (NOT OFFICIAL DEFINITION)
• Prices are simply the value of a unit in one
  thing in terms of units of another
• Subjective?

8
Prices

• My understanding (NOT OFFICIAL DEFINITION)
• Prices are simply the value of a unit in one
  thing in terms of units of another
• Subjective?
• The prices we are used to are denominated in
  dollars, but it is the same thing
• Cappuccino
• 2
• R12 (South African Rand)
• Value?

9
Money

• Defined by its functions
• Unit of Account
• So if we denote all prices in terms of this one
  thing, money, it serves as a unit of account
• Store of Value
• Medium of Exchange

10
Money

• Defined by its functions
• Unit of Account Prices are in money terms
• Store of Value
• Medium of Exchange

11
Assets Stores of Value

• An asset (again MY DEFINITION) is anything that
  allows us to
• Transfer wealth over time (already valuable)
• Earns a return (nominal/real?)

12
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons

13
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return

14
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return
• Invest in stocks at 100 per stock
• Yields on sale 200

15
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return
• Invest in stocks at 100 per stock
• Yields on sale 200 gt 100 Nominal return

16
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return
• Invest in stocks at 100 per stock
• Yields on sale 200 gt 100 Nominal return
• If all prices had doubled at the same time?

17
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return
• Invest in stocks at 100 per stock
• Yields on sale 200 gt 100 Nominal return
• If all prices had doubled at the same time?
• Nominal return?
• Real return?

18
Digression Nominal vs Real

• Since we measure all relative values (prices)
  in terms of this one thing, money, we can define
  all changes in terms of it too, or not
• invest in planting 100 tons of wheat
• Yields 1000 tons gt 900 Real return
• Invest in stocks at 100 per stock
• Yields on sale 200 gt 100 Nominal return
• If all prices had doubled at the same time?
• Nominal return 100
• Real return 0

19
Digression² Price indices

• In previous example, Mr Stock-investor got
  nominal return of 100
• If all prices double (increase by 100), real
  return is 0

20
Digression² Price indices

• In previous example, Mr Stock-investor got
  nominal return of 100
• If all prices double (increase by 100), real
  return is 0
• If some prices double (others stay constant), but
  Mr S-i does not buy any of those goods
• Real return?

21
Digression² Price indices

• In previous example, Mr Stock-investor got
  nominal return of 100
• If all prices double (increase by 100), real
  return is 0
• If some prices double (others stay constant), but
  Mr S-i does not buy any of those goods
• Real return 100

22
Digression² Price indices

• In previous example, Mr Stock-investor got
  nominal return of 100
• If all prices double (increase by 100), real
  return is 0
• If some prices double (others stay constant), but
  Mr S-i does not buy any of those goods
• Real return 100
• If all prices of the goods Mr S-i buys double,
  but no one else buys any of those goods?
• Real return?

23
Digression² Price indices

• In previous example, Mr Stock-investor got
  nominal return of 100
• If all prices double (increase by 100), real
  return is 0
• If some prices double (others stay constant), but
  Mr S-i does not buy any of those goods
• Real return 100
• If all prices of the goods Mr S-i buys double,
  but no one else buys any of those goods?
• Real return 0

24
Digression² Price indices

• But we dont care particularly about Mr S-i, so
  what are we to do?
• Price indices are weighted average prices of
  bundles of goods that the average household
  consumes

25
Digression² Price indices

• But we dont care particularly about Mr S-i, so
  what are we to do?
• Price indices are weighted average prices of
  bundles of goods that the average household
  consumes
• Never exactly right for anyone

26
Digression² Price indices

• But we dont care particularly about Mr S-i, so
  what are we to do?
• Price indices are weighted average prices of
  bundles of goods that the average household
  consumes
• Never exactly right for anyone
• Necessary to be able to compare countries, look
  at macro issues
• Digressions end

27
Assets Stores of Value

• An asset (again MY DEFINITION) is anything that
  allows us to
• Transfer wealth over time (already valuable)
• Earns a return (nominal/real?)
• Money as an asset?

28
Assets Stores of Value

• An asset (again MY DEFINITION) is anything that
  allows us to
• Transfer wealth over time (already valuable)
• Earns a return (nominal/real?)
• Money as an asset
• Transfer wealth over time
• Return?

29
Assets Stores of Value

• An asset (again MY DEFINITION) is anything that
  allows us to
• Transfer wealth over time (already valuable)
• Earns a return (nominal/real?)
• Money as an asset
• Transfer wealth over time
• Return?
• Depends on definition of Money
• Currency
• Checking deposits

30
Digression³ Inflation, Nominal and Real interest
rates

• What is inflation?

31
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level

32
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level

?
33
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index

34
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index
• Currency bears no interest 0 nom. ret.

35
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index
• Currency bears no interest 0 nom. ret.
• If general price level rises? Real return?

36
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index
• Currency bears no interest 0 nom. ret.
• If general price level rises Real return where
  is the inflation rate

-p
p
37
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index
• Currency bears no interest 0 nom. ret.
• If general price level rises Real return where
  is the inflation rate
• Checking deposits small nom. ret.
• Real return R - Real interest rate

-p
p
p
38
Digression³ Inflation, Nominal and Real interest
rates

• Inflation general increase in the price level
  as defined by the price index
• Currency bears no interest 0 nom. ret.
• If general price level rises Real return where
  is the inflation rate
• Checking deposits small nom. ret.
• Real return R - Real interest rate

-p
p
p
39
Digression³ Inflation, Nominal and Real interest
rates

• Let Pt be the price level in period t
• Then the inflation rate ( ) is defined as
  (Pt1 - Pt)/ Pt
• The nominal interest rate Rt
• The real interest rate rt

p
pt
40
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
41
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
1
(1R)
42
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
1
(1R)
Real (denominated in goods)
1
(1r)
43
Digression³ Relationship
Today
Next Month
Invest
Receive back
Nominal (denominated in money)
1
(1R)
Sell good
Real (denominated in goods)
1
?
44
Digression³ Relationship
Today
Next Month
Invest
Receive back
Nominal (denominated in money)
Pt
(1R)
Sell good
Real (denominated in goods)
1
?
45
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
Pt
(1R)
Sell good
Real (denominated in goods)
1
?
46
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
Pt
Pt(1R)
Sell good
Real (denominated in goods)
1
?
47
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
Pt
Pt(1R)
Sell good
Buy good
Real (denominated in goods)
1
?
48
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
Pt
Pt(1R)
Sell good
Buy good
Real (denominated in goods)
1
Pt / Pt1(1R)
49
Digression³ Relationship
Today
Next Month
Invest
(Earn Returns)
Receive back
Nominal (denominated in money)
Pt
Pt(1R)
Sell good
Buy good
By definition of r
Real (denominated in goods)
(1r)Pt / Pt1(1R)
1
50
Digression³ Relationship
51
Assets Stores of Value

• An asset (again MY DEFINITION) is anything that
  allows us to
• Transfer wealth over time (already valuable)
• Earns a return (nominal/real?)
• Money as an asset
• Transfer wealth over time
• Return?
• Depends on definition of Money
• Currency - inflation rate
• Checking deposits (usually small) R inflation
  rate

52
Money

• Defined by its functions
• Unit of Account Prices are in money terms
• Store of Value Money as an Asset
• Medium of Exchange

53
Money medium of exchange

• Since all prices are quoted in terms of this one
  thing, it is easier to exchange it than to find
  someone who has something I want while
  simultaneously wanting what I have.
• Money replaces barter
• More efficient
• True economic gain valuable

54
Money medium of exchange

• Since all prices are quoted in terms of this one
  thing, it is easier to exchange it than to find
  someone who has something I want while
  simultaneously wanting what I have.
• Money replaces barter
• More efficient
• True economic gain

55
Money

• Defined by its functions
• Unit of Account Prices are in money terms
• Store of Value Money as an Asset
• Medium of Exchange Replaces Barter

56
Money

• Defined by its functions
• Unit of Account Prices are in money terms
• Store of Value Money as an Asset
• Medium of Exchange Replaces Barter
• How do we know how much money is desired?

57
Money

• Defined by its functions
• Unit of Account Prices are in money terms
• Store of Value Money as an Asset
• Medium of Exchange Replaces Barter
• How do we know how much money is desired?
• Depends on trade-offs
• Money is valuable (ease of transaction)
• But costly (lower return than other assets)

58
Money Demand Portfolio choice

• Demand for Money the portion of wealth stored
  in Money relative to other assets
• Hard think of equity market, forex, timing,
  checking accounts, saving accounts, money market
  accounts

59
Money Demand Portfolio choice

• Demand for Money the portion of wealth stored
  in Money relative to other assets
• Simplifications
• Only one other asset
• The other asset cannot be used for transactions
• Money has zero nominal return
• Valid?

60
Money Demand Portfolio choice

• As always in economics, we consider trade-offs
• Money can be used for transactions, but
  earns no return
• Bonds earns return, but cannot be used for
  transactions

61
Money Demand Portfolio choice

• As always in economics, we consider trade-offs
• Money can be used for transactions, but
  earns no return
• Bonds earns return, but cannot be used for
  transactions
• As good economists, we know we work with
• _________ costs

62
Money Demand Portfolio choice

• As always in economics, we consider trade-offs
• Money can be used for transactions, but
  earns no return
• Bonds earns return, but cannot be used for
  transactions
• As good economists, we know we work with
• opportunity costs

63
Money Demand Portfolio choice

• Opportunity costs of holding money

64
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Rate of return to alternative assets- Rate of
  return to moneyOpportunity Cost

65
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Rate of return to alternative assets- Rate of
  return to moneyOpportunity Cost
• Nominal or Real?

66
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets - Rate of
  return to money Opportunity Cost

67
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money Opportunity Cost

68
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost

69
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost R

70
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost R
• Real
• Rate of return to alternative assets - Rate of
  return to money Opportunity Cost

71
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost R
• Real
• Rate of return to alternative assets R-p- Rate
  of return to money Opportunity Cost

72
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost R
• Real
• Rate of return to alternative assets R-p- Rate
  of return to money -pOpportunity Cost

73
Money Demand Portfolio choice

• Opportunity costs of holding money
• Forgone return
• Nominal
• Rate of return to alternative assets R- Rate
  of return to money 0Opportunity Cost R
• Real
• Rate of return to alternative assets R-p- Rate
  of return to money -pOpportunity Cost R

74
Money Demand Portfolio choice

• Opportunity costs of holding money
• R per dollar
• Total dollars held M
• Total opportunity cost RM

75
Money Demand Portfolio choice

• Opportunity costs of holding bonds
• Cannot transact
• Since transacting has value (eliminates barter),
  we attach a cost to keeping wealth in bonds
• To simplify real cost per withdrawal f
• Number of withdrawals N
• Total NOMINAL opportunity cost PNf

76
Money Demand Portfolio choice

• Opportunity costs of holding bonds
• What does N mean in macro?

77
Money Demand Portfolio choice

• Opportunity costs of holding bonds
• What does N mean in macro?
• Relate N to M and PY
• i.e. the average amount of money you carry is
  related to how many times withdrawals are made,
  which is related to how much you wish to spend
  (in dollars) in total, which is related to your
  income (in dollars)
• M(PY/2)(1/N)
• Does this make sense?

78
Money Demand Portfolio choice

• Opportunity costs of holding bonds
• M(PY/2)(1/N)
• Or N(PY/2M)
• Total cost opportunity cost of money
  opportunity cost of bonds
• TC MR PNf
• TC MR (P²Yf/2M)
• Choose optimal M gt Blackboard