## Advanced Lecture Notes for Hall and Taylor, Chapter 7

Course Instructor: Professor Leigh Tesfatsion
Email: tesfatsi@iastate.edu
Last Updated: 23 February 1996

# HT7: Financial Markets and Aggregate Demand--The IS-LM Model

```
Basic References:  Hall and Taylor, Chapter 7;
Study Guide, Chapter 7.

#THE IS-LM MODEL#

INTRODUCTION

In HT5 we developed money supply and demand relationships,
and in HT6 we developed the IS product market relationship.  In
the current chapter these money and product market relationships
are brought together within a single framework---the IS-LM model.
This model will allow us to begin to analyze the impact of
monetary and fiscal policies on key macroeconomic variables.

As a first step in the construction of the IS-LM model, the
previous HT6 modellings of investment and net exports will be
generalized to permit dependence on the interest rate.

INVESTMENT AND THE INTEREST RATE

#Behavioral Assumptions for Investment Based on Empirical Observation#:

The demand for investment goods (i.e., physical capital
goods) depends #negatively# on the expected real interest rate R^e
paid on financial assets.  That is, investment demand is #low#
when R^e is #high# and investment demand is #high# when R^e is
#low#.

#Intuitive rationale#:

High  R^e  -->  high expected cost      -->  fewer planned investment
of borrowing to finance      good purchases
investment

High R^e   -->  high expected return    -->  more planned purchases of
to lending                   financial assets

#Algebraic Representation for the Investment Demand Function#:

I^D  =  e  -  dR^e    ,

where

R^e   =   the expected real interest rate;

e, d  =   exogenously given positive coefficients .

NET EXPORTS AND THE INTEREST RATE

#Key Observation#:  An #increase# in the expected HC interest rate
R^e tends to cause an expected #appreciation# in the HC currency
(hence an expected increase in the exchange rate), which in turn
leads to a #decline# in net exports.

more attractive for ROW nationals
to buy HC assets, that is, to lend
to HC firms and households by buying
assets denominated in HC currency

R higher ->                                   -> relative demand for HC
currency increases
as ROW nationals try to
to sell ROW assets

-> relative demand for HC
currency increases
less attractive for HC nationals       as HC nationals try to
for HC nationals to put their funds    to sell ROW assets
into HC assets

-->  the price of HC currency   -->  increase in the
relative to ROW currency        exchange rate
increases                       (ROW currency per unit
of HC currency)

-->  HC goods more expensive to ROW nationals       -->  EX^D lower and
and ROW goods less expensive to HC nationals        IM^D higher

-->  net export demand  NE^D = [EX^D - IM^D]  declines.

#Algebraic Formulation#:

These relations are more carefully developed by HT in
Chapter 12.  For now, we only use the implication that R is
#negatively# related to net export demand.

Specifically, HT make the behavioral assumption that net
export demand is a simple linear function of the (expected) real
interest rate R^e as well as of (expected) real income:

(*)       NE^D  =  g  -  mY^e  -  nR^e ,

where g, m, and n are exogenously given positive coefficients.
Note that (*) implies that net export demand is a decreasing
function of both expected income and the expected real interest
rate.

THE IS-LM MODEL: ALGEBRAIC FORMULATION

The objective of this section is to combine the various
behavioral assumptions for consumption, investment, net exports,
and money demand into an "IS-LM model" explaining how real income
might be determined in the short run, taking the general price
level P as given (predetermined).  The term "IS-LM" will be
clarified below.

The Basic IS-LM Model Equations for the Economy During Period T

Equation                Verbal Description

Product Market (Spending Balance) Relations:

#Supply Side#:

(1) Realized income      Y  =  C + I + G + NE          Accounting Identity
For Realized Income

#Demand Side#:

(2) Consumption Function   C^D  =  a + bY^e_d          Behavioral Assumption

(3) Exp. Disp. Income      Y^e_d   =  [1-t]Y^e         Definitional Equation

(4) Inv Demand Function    I^D   =  e - dR^e          Behavioral Assumption

(5) NE Demand Function     NE^D  =  g - mY^e - nR^e   Behavioral Assumption

(6) Aggregate Demand   Y^D   =  C^D + I^D + G + NE^D   Definitional Equation

#Product Market Equilibrium#:

(7)   Supply=Demand        I = I^D              Equilibrium Condition

(8)   Supply=Demand        C = C^D              Equilibrium Condition

(9)   Supply=Demand        NE = NE^D            Equilibrium Condition

(10)  Fulfilled Exp's      Y^e = Y              Equilibrium Condition

(11)  Fulfilled Exp's      R^e = R              Equilibrium Condition

#Remark#:  What about the equality of realized output supply
Y and aggregate demand Y^D?  The equality Y=Y^D is an implication
of equations (1) and (6)-(9) and so does not have to be separately
assumed.

Money Market Relations:

#Supply Side#:

(12)  Money Supply Function    M^S = M     Government Monetary Policy Rule

#Demand Side#:

(13)  Money Demand Function    M^D/P = kY^e - hR^N^e    Behavioral Assumption

(14)  Exp. Nom. Interest Rate  R^N^e  =  R^e + INF     Definitional Equation

#Money Market Equilibrium#:

(15)  Supply=Demand            M^S  =  M^D            Equilibrium Condition

(16)  Fulfilled Exp's          R^N^e = R^N             Equilibrium Condition

REMARK:  Equations (10) and (11) are also needed for money
market equilibrium, but restating them again here would be
redundant.

Classification of Variables

#Endogenous Variables#: (Variables appearing in the model equations
for period T whose solution values are determined by these equations,
hence #during# period T)

Sixteen equations in sixteen endogenous variables to be solved for:

Y^D and Y, C^D and C, I^D and I, NE^D and NE, M^D and M^S,

plus Y^e_d, R, R^N, Y^e, R^e, R^N^e

#Predetermined Variables#: (Variables appearing in the model equations
for period T whose values are determined by model equations relating
to periods #prior# to period T)

The general price level, P

#Exogenous Variables#: (Variables appearing in the model equations
for period T whose values are given known quantities determined
outside of the model equations for #any# period T)

Three government policy variables:  t, G, M

Plus the coefficients: a, b, e, d, g, m, n, k, h

Plus the inflation rate INF  (temporary classification)

THE IS-LM MODEL: GRAPHICAL REPRESENTATION

We will now reduce the relationships (1)-(16) down to just
two relationships in the two endogenous variables Y and R---the
IS and LM curves---which can be graphically depicted.

Key Definitions:

The #IS Curve# shows all combinations of the real interest
rate R and the level of real income Y which satisfy the spending
balance relations (1)-(11).

The #LM Curve# shows all combinations of the real interest
rate R and the level of real income Y which satisfy the money
market relations (10)-(16).

THE IS CURVE

By definition, the IS Curve is the graph of the spending
balance relations (1)-(11) in the Y-R plane after all endogenous
variables except Y and R have been substituted out.

Intuitively, Y and R should depend #negatively# on each other
through these spending balance equations; i.e., the IS Curve
should be downward sloping, since an #increase# in the interest
rate causes a #decrease# in both investment and in net exports,
and hence leads to a decrease in Y through the multiplier
process.

It is fairly straightforward to establish algebraically that
this intuition is correct.  Substituting out all endogenous
variables from (1)-(11) except Y and R leaves one relation in the
#two# unknowns, Y and R:

Y  =  (a + b[1-t]Y)  +  (e - dR)  +  G  +  (g - mY - nR)

For our purposes, we want to solve this relation for R as a
function of Y, i.e., we want R isolated by itself on the left
side.  Let A denote the positive quantity [1-b(1-t)+m].  Then,
combining terms in Y and R, and solving for R, one obtains the
following relation:

#IS Equation#:

(IS)   R  =  [a + e + G + g]/[d + n]    -    (A/[d + n])Y  .

R-intercept            slope = dR/dY = -A/[d+n]
(Value of R when Y=0)      (note the sign is #included#)

[Compare Hall and Taylor, equ.(7-5), p. 188.]  Since the coefficient
terms A, d, and n are all positive, it follows from (IS) that R
is a linear function of Y that depends #negatively# on Y.   The
IS curve is the #graph# of the IS equation (IS).

R
|
|
[a+e+G+g]   *
---------   |
[d+n]     |                          IS Curve with slope
|
|                           dR       - A
|                           --  =   ------
|                           dY       [d+n]
|
|
|
|
|
|
|
--------------------------------------------  Y
0

The IS Curve
By construction, the product market is in
equilibrium at every point on the IS curve.

FOUR DIFFERENT WAYS THE IS CURVE MIGHT BE AFFECTED BY VARIABLE CHANGES:

1. Movements Along the IS Curve:  Given fixed values for all
exogenous and predetermined variables, a change in Y causes a
movement #along# the IS curve as R correspondingly adjusts, since
R and Y appear as variables along the axes.

2. Parallel Shifts of the IS Curve:  A change in any exogenous
or predetermined variable entering into the R-intercept of the IS
curve (but not the slope) #shifts the IS Curve in a parallel
fashion#.

#Examples#:

What happens if there is an #increase# in the consumption
function intercept term a ("subsistence consumption")?  For each
given Y, the right hand side of (IS) is #larger# in magnitude,
hence the corresponding R on the left must be #larger# in
magnitude.  In short, for each Y, R is larger; hence the IS Curve
#shifts up#.

What happens if real government expenditure G #decreases#?
For each Y, the right hand side of (IS) is smaller, hence R on the
left is smaller.  The IS Curve #shifts down#.

3. Rotations of the IS Curve:  A change in any exogenous or
predetermined variable entering into the slope of the IS curve
(but not the R-intercept) #rotates the IS Curve around the
R-intercept#.  A change in any exogenous or predetermined variable
entering into the slope of the IS curve (but not the Y-intercept)
#rotates the IS curve around the Y-intercept#.

#Example#:

What happens if t #increases#?  First note that t enters
into the slope of the IS curve and into the Y-intercept; but it
does not enter into the R-intercept, implying the R-intercept
stays fixed.  If t increases, then A #increases#; hence, for given
Y, the right hand side of (IS) is #smaller#, hence R on the left
must be smaller.  The IS curve #rotates downward# around the
unchanged R-intercept.

4. Simultaneous rotation and shift of the IS Curve:  A change in
any exogenous or predetermined variable entering into the #slope#
of the IS curve #as well as both intercepts# would simultaneously
rotate and shift the IS curve.  For the model at hand, it happens
that no such variables exist for the IS curve.

THE LM CURVE

By definition, the LM curve is the graph of the money market
relations (10)-(16) in the Y-R plane, after all endogenous
variables other than Y and R have been substituted out.  This
substitution out leaves #one# relation in the two endogenous
variables Y and R, given by:

#LM Equation#:

(LM)*                  M/P  =  kY - hR - hINF

where P, k, h, and c are given predetermined or exogenous
variables.

Relation (LM)* should be compared with Hall and Taylor,
equ.(7-3), p. 186.  Recall that, for now, we are retaining the
dependence of money demand on the #nominal# interest rate, R+INF,
the true opportunity cost of holding money.  Hall and Taylor
simplify their analysis by assuming money demand depends on the
real interest rate R rather than the nominal interest rate R+INF.

The LM curve (i.e., the graph of (LM)* in the Y-R plane)
slopes #upward#, in the sense that Y and R increase and decrease
#together# along the LM curve.  The intuitive reason for the
upward slope of (LM)* is as follows:  Recall that the demand for
money (with fulfilled expectations) takes the form

M^D/P = kY - hR - hINF.

Thus

higher Y  ->  #higher# level of transactions

->  demand for money #increases#

But the money supply is fixed at M, and (LM)* implies M^D must
equal M.  Thus, the interest rate R must adjust until the private
sector is once again content to hold M; that is, money demand
must be #discouraged#.  But this requires an #increase# in R, so
that people reduce their demand for money holdings because the
opportunity cost of holding money has increased.

To see this algebraically, let (LM)* be re-expressed as

(LM)   R   =  - [ (M/hP) + INF ]    +     [k/h]Y

R-intercept         slope = dR/dY = k/h
(Value of R when Y=0)

[Compare Hall and Taylor, equ.(7-7), p. 189.]  Then it is clearly
seen that the slope of the LM Curve is k/h, a #positive# number.
The R-intercept is negative if the inflation rate INF in
nonnegative; otherwise it could be positive.

R
|
|
|
|                                  LM Curve with slope
|
|                                   dR      k
|                                   --  =  ---
|                                   dY      h
|
0   -------------*--------------------------------- Y
|
|           [M/kP] + hINF/k
|
-[M/hP]-INF *
|

The LM Curve
By construction, the money market is in
equilibrium at each point on the LM curve.

How is the LM curve affected by variable changes?  As for the
IS Curve:

(a) A change in an exogenous or predetermined variable
appearing in the R-intercept of the LM Curve (but not the slope)
causes the curve to #shift#;

(b) A change in an exogenous or predetermined variable
appearing in the slope of the LM Curve (but not the R-intercept)
causes the curve to #rotate around the R-intercept#;

(c) A change in an exogenous or predetermined variable
appearing in the slope of the LM curve (but not the Y-intercept)
causes the LM curve to #rotate around the Y-intercept#;

(d) A change in any exogenous or predetermined variable
entering into the slope, the R-intercept, #and# the
Y-intercept of the LM curve results in a combined rotation and
shift in the LM curve.  [Consider, for example, a change in h.]

FINDING SHORT-RUN EQUILIBRIUM VALUES Y^o and R^o FOR Y AND R

DEFINITION:  An economy with income level Y^o and real
interest rate R^o is said to be in a "short-run equilibrium" (or
"IS-LM equilibrium") if Y^o and R^o represents the intersection
of the IS and LM curves in the Y-R plane.

Thus, the economy is in a short-run equilibrium if both the
product market and the money market are in equilibrium, in the
sense that plans are fulfilled (supply = demand) and expectations
are realized in both the product and money markets.  However,
note that labor demand may fail to equal labor supply in a
short-run equilibrium---that is, there is no guarantee that the
#labor# market is in equilibrium, and hence no guarantee that Y^o
equals the full employment level of income Y*.

R
|
|
|
|
|
|
|                     E^o
R^o |...................
|                   .
|                   .
|                   .
|                   .
|                   .
--------------------------------------------- Y
0                   Y^o

Short Run Equilibrium at E^o

How can the short-run equilibrium values for Y and R be determined
algebraically?

The IS-LM model (1)-(16) has now been reduced down to just
two relations in the two unknowns R and Y.  Recalling that A
denotes the expression (1-b[1-t]+m), these two relations are as
follows:

(IS) [Product Market Equilibrium]

R   =   [a+e+G+g]/[d+n]  -  (A/[d+n])Y ;

(LM) [Money Market Equilibrium]

R   =  - [ (M/hP) + INF ]  +  [k/h]Y  .

The values Y^o and R^o for Y and R which solve the IS-LM model
occur at the intersection of the IS and LM Curves in the Y-R
plane; i.e., they are the values for Y and R which simultaneously
satisfy equations (IS) and (LM).  These values are found by using
one of the equations to solve for R as a function of Y, and then
substituting this value for R into the second equation.

For the linear equation model at hand, obtaining the
solutions for Y and R by this means is messy but straightforward.
For example, use (LM) to solve for R, and substitute this value
into (IS).  One obtains one equation in the one unknown Y:

- [ (M/hP) + INF ]  +  [k/h]Y

=     [a + e + G + g]/[d + n]  - (A/[d + n])Y .

Collecting terms in Y on the left, and putting all other terms on
the right,

(A/[d+n])Y + [k/h]Y  =  [ (M/hP) + INF ] + [a+e+G+g]/[d+n]

or

(A/[d+n] + [k/h])Y   =  [ (M/hP) + INF ] + [a+e+G+g]/[d+n] .

Now divide through by the terms multiplying Y to obtain the
short-run equilibrium solution Y^o for Y:

Y^o  =  ( (M/hP) + INF + [a+e+G+g]/[d+n] )/( A/[d+n] + [k/h] )

The short-run equilibrium solution R^o for R is then found by
substituting this value Y^o for Y either in the IS equation or
the LM equation.

Once the solution values Y^o and R^o are obtained for Y and
R, solution values for all remaining endogenous variables in
equations (1)-(16) can be obtained by substituting the solution
values for Y and R back into these equations.  For example, given
Y^o and R^o, the solution value for consumption C is given by

C^o  =   a   +   b[1-t]Y^o  .

THE AGGREGATE DEMAND CURVE

DEFINITION:  The #aggregate demand curve# is a schedule
showing the aggregate spending Y of the economy at each general
price level P, assuming the economy is in a short-run
equilibrium at that price level.

As one would expect, the AD curve is downward sloping---the
higher the general price level, the lower the demand.  There are,
however, major differences between the macro concept of aggregate
demand and the concept of a demand curve in microeconomics.

The AD curve is derived from the succession of intersection
points (Y^o,R^o) of the IS and LM Curves and the general price
level P is varied.  Specifically, it is the graph of the
resulting solution values Y^o against the corresponding P values.
Note that P enters only into the LM curve; the IS Curve is not
affected by changes in P.

P increases --->  M/P decreases      --> For each possible Y, R goes
[excess demand for money]     #up# to dampen money demand

--> LM curve shifts #up#

--> New intersection point of the
IS and LM curves occurs at
a #lower# level of Y

Consequently, the AD curve is a #downward# sloping curve in the
Y-P plane.

ALGEBRAIC DERIVATION:

Step 1:  Consider once again the IS and LM Curves:

(IS Curve)    R  =  [a+e+G+g]/[d+n]   -  (A/[d+n])Y

(LM Curve)    R  =  - [ (M/hP) + INF ]  +   [k/h]Y

Step 2:  Substitute out for R, leaving one equation in Y and P:

[a+e+G+g]/[d+n] - (A/[d+n])Y =  - [ (M/hP) + INF ] +  [k/h]Y

Step 3:  Collect terms in Y #and in P#:

( [a+e+G+g]/[d+n] + INF) +  (M/hP)  =  (A/[d+n] + [k/h])Y .

Dividing through by the coefficient multiplying Y yields the
short-run equilibrium value for Y as a function of P, given by

Y    =    V  +  B/P    =    Y^o(P) ,

where

( [a+e+G+g]/[d+n]  +  INF)
V     =     -----------------------------
(A/[d+n]) + [k/h]

[M/h]
B     =         -------------------     .
(A/[d+n]) + [k/h]

Alternatively, solving for P as a function of Y, one obtains the
"inverse aggregate demand function"

P  =   B/[Y - V]   =  P^o(Y)  ,

which is defined only for Y greater than V.  This latter
restriction is necessary for economic meaningfulness.  If Y were
strictly less than V, note that P would take on negative values.
Moreover, if Y were equal to V, the price level would "blow up"
because the first term would involve division by zero.

QUESTION:  When will the AD curve shift and/or rotate in
response to a change in some exogenous variable?  Answer:
Whenever the exogenous variable enters into either V or B.  Or
equivalently, whenever the exogenous variable appears somewhere
in the IS and LM equations which are used to derive the AD curve.
Note that changes in the #predetermined# variable P result in
movements #along# the AD curve, not in shifts and/or rotations of

GRAPHICAL DERIVATION OF THE AGGREGATE DEMAND CURVE:

R
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
------------------------------------------------------  Y
0        Y^o(P_1)     Y^o(P_2)        Y^o(P_3)

.    "asymptote" (Y approaches ever closer to V as P increases)
.
P    .
|    .
|    .
P_1 |...........
|    .     .
|    .     .
|    .     .
P_2 |.........................
|    .     .             .
|    .     .             .
|    .     .             .
P_3 |.........................................
|    .     .             .               .
-------------------------------------------------  Y
0    V   Y^o(P_1)     Y^o(P_2)        Y^o(P_3)

The Aggregate Demand Curve in the Y-P Plane

POLICY IN THE IS-LM MODEL: INTRODUCTORY COMMENTS

BASIC QUESTION:  What #can# government do in the short run
to affect Y and R through changes in its monetary policy variable
M and its fiscal policy variables G and t?

Monetary Policy

What happens to the IS curve, the LM curve, and the AD curve
if the Fed #decreases# the money supply M?

ALGEBRAIC ANSWER:  The LM Curve shifts #up#, that is, R is
#larger# for each given Y.  The IS Curve is not affected.  The
new IS-LM intersection point is at #higher# R and #lower# Y.
Since the predetermined level of P is unaffected by this change
in M, this implies a #lower# value of Y for the given P, i.e.,
the AD curve #moves to the left#.

Such a monetary policy change is called a #contractionary#
monetary policy change, for obvious reasons.

#ECONOMIC INTUITION#:  With a #decrease# in the money #supply#,
there is more demand for money in the economy than supply---that
is, there is an #excess demand# for money in the money market.
In order to convince people to demand less money (i.e., to hold
more bonds) so that the money market can regain a state of
equilibrium, the interest rate (i.e., the opportunity cost of
holding money) must #increase# for any given level of Y.  The
higher interest rate R also discourages investment and net
exports, which lowers real income Y through the multiplier
process.

Conversely, an increase in M would result in a new
intersection point at a #lower# R and a #higher# Y, implying a
#move to the right# of the AD curve.

Fiscal Policy: Government Expenditure

What happens to the IS curve, the LM curve, and the AD curve
if the government #increases# its expenditure level G?

ALGEBRAIC ANSWER:  The expenditure level G enters into the
numerator of the #R-intercept# of the IS Curve but not the slope
of the IS curve.  Thus, an increase in G #shifts up# the IS
curve.  That is, R is higher for each given Y.  Since G does not
enter into the LM curve, the LM curve is not affected by a change
in G.  It follows that the new intersection point with the LM
curve is at a #higher# value for R and a #higher# value for Y.
Since P is unaffected by the change in G, this implies a #higher#
Y for the given P; that is, the AD curve #shifts to the right#.

Such a policy change is called an #expansionary# fiscal
policy change, for obvious reasons.

#ECONOMIC INTUITION#:  The first-round effect of an increase
in G causes Y to increase.  This leads to an increase in M^D
(hence an #excess demand for money#), and also to an increase in
C which tends to further increase Y (although this increase in Y
is partially offset by a decrease in net exports in response to
the first-round increase in Y).  To encourage people to hold less
money, the opportunity cost of holding money must increase, i.e.,
R must increase;  but this leads to decreases in investment I and
net exports NE which partially offset the initial increase in Y.

REMARK:  The latter partially offsetting decrease in I in
response to the initial increase in G is referred to as the
"crowding out effect"---the increase in government expenditures
is said to have "crowded out" private investment I.

By similar arguments, a #decrease# in G would lead to a
#lower# value for R and a #lower# value for Y, and hence a #shift
to the left# in the AD curve.

Fiscal Policy: Tax Rate

What happens to the IS curve, the LM curve, and the AD curve
if the government #decreases# the tax rate t?

ALGEBRAIC ANSWER:  The tax rate t enters into the #slope# and
the #Y-intercept# of the IS Curve, but not into the R-intercept of
the IS curve.  Specifically, a decrease in t causes the negative
slope of the IS curve to #decrease# in magnitude (i.e., become
less negative) and the positive Y-intercept to #increase# in
magnitude.  The R-intercept stays fixed.  The IS curve thus
rotates outward around the R-intercept, implying that R is higher
for each given Y.  Since t does not enter into the LM curve, the
LM curve is not affected by a change in t.  It follows that the
new intersection point with the LM curve is at a #higher# value
for R and a #higher# value for Y.  Since the predetermined price
level P is unaffected by the change in t in the current period,
this implies a #higher# SR-equilibrium value for Y for any given
P; that is, the AD curve #shifts to the right#.

Such a policy change is called an #expansionary# fiscal
policy change, for obvious reasons.

#ECONOMIC INTUITION#:  The first-round effect of a decrease
in t causes C and hence Y to increase.  This leads to an increase
in M^D (hence an #excess demand for money#), and also to a
further increase in C in response to the first-round increase in
Y which tends to further increase Y (although this increase in Y
is partially offset by a corresponding decrease in net exports).
To encourage people to hold less money, the opportunity cost of
holding money, R, must increase; but this leads to decreases in
investment I and net exports NE which partially offset the
initial increase in Y.

Statements in the financial pages of newspapers and
magazines and in T.V. economic commentary concerning the effects
of government policy actions often appear to be based on an
underlying IS-LM analysis.  However, caution must be exercised in
applying the IS-LM apparatus to real-world problems.

One difficulty is that the behavioral assumptions underlying
the IS-LM model can be criticized on the grounds that agents
(particularly households) do not exhibit a realistic degree of
rationality and are not modelled as solving plausible
optimization problems.  This is the problem of inadequate
"microfoundations" that many economists (particularly of the new
Keynesian school of thought) are currently trying to correct.

A second difficulty is that the IS-LM model as developed to
date is static, in the sense that it does not consider affects on
#future# income etc. of government policy decisions taken #now#.
It only predicts affects on #current# income.

One connection between the current time and the future time
comes from a consideration of how the government #finances# its
expenditures:

#Government Budget#:   G   =    tY   +   DM/P    +    DB/P

Any part of real government expenditure G which is not financed by
an increase in current income taxes must be financed either by new
money issue DM/P or by new bond issue DB/P.  Changes in money have
implications for the future inflation rate (a higher inflation rate
means a higher inflation "tax" on private and foreign sector
agents holding assets denominated in dollars); and changes in
bonds have implications for future tax obligations (the government
must somehow raise additional money from future taxpayers to
service the new debt).

Another connection between the current time and the future
time comes from a consideration of how net investment #changes#
the size and composition of the current capital stock, and how
population trends #change# the size and composition of the current
labor force.

THE RELATIVE EFFECTIVENESS OF MONETARY AND FISCAL POLICY

#When is monetary policy relatively weak, in the sense that changes
in M have a correspondingly small impact on real income Y?#

Consider the sequence of events which follows upon an
expansionary monetary policy (an increase in M) starting from a
point of short-run equilibrium (i.e., an intersection point of
the IS and LM curves).

M  #increases#  ->   #Excess# supply of money develops as M rises
above M^D

->   #Drop# needed in the opportunity cost R of
holding money to get people to hold more of it
(i.e., to increase M^D)

->   Lower R encourages #more# I and NE

->   #Raise# in Y through the multiplier process.

An expansionary monetary policy (M increased) might therefore have a
relatively #weak# impact on Y if either of the following situations occurs:

(1)  The drop in the interest rate R that occurs when M increases
is #very small# because the money demand M^D is #very
sensitive# to changes in R

--> h is #very large# in the money demand relation

M^D/P = kY - hR - hINF.

--> Slope [k/h] of the LM Curve is a #very small positive number#

(LM Curve)  R  =  - [ (M/hP) + INF ]  +   [k/h]Y  .

and/or

(2)  Investment I = e - dR and net exports NE = g - mY - nR are
#very insensitive# to changes in R

--> d and n are #very small positive numbers#

--> IS Curve has a #very large negative slope#

(IS)  R  =  [a+e+G+g]/[d+n]  -  (A/[d+n])Y

Note that shifts in the LM Curve will tend to have little effect
on Y if one or both of these conditions holds.  Monetary policy
is relatively strong in the reverse case.

#When is fiscal expenditure policy relatively weak, in the sense
that changes in G result in a correspondingly small change in real
income Y?#

An expansionary fiscal policy will have a relatively #weak#
impact on Y if crowding out effects are significant.  Recall the
sequence of events in crowding out, starting from a point of
equilibrium:

G increases -> Y increases (both directly, and through multiplier
effects working through increases in C partially
offset by decreases in NE)

-> M^D increases in response to the increase in Y

-> R increases to offset the increase in M^D

-> I and NE decrease in response to the increase in R

-> increase in Y is partially offset

Clearly the overall impact of an increase in G on Y will be #weak#
if the offset is #large#.  The offset will be large if the
following statements hold to a suitable degree:

(1)   The sensitivity of money demand to the interest rate is
#very small# (i.e., h is very small), so that #very large#
increases in R are needed to dampen money demand.

M^D/P = kY - hR - hINF.

--> LM Curve is #very steep# [has a #large positive slope# k/h]

(LM Curve)  R  =  - [ (M/hP) + INF ] + [k/h]Y  .

(2)  The sensitivity of investment I = e - dR and/or net
exports NE = g - mY - nR to the interest rate R is #very
large# (i.e., d and/or n are #very large#)

--> IS Curve #very flat# [has a small negative slope -A/[d+n] ]

(IS Curve)  R  =  [a+e+G+g]/[d+n]  -  (A/[d+n])Y

In other words, shifts in the IS Curve will tend to have little
effect on Y if one or both of these conditions hold.

In the case where each of these statements holds in reverse
[i.e., the LM Curve is relatively flat and/or the IS Curve is
steeply sloped], the overall impact of an increase in G on Y will
be #strong#, i.e., fiscal policy will have a significant impact on Y.

#Remark#:  One might argue that the impact of an increase in G
on Y will be #strong# if the government multiplier dY/dG =
(1/[1-b(1-t) + m]) is #large#.  Note, however, that the inverse
of this multiplier is the expression A that appears in the slope
term for the IS Curve, with [d + n] in the denominator, where A is
bounded below by 0 and (typically) would also be bounded above by 2.
Thus, having d and/or n suitably large or small would outweigh any
effects on Y through the multiplier process.

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