
© 19992003 Douglas A. Ruby
Revised: 02/06/2003
Aggregate Demand
Macroeconomic Policy
The Accelerator
Macroeconomic Principles
Macroeconomic Theory

Aggregate
Expenditure,
the Spending Multiplier and Income Determination
Using the methods of
National Income Accounting, one method of calculating
nominal GDP (Y^{N}) was through the expenditure approach
such that:
NGDP = ΣP_{i}Q_{i}
= Y^{Nominal}
or
Y^{Nominal} = C + I + G +
NX
where the variables on the righthand side represent the four expenditure
categories that make up GDP. What is important is that certain expenditure
decisions are proportional to the level of income such that as aggregate
income increases, expenditure increases by some fraction of this income
change. We can think in terms of this expression representing an equilibrium
condition (Y_{e}) such that for one unique level of income, expenditure
is exactly equal to that level of income:
Y_{e} :
Aggregate Income = Aggregate Expenditure
We will begin with consumption
expenditure 'C' as being proportional to disposable
income (gross income less taxes paid) with the
proportional relationship being defined by the marginal propensity to consume
'b':
C = C_{o} + b(YT), 0 < b < 1
Tax revenue 'T' is defined to be some fraction of
income via the tax rate 't':
T = tY, 0 < t < 1
For algebraic simplicity we will define the other
expenditure categories; investment 'I', government 'G',
and net exports 'NX' as being autonomous with respect to
income (i.e., spending decisions independent of the level
of national income). We will summarize this via a single
variable 'A_{o}' known as autonomous expenditure:
A_{o}
= C_{o} + I_{o} + G_{o} + NX_{o}
Thus, the expenditure equation can be written as:
Y = C_{o} + b(YtY) + I_{o}
+ G_{o} + NX_{o}
or
Y_{e} :
Y = A_{o}
+ b(1t)Y
as shown in the diagram below:
Figure 1, Aggregate Expenditure
Solving for 'Y_{e}', the equilibrium value of
income, we have
Y_{e} = α'[A_{o}],
where α' = 1 / [1b(1t)] and
represents, what is commonly known as, the simple spending multiplier.
The Multiplier
Any time new spending is introduced into the economy (or
if spending is removed), it will cause GDP (and other
measures of national income) to change by some multiple
of that spending shock. This takes place through the
multiplier process in aggregate spending largely via
changes in consumption expenditure. For example, suppose
that the marginal propensity to spend (changes in
spending induced by changes in income) is equal to 0.50
Expenditure = A_{o} + 0.75(Y  0.333Y)
=A_{o} + 0.50Y
Given our equilibrium condition:
Y = AE (Aggregate Expenditure)
Y = A_{o} + 0.50Y
Since [1b(1t)] < 1, the spending multiplier α' will
be greater than one such that:
Y_{e} = 2.0[A_{o}]
and ΔY_{e} = 2.0[ΔA_{o}]
Figure 2, An Autonomous Spending Shock
note: [Y_{1}  Y_{0}] =
2.0[A'_{o}  A_{o}]
Interactive Graph  Product Market Equilibrium

In the interactive diagram below, autonomous expenditure
A_{o} is equal to $5,000 (billion).
1) You may use your mouse to
drag any slider to simulate changes to 'Autonomous Consumption Exp.', 'the Tax Rate',
'Govt. Exp.', 'Investment Exp.' or 'Net Export Exp.'.
2) Press the 'Income Adjustment' button to see the change to a new equilibrium.
3) Press 'Reset'
to start over.
The Process
An initial change in autonomous spending
(for example, a shock in the form of an increase in
government spending) of $20 (billion) is received as income by
some person or business in the aggregate economy. This
spending translates into an increase in income for that
person who, given the propensity to spend, will increase
his expenditure by $10 . This $10 in additional spending
is received by someone else as income who spends 50% of
that amount.
> iteration 
ΔIncome 
ΔExpenditure 
0 
Δ
Ao=
$20 (billion) 
10 
: 
: 
: 
n 
0.001 
 
Total Change in Income: 
40 (billion) 

The spending flows through the
aggregate economy such that when we total up all of the
increases in income we find that aggregate income has
increased by $40 billion  2.0 times the initial spending
shock. This is known as the multiplier process. Try it using different values
of the MPC, tax rate, and Autonomous spending shock in the table below:
Interactive Table  the Spending Multiplier

1) You may adjust the value for the Change in Autonomous Expenditure,
Marginal Propensity to Consume (MPC),
or Tax Rates:
by clicking on the boldfaced numbers in the appropriate number box.
Just click on any of these three numbers and enter a new value.
2) Note the following:
 $50,000.00 < Change in A_{o} < $50,000.00,
 0.010 < MPC < 1.00
 0.010 < Tax Rate < 1.00
3) Press the Spending button to display the process.
4) Press Reset to start over.
Concepts for Review:
 Aggregate Income
 Aggregate Expenditure
 Autonomous Consumption
 Autonomous Expenditure
 Equilibrium Income
 Marginal Propensity to Consume
 Spending Multiplier
