Demand 10
Aggregate I:
Aggregate
Building the IS-LM Model
Building
IS
In this chapter, you will learn:
the IS curve, and its relation to:
the Keynesian cross
the LM curve, and its relation to:
the theory of liquidity preference
how the IS-LM model determines income and
the interest rate in the short run when P is
fixed
Context
Chapter 9 introduced the model of aggregate
demand and aggregate supply.
Long run
prices flexible
output determined by factors of production &
technology
unemployment equals its natural rate
Short run
prices fixed
output determined by aggregate demand
unemployment negatively related to output
Context
This chapter develops the IS-LM model,
the basis of the aggregate demand curve.
We focus on the short run and assume the price
level is fixed (so, SRAS curve is horizontal).
This chapter (and chapter 11) focus on the
closed-economy case.
The Keynesian Cross (Simple Keynesian)
Model
A simple closed economy model in which income
is determined by expenditure.
Notation:
I = planned investment
PE = C + I + G = planned expenditure (note!)
Older edition uses E = C + I + G
Y = real GDP = actual expenditure
Difference between actual & planned expenditure
= unplanned inventory investment
Elements of the Keynesian Cross Model
consumption function:
C C ( T )
Y
govt policy variables:
G G , T T
for now, planned
investment is exogenous:
planned expenditure:
I I
PE C ( T ) I G
Y
equilibrium condition:
actual expenditure = planned expenditure
Y PE
Planned Consumption = Expenditure
C
planned
consumption
C mpc x (Y-T)
MPC
1
income, output, Y
Graphing planned expenditure
PE
planned
expenditure
PE =C +I +G
MPC
1
income, output, Y
45O line - Graphing the equilibrium
condition
PE
planned
expenditure
PE =Y
45
income, output, Y
The equilibrium value of income
PE
planned
expenditure
PE =Y
PE =C +I +G
income, output, Y
Equilibrium
income
Why this is the equilibrium value of
income.
PE
planned
expenditure
PE =Y
PE =C +I +G
income, output, Y
Equilibrium
income
An increase in government purchases
PE
=
Y
PE
At Y1,
there is now an
unplanned drop
in inventory
PE =C +I +G2
PE =C +I +G1
G
so firms
increase output,
and income
rises toward a
new equilibrium.
Y
PE1 = Y1
Y
PE2 = Y2
Solving for Y
Y C I G
equilibrium condition
Y C I G
in changes
C
G
MPC Y G
Collect terms with Y
on the left side of the
equals sign:
(1 MPC) Y G
because I exogenous
because C = MPC Y
Solve for Y :
1
Y
G
1 MPC
The government purchases multiplier
Definition: the increase in income resulting from a
$1 increase in G .
In this model, the govt
purchases multiplier equals
Y
1
G
1 MPC
Example: If MPC = 0.8, then
Y
1
5
G
1 0.8
An increase in G
An increase in G
causes income to
causes income to
iincrease 5 times
ncrease 5 times
as much!
as much!
Why the multiplier is greater than 1
Initially, the increase in G causes an equal increase
in Y :
Y = G.
But Y C
further Y
further C
further Y
So the final impact on income is much bigger than
the initial G.