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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 33-34: Consumption

Lecture Outline:
- Keynesian consumption function and the “consumption puzzle”;
- Fisher’s two period model of consumption;
- Life Cycle and Permanent Income theory of consumption;
- Consumption as a random walk;
Essential reading:
Mankiw: Ch
...

Property b) means that only a part of current income is consumed and so a proportion
1 − c becomes saving
...

Graphically the Keynes Consumption function looks like:

1

C

C=C0+cY

MPC

C0
slope=APC
Y

The slope of any ray connecting zero with a point on the consumption function is the
Average Propensity to Consume
...

Why the slope those rays is the APC? Consider the point C1 ,Y1 on the consumption
function
...
Then you
have a triangle (a right triangle)
...


C

C=C0+cY

C1
slope=C1/Y1
Y1

Y

Now we can ask: Is the Keynesian Consumption function a good representation of
consumers’ behaviour?
This is an empirical question
...
For example a sample of 1000 consumers
in 1934
...

c) Richer households saved larger fractions of their income ⇒ APC ↓ asY ↑
...
The correlation between current income and current consumption was
found to be very strong (this was found during the Great Depression)
...

2) Time series evidence: in 40s new pieces of evidence about aggregate
consumptions were found by Simon Kuznets (a Nobel prize winner)
...
According to the Keynes Consumption Function aggregate
consumption should grow more slowly than income
...
Moreover as
income increases APC should decrease
...
This implies that C grew at the same rate
as income and as income increased APC did not fall
...

The difference between the two was that the first one was cross-sectional in detail
(they looked at a snapshot of the economy at a point) whereas Kuznet’s study was of a
time series nature (it looked at the economy over many points in time)
...
This is known as
the Consumption Puzzle
...
It is not derived from a
model of optimal behaviour of consumers
...
The following analysis is due to Irving Fisher (the one
of the Fisher Effect)
...

Consider a representative consumer (there are many consumers but they are all equal)
that lives for only two periods
...
The consumer is rational and
forward looking
...
The consumer can lend and borrow at the real
interest rate r
...
In period 2 the budget
constraint is:

C 2 = Y2 + (1 + r ) S1

3)

Obviously in period 2 there is no saving since the consumer dies and so it will
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consume all his income in period 2
...

Graphically the intertemporal budget constraint looks like:

C2

(1 + r )Y1 +Y 2

Consumption
Saving

income
periods

in

=
both

Y2
Borrowing

C1

Y1
Y1 +Y 2 (1 + r )

On the vertical axis we put consumption in period 2 and on the horizontal axis the
consumption in period 1
...

The point C1 = Y1 and C 2 = Y2 showed in the graph is always feasible and is on the
budget line
...

The intertemporal budget constraint implies a trade-off between consumption in

period 1 and in period 2
...
By doing that
he moves up on the budget line
...
The slope of the intertemporal budget constraint is − (1 + r )
...
For a given

5

stream of income if the consumer wants to decrease consumption in period 1 by ∆C1 ,
then according to 4) he can increase consumption in period 2 by ∆C 2 = −(1 + r )∆C1
so

∆C 2
= −(1 + r )
...

An indifference curve shows all combinations of C1 and C2 that make the consumer
equally happy
...

At point O we have that MRS = 1 + r
...


How Consumption Responds to Changes in Income
Now we can ask what happens to the consumption choice over the life time if there is
an increase in current Y1 or future income Y2
...
Provided the consumption in
both periods is a normal good, then both C1 and C 2 increase, regardless whether the
income increase occurs in period 1 or period 2
...

In the two period model current consumption depends only on the present value of
lifetime income
...

How Consumption Responds to Changes in Interest Rate
The interest rate is a price so a change in the interest rate creates an income and
substitution effect
...

The optimal consumption bundle before the change in the interest rate is point A
...
As depicted
in the graph C1 falls and C2 rises
...

Income effect: If consumer is a saver, the rise in r makes him better off since he
becomes richer
...

Substitution effect: The rise in r increases the opportunity cost of current
consumption, which tends to reduce C1 and increase C2
...
Whether C1 rises or falls depends on the
relative size of the income and substitution effects
...
If our consumer learns that
his future income will increase, he can spread the extra consumption over both
periods by borrowing in the current period
...

Therefore the Keynesian Consumption Function seems not be very consistent with
this microfounded analysis
...

The borrowing constraint takes the form: C1 ≤ Y1
...
Graphically:

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C2

The budget line
with a borrowing
constraint

Y2

C1

Y1

The borrowing constraint can be non binding: C1 < Y1
...
He does not want to
borrow
...
If the consumer wants to consume
more than his income in period 1 he cannot
...
But since the consumer cannot borrow, the best he
can do is point E
...


The Life Cycle Hypothesis (LCH) of Consumption
The Keynesian Consumption Function while able to explain aggregate consumption
of an economy at a point in time was not able to explain it over time
...
Therefore there was the need to have a theory to explain
the behaviour over time of the aggregate consumption
...
The other theory was developed by
Milton Friedman called Permanent Income Hypothesis
...

Extending the idea of the Fisher’s model the Life Cycle model says that it is not only
income in the current period that affected people’s observed consumption choices, but
also income they expected in the future
...


10

Basic Assumptions of the Life Cycle Hypothesis
a) Perfect Knowledge of Lifetime: individuals know with certainty how much
they are going to live and when they are going to die;
b) Uniform Consumption: individuals prefer to have a constant stream of
consumption over their lifetime;
c) Zero Bequests: individuals do not die with positive income
...

Denote with:
- W the initial wealth of the consumer (this includes financial and real assets)
...

- R is the number years until retirement
...
To achieve constant consumption over time our consumer divides
lifetime resources equally over time:

C=

1
(W + RY )
T

6)

Or written differently:
C = αW + β Y

where α =

7)

1
R
is the marginal propensity to consume out of wealth and β =
is the
T
T

marginal propensity to consume out of income
...

The Average Propensity to Consume (APC) is:
C
W
=α +β
Y
Y

8)

Since over time aggregate wealth and aggregate income tend to grow together (given

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the assumption of consumption smoothing if income increases, consumption remains
constant and so saving (and wealth) will grow proportionally to income) then APC
should remain stable over time
...
Over time the individual starts to
accumulate saving and keeps constant consumption
...


The Permanent Income Hypothesis (PIH) of Consumption
Due to Milton Friedman (1957)
...
Similarly as in the Life Cycle Hypothesis under the Permanent Income
Hypothesis consumption should depend on more than just current income and people
want to avoid fluctuations in their consumption over their lives
...
This is given by your lifetime resources as in the
LCH (wealth plus income over the future) divided by he number of years you expect
to live (average)
...

This is the random part of income that is unexpected
...

Suppose that you expect to get that salary every year in the future
...
However assume that this year, since you have been very
productive, you receive a bonus of £5000
...


According to PIH consumers use saving and borrowing to smooth consumption in
response to transitory changes in income
...
Thus,
permanent income changes are mostly consumed while temporary income changes are
mostly saved
...
If instead
you win the lottery, this represents a transitory income and you will probably not
consume all of this transitory income
...

Equation 10) is in practice the same as equation 7), the only difference is the
economic reasoning behind the two
...

Y ↑ because Y P ↑ while Y T does not change
...

Y

The Random Walk Hypothesis of Consumption
This is due to Robert Hall (1978)
...

If PIH-LCH is correct and consumers have rational expectations, then consumption
should follow a random walk: changes in consumption should be unpredictable
...
Only unanticipated
changes in income or wealth that alter expected permanent income will change
consumption
...

Assume that r = 0 (real interest rate is zero for simplicity) and there is no
discounting
...

A consumer chooses consumption in each period to maximise the sum of his per
period utility over his lifetime given by:

U (C1 ) + U (C 2 ) +
...
+ CT = W0 + Y1 + Y2 +
...

Assume that: per period utility function is: U (C ) = C −

a 2
C where a > 0 is a
2

constant (this is a quadratic utility function)
...

Since r = 0 the condition here becomes: MRS = 1
...
Using the specific quadratic utility function above, the MRS between C1 and C 2
is:

1 − aC1

...

1 − aC 2

This implies C1 = C 2
...
= CT
...
Using C to denote the per
period consumption, the constraint 13) implies that:

C=

T
1
(W0 + ∑ Yt )
T
t =1

14)

The right-hand side of 14) is exactly the permanent income and the right hand side of
equation 6) in the Life Cycle model
...
The main difference is that now you must form an
expectation about future variables
...
etc
...
Given that 1 and a are constants
we have E1 (1 − aC 2 ) = 1 − aE1 (C 2 )
...
Equation 18) says that the forecasting error is a random
variable in average zero (no systematic error in expectations)
...


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C t − C t −1 = ε t
Or
C t = C t −1 + ε

19)

Equation 19) is the equation of a Random Walk
...
This implies that the best prediction for tomorrow
consumption C t is today consumption C t −1 and no other variable can be helpful in
predicting future aggregate consumption
...

Moreover equation 19) says that changes in consumption are totally unpredictable
since C t − C t −1 = ε t
...


Does Aggregate Consumption Follow a Random Walk? The answer is normally no
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