HO #4
Aggregate Consumption Function
Let’s start with the simple Keynesian
consumption function:
C = Ac + b1 (Y - T)
where:
Ac
b1
Y
T
autonomous consumption
marginal propensity to consume
national income
taxes
Marginal propensity to consume
b1 = MPC = C/(Y – T)
Marginal propensity to save
MPS = 1 – MPC
= S/(Y – T)
Saving:
S=Y–T–C
Let’s assume that consumption increases from
$3,600 to $4,300 as income increases from $3,000
to $4,000. This means the marginal propensity to
consume is (MPC) would be equal to:
MPC = (4,300 – 3,600)/(4,000 – 3,000)
= 700/1,000
= 0.70
If autonomous consumption is $1,500, then the
aggregate consumption function would take the
form:
C = 1,500 + 0.70 (Y - T)
If the disposable personal income were to fall to
$3,000, then aggregate consumption would fall to:
C = 1,500 + 0.70 (3,000)
= 3,600
If the marginal propensity to consume 0.70, then
the marginal propensity to save would be:
MPS = 1 – MPC
= 1 – 0.70
= 0.30
If the disposable personal income is 3,000, then
the level of saving would be:
S = 3,000 – 3,600
= -600
which represents a “dis-saving” of $600.
Absolute Income Theory
Consumption depends on income from current
work and from the level of consumer real wealth,
or:
C = Ac + b1(Y - T) + b2(W)
where:
W
existing real wealth
b1
marginal propensity to consume out of
income
b2
marginal propensity to consume out of
wealth
This equation thus reflects the “real wealth effect”
that is often referred to when discussing
consumption behavior
Permanent Income Theory
Transitory income does not change consumer
spending on non-durable goods. This theory
suggests that consumers’ permanent income
changes this consumption, or:
Yperm,t = a1(Y – T)t + a2(Y – T)t-1 + a3(Y – T)t-2 + …
where:
(Y – T)t disposable personal income in time “t”
Yperm permanent income
Consumer spending on non-durable goods
according to this theory is therefore also
influenced by consumers’ permanent income, or:
CN,t = b2(Yperm,t)
Substituting the lagged dependent variable into
the initial Keynesian equation, the consumption
equation for non-durable goods is given by:
CN,t = Ac,n + b1(Y – T)t + b2 Yperm,t-1
Life Cycle Hypothesis
Consumption in a particular year is part of
lifetime consumption decisions, reflecting utility
derived from spending and asset accumulation.
Ct = {(Y – T)t + (N-T) Yperm + ASt}/Lt
where:
ASt
assets in time period t
N–T
remaining earning years
Lt
lifetime expressed in years
This reflects the observation that young
consumers tend to have a much higher level of
consumption that older consumers. Their number
of remaining earning years is greater. This is
particularly true if the current disposable income
(Y – T)t and assets (ASt) for the two age groups
are identical.
In summary, the variables that can affect
aggregate consumption behavior include:
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Current income
Wealth
Permanent income
Life expectancy
Prices
Interest rates
Regularity of income
Demographics
Consumer attitudes