Money and Prices
Prof. Eric Sims
University of Notre Dame
Fall 2010
Sims (ND)
Money and Prices
Fall 2010
1 / 17
Money
Money has been conspicuous in its absence
Isn’t economics “all about money”?
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Money and Prices
Fall 2010
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Money and Frictions
Money was/is the response to a trade friction – barter and the
“double coincidence of wants”
Money makes conducting transactions easier
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Money and Prices
Fall 2010
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What is Money?
We will give money a functional definition. Money is anything which
serves the following three functions:
Medium of exchange
Store of value
Unit of account
Sims (ND)
Money and Prices
Fall 2010
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Modeling the Decision to Hold Money
Think of decision of how much money to hold as a portfolio decision
How does one want to hold one’s real wealth? In interest-bearing
bonds or non-interest paying money?
Non-interest payment makes money an unattractive thing to hold
But because money makes conducting transactions “easier”, one
might still hold it
We will accomplish this by including real money balances (nominal
money divided by prices) as a source of utility
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Money and Prices
Fall 2010
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Utility Function
You hold dollars, M, and carry them from today to tomorrow
You receive utility today from how many real dollars you hold
Let p be the nominal price of goods – how many dollars, M, it takes
to buy one unit of output. Therefore M/p is how many goods you
can buy with M dollars – “real money balances”
Lifetime utility function:
U = u (c ) + v (l ) + φ
Sims (ND)
M
p
Money and Prices
+ βu (c 0 ) + βv (l 0 )
Fall 2010
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Budget Constraints
First period flow budget constraint:
c +s +
M
= wn + Π
p
Second period flow constraint:
c 0 = w 0 n 0 + Π 0 + (1 + r )s +
M
p0
If p 0 > p, then money loses value over time
Sims (ND)
Money and Prices
Fall 2010
7 / 17
Intertemporal Budget Constraint
Recall Fisher relationship:
1 + r = (1 + i )
p
p0
Use this, solve for s, and get:
c+
i 1
1+i p
c0
i M
w 0 n0 + Π0
+
= wn + Π +
1+r
1+i p
1+r
is essentially the cost of holding money
Sims (ND)
Money and Prices
Fall 2010
8 / 17
Solving the problem
Same as always. Sub constraint into objective function, take
derivatives, set to zero. New choice variable now: M
Consumption Euler equation and labor supply condition look identical
New first order condition:
φ0
M
p
u 0 (c )
=
i
1+i
MRS = price ratio
Sims (ND)
Money and Prices
Fall 2010
9 / 17
Money Demand
This FOC implicitly defines a money demand function:
M d = PL(y , i ) = PL(y , r + π 0 )
Money demand (i) increasing in the price level; (ii) increasing in
economic activity; and (iii) decreasing in the nominal interest rate
Take expected inflation, π 0 , as an exogenously given variable
Intuition?
Sims (ND)
Money and Prices
Fall 2010
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Money Supply
We assume money supply is set exogenously by the central bank
Long and complicated money creation process in a fractional reserve
banking system. We ignore that complication.
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Fall 2010
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Classical Dichotomy
Classical dichotomy: real variables are determined independently of
nominal variables
Classical dichotomy holds here in our model up to this point
Determining endogenous real variables exactly the same as before
when we made no mention of money
Competitive equilibrium: given exogenous variables, determine real
endogenous variables just as before. Then determine i and P, taking
π 0 as exogenous
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Fall 2010
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Money Market Equilibrium
Now have three markets: labor, goods, and money. All must clear
Money market equilibrium: money demand = money supply. The
nominal price and nominal interest rate adjust to clear money market
Plot money demand as upward sloping function of p
Sims (ND)
Money and Prices
Fall 2010
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The complete model
r
ns
w
ys
r0
w0
nd
yd
n
n0
y
y0
Ms
p
Md
p0
M0
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Money and Prices
M
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Comparative Statics: Increase in z or M
Increase in y , decrease in r on the real side
Both work to “increase” money demand in (p, M ) space. Leads to
lower p and lower i in equilibrium
Increase in M: only effect is to raise p
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Fall 2010
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Money, Inflation, and Nominal Interest Rates
Over long horizons, output growth, real interest rates, and inflation
are basically constant. Real variables always independent of nominal
variables in this model
Looking at money demand function, this means that inflation is
proportional to money growth relative to output growth.
Correlation between money growth and inflation in data is about 0.5
“Inflation is everywhere and always a monetary phenomenon” –
Milton Friedman
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Money and Prices
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Money and Inflation
14
12
10
8
6
4
2
0
60
65
70
75
80
85
Inflation
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Money and Prices
90
95
00
05
M2 Growth
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