Transcript The IS Schedule

The Modern Approach to
Aggregate Demand
The Demand for Money and the LM
Curve
Learning Objectives
• Understand how people choose how much
money to demand.
• Learn how money demand changes when
interest rates and income change.
• Understand how money supply and money
demand interact to determine the equilibrium
rate of interest.
• Learn how changes in money supply and
money demand change the equilibrium rate
of interest.
Learning Objectives
• Learn how to use the money demand function
and the money supply function to graphically
and algebraically derive the LM curve.
• Learn how changes in money demand and
money supply shift the LM curve.
The Money Market
• Interest rates are determined through the
interaction of money demand and money
supply.
Money Demand
• The Theory of Liquidity Preference
– Assumptions:
• Assets can be divided into two types:
– Assets that pay interest, bonds.
– Assets that do not pay interest, money.
The Theory of Liquidity Preference
• According to the theory of liquidity
preference, people are willing to hold
money because it is readily accepted in
exchange for goods and services.
– The relationship between liquidity and the
interest rate is inverse.
• As an asset’s liquidity increases, its rate of return
falls.
Household Budget Constraint
• Households hold their wealth as money or bonds.
 W = M + P BB
• Households accumulate real wealth by saving.
 /\W/P = S = Y – C
• Household income is divided into two parts: the
income from owning bonds and labor income.
 Y = i(PBB/P) + (w/P)L
Household Budget Constraint
• If a household were to transfer its entire
portfolio to bonds, it would maximize
income.
• Therefore, maximum income equals the
household’s accumulation of bonds plus its
labor income.
 YMAX = i(PBB/P) + (w/P)L
Household Budget Constraint
• A household that transfers its entire portfolio
to bonds sacrifices the convenience of using
money in transactions.
• When the household chooses to hold some of
its wealth as money, it loses the income it
could have received on those balances.
Therefore, its budget constraint is:
 Y = YMAX – i(M/P)
Household Budget Constraint
• According to the budget constraint,
households choose how much income to
earn and how much money to hold.
• As individuals transfer their wealth from
money to bonds, they increase their income,
but simultaneously decrease their liquidity.
Demand for Money: Utility
• People choose to hold money because it
yields utility.
• Utility is gained by the interaction of the
income received by households and the real
balances held to facilitate transactions.
• We measure that utility or value in units of
commodities called real money balances
where real money balances equal MD/P.
Money Demand and Interest Rates
• Money balances confer utility on individuals.
• But, according to the law of diminishing utility,
the utility gained from holding an extra unit of
money decreases as the household holds an
increasingly larger portion of its wealth in cash.
• The household chooses how much money to hold
by equating the marginal utility of holding
money to its marginal cost, the interest rate.
Money Demand and Interest Rates
• The interest rate, i, is the cost of holding
money.
– As i rises, the opportunity cost of holding
money rises and people hold less.
– As i falls, the opportunity cost of holding
money falls and people hold more.
Money Demand and Interest Rates
i
As the interest rate falls from i1 to i2,
the household reallocates its portfolio
from bonds to money.
i1
Money demand increases from (M/P)1
to (M/P)2
i2
MD
0 (M/P)1
(M/P)2
MD/P
Money Demand and Income
• A household attains a higher level of utility if
it receives a higher income.
• Liquidity increases the utility of any given
income, but as income increases, the
household must hold more cash to generate
the same level of utility.
• Therefore, the demand for money increases
as income increase.
Money Demand and Income
• People hold money to make transactions.
– Higher levels of income are associated with
more transactions. Money demand increases.
– Lower levels of income are associated with
fewer transactions. Money demand decreases.
Money Demand: Shifts
Increases in income mean the
household needs more money for
transactions. Money demand
shifts to the right from MD(Y2) to
MD(Y3).
i
0
MD(Y3)
MD(Y2)
MD(Y1)
Money
Decreases in income mean the
household needs less money for
transactions. Money demand
shifts to the left from MD(Y2) to
MD(Y1).
Derivation of the Money Demand
Function
U = (Y – i(M/P)) (M/P)h
dU/d(M/P) = (M/P)h(– i) + (Y – i(M/P)) h(M/P)h-1
dU/d(M/P) =
(M/P)h (–i)
+
(Y – i(M/P))(M/P)h
dU/d(M/P) = – i/Y + h/(M/P) = 0
i/Y – h/(M/P) = 0
i/Y = h/(M/P)
i(M/P) = hY
(MD/P) = (h/i)Y
(Y – i(M/P)) h(M/P)h-1
(Y – i(M/P))(M/P)h
Other Money Demand Shifters
• Price Level
– An increase in the price level increases money
demand because the number of dollars needed
for transactions rises.
• Inflationary Expectations
– Higher expected inflation means a decrease in
the purchasing power of money; thereby,
decreasing demand.
Other Money Demand Shifters
• Risk
– Higher risk of alternative assets increases money
demand.
• Liquidity of Alternative Assets
– Higher liquidity increases the attractiveness of
alternative assets and decreases money demand.
• Payments Technology
– As the efficiency of payments technology increases,
money demand decreases.
Money Supply
• The supply of real money balances is
defined as the ratio of nominal money
balances and the price level, MS/P.
– where M is the nominal money supply
and P is the price level.
Money Supply
– The real money supply is assumed to be fixed
in supply and invariant with respect to the
interest rate.
• The money supply is assumed to be an exogenous
variable determined by the central bank.
• The price level is also assumed to be exogenous as
well as fixed in the short run.
The Money Market
The equilibrium rate of interest is
determined by the intersection of
money demand and money supply.
i
Money supply is vertical because MS
does not vary with the interest rate.
i*
MD
0
MS
Money
Money demand slopes down because
the opportunity cost of holding money
rises and falls with interest rates.
Money Supply: Shifts
i
A decrease in the money supply shifts
MS to the left from MS2 to MS2, increasing
the equilibrium interest rate.
i2
An increase in the money supply shifts
MS to the right from MS2 to MS3,
decreasing the equilibrium interest rate.
ie
i1
MD
0
MS1 MS2 MS3
Money
Monetary Policy
• Transmission Mechanism
– The increase in the money supply increases
liquidity in the portfolios of individuals.
• Money supply is now greater than money demand at
the current rate of interest.
– People rebalance their portfolios by using the
excess liquidity to buy other assets such as
bonds.
– As the price of bonds rises, interest rates fall.
Equilibrium in the Keynesian Model
• Unlike the classical model, in the Keynesian
model, changes in the money supply result in
changes in the interest rate.
• In the classical model, the price level adjusts
immediately to restore the equality between
money demand and money supply.
• In the Keynesian model, prices are slow to adjust
because of rigidities in the system. Income is also
slow to adjust, so interest rates must adjust to
restore equilibrium.
Evidence for the Modern Theory
• The introduction of interest rates as a
determinant of money demand means that
changes in interest rates will change the
velocity of money.
• Data collected over the period 1890 to 2000
(see text) demonstrate that velocity is not a
constant, and that it has closely paralleled
the interest rate as predicted by the theory.
The LM Schedule
• The LM schedule plots every income and
nominal interest rate (Y, i) combination that
results in equilibrium in the money market.
– The LM schedule is an equilibrium schedule.
• At every point on an LM schedule, money demand
just equals money supply.
The LM Schedule: Derivation
i
i2
i1
LM
i
E2
E2
E1
E1
MD(Y2)
MD(Y1)
0
MS/P
Money
0
Y1 Y2
Y
The LM Schedule: Derivation
• At point E1, money demand equals money
supply
– The equilibrium interest rate and level of
income are i1 and Y1.
– This combination is one point on the LM
schedule.
• Let Y rise to Y2.
The LM Schedule: Derivation
• At the point E2, money demand equals money
supply
– The equilibrium interest rate and level of
income now are i2 and Y2.
– This combination is another point on the LM
schedule.
LM Derivation: Algebra
• Quantity of money demanded equals the quantity
supplied.
 MD = MS where MS = M, an exogenously determined
quantity of money.
• Money demand equals:
 MD/P = h/iY
• Solve for i:
 MD/P = h/iY = P(h/i)Y = M = h/i = M/PY =
 i/h = PY/M = i = (hP/M)Y
The LM Schedule: A Decrease in the
Nominal Money Supply
i
i2
i1
LM2
i
E2
LM1
E2
E1
E1
MD
0
M2/P M1/P
Money
0
Y1
Y
A Decrease in the Money Supply
• At the point E1, money demand equals money
supply.
– The equilibrium interest rate and level of
income are i1 and Y1 respectively.
• Let the nominal money supply decrease, causing
the interest rate to rise to i2. Income is still Y1.
• Equilibrium now occurs at the point E2.
• The point E2 lies on LM2 because it represents
equilibrium in the money market when Y = Y1
and i = i2.
The LM Schedule: An Increase in
the Money Demand
LM2
i
i
i2
E2
i1
E1
LM1
E2
MD(Y2)
E1
MD(Y1)
0
MS/P
Money
0
Y1
Y
An Increase in Money Demand
• At the point E1, there is equilibrium in the money
market.
– The equilibrium interest rate and level of income are
i1 and Y1 respectively.
• Let money demand increase. Y is still Y1.
• Equilibrium now occurs at E2, where r is i2 and Y
is Y1.
• The point E2 lies on LM2 because it represents
equilibrium in the money market when Y is Y1
and i is i2.
Other LM Shifters
• A change in the price level
– If the price level rises (falls), the real money
supply falls (rises).
• Any factor that changes money demand
– Changes in wealth, the risk of alternative assets,
the liquidity of other assets, inflationary
expectations, etc.