CONSUMPTION NOTES
We discuss the consumption choices of individuals .the theory of
intertemporal choice was developed by irving fisher (1867-1947)the
intertemporal choice theory is about individual not aggregate
consumption but it does not have important implication for aggregate
consumption because aggregate consumption is the sum of consumption by individuals fisher observed that people do not just have a budget constraint for today or for the current period but also for tomorrow or the future .he further observed that people can trade off consumption today for consumption tomorrow by saving or not saving. This means that the budget constraints for each period are linked together. The collection of budget constraint for all the periods plus the linkages between them gives us the inter-temporal budget constraints. This is the constraint limiting the choices; people have between consuming today and consuming tomorrow
YC=current received by consumers
Yf=future income received by consumers
Cc=current consumption of the consumers
Cf=future consumption
S=how much the currently save
R=interest rate R>0.
If people prefer consuming today rather than in the future This implies
that the budget constraint today can be written as Cc=Yc-S Or the level
of consumption today equals the level of income less what was saved.
If borrowing occurs, then s is <0 so, current consumption is greater than current income S<0 and Cc>Yc The budget constraint in the future is
given by Cf=(1+r)s+Yf Or the level of consumption in the future +future
income +whatever has been saved from today.
if S>0, then there is positive interest positive interest as well as
future Y.if S>0,then the consumer pays some of their income to repay the
borrowing that occurred today at the interest rate incurred S+Yc-Cc
Substituting the equation tomorrow‘s budget constraint
Cf+(1=r)(Yc-Cc)+Yf…………………2 Rearranging this equation and dividing both
sides by (1+r) we get the following equation Cc+Cf(1+r) 1 =Yc+Yf(1+r) 1
…………………………intertemporal budget constraint
It is important to note that if r>0, then future income and consumption
are discounted. This discounting of future income and consumption occurs
because of the interest earned on savings The discount factor(1+r) is
the price of the future consumption measured in terms of today‘s
consumption .it is the amount of current consumption that the consumer I
must give up to obtain one unit of future consumption .Since r>0,then
(1+r)1 is a unit of current consumption If borrowing or saving did not
take place then the budget constraint would just be Yc=Cc and future
budget constraint will be Yf=Cf
7.2 Consumer preference
Fischer observed that people will have preferences regarding consumption
over different periods .we represent such preferences in the following
diagram
The indifference curve shows the combination of current and future
consumption that makes the consumer equally happy. The slope at any
point on an indifference curve measures the MRS between current and
future consumption. Higher Indifference curves are preferred to lower
indifference curve
7.3 Optimal consumption point
Assume that consumers chose their consumption to maximize their utility.
Given the income of the consumer and the interest rate, the consumer
will therefore choose the highest indifference curve that their budget
constraint allows. This occurs where the budget line is target to
indifference curve
It is important to note that there is a key characteristic of this point
of tangency .it occurs where the slope of the budget line we =slope of
the indifference curve. A long the budget line, any substitution s
between current and future substitution must offset each other
A long the indifference curve, the utility a person gets is the same
,this means that any substitution on the indifference curve between the
current and future period consumption must offset each other
Factors Affecting Consumption
7.4.1 Effect of changes in income on consumption
Say the current of future income increases. A change in income either
today or in the future has the same effect; it increases a person’s
present value income. That is it increases, yc+yf(1+r).we show this by a
shift outwards in the budget line
If Cc and Cf are both normal goods then their consumption increases.
That is, the consumer spreads the increase in income over both current
and future consumption regardless of when the income increases. This
tells us that current consumption primarily depends on the present value
over income over the life time of a person not just on current income.
Current income does not affect current consumption because it affects
the present value of lifetime income, but is only a small part of it and
so changes in current income will have only a small effect on current
consumption. Not that this can occur because the consumer will have only
small effects on current consumption. Note that this can occur because
the consumer is free to borrow and lend as much as they wish at the
going interest rate subject to their not going bankrupt
7.4.2 Effects of changes in the interest rate on consumption
An obvious variable that is part of the intertemporal budget constraint
is the interest rate .it determines the price for trading off
consumption between periods and the value to saving or the cost of
borrowing. When we think about an individual and a change in the
interest rate we have to consider two cases
- When the consumer borrows ,or is a dissever(s,0)
- When the consumer lends or is a saver(s>0)
There are two effects arising from increase in interest rates
- Income effect –this is the change in consumption resulting from the
movement to a different indifference curve. Given that the consumer
is a lender, rather tan a borrower they are better off and end up on
a higher indifference curve in period 1.income effect implies
increases in cc and increases in cf - Substitution effect-refers to a change in consumption resulting from
the change in relative price of consumption in two periods. Given
that r has increased then current consumption is relatively more
expensive compared to future consumption? Substitution effect
implies a fall in cc and an increase in cf. Overall .we know that cf
increases but we cannot say for certain what happens to cc. The end
result depends on which effect is stronger the graph
www.masomomsingi.com 73 shows that the case where substitution
effect dominates the income effect. Note that we are assuming that
Cc and Cf are normal goods when analyzing the income effect
7.4.3 Effects of changes in wealth on consumption
A common item which s thought to affect people‘s consumption is people‘s
wealth. In Newzealand and Australia it is commonly claimed that when
people‘s houses increase in value then this leads to an increase in
their consumption. Similarly for increases in the value of shares in the
US. How can we think about this when the intertemporal budget constraint
does not contain a wealth variable? Easy .wealth, or our stock of
assets, simply increases the present value of resources we have
available to spend on consumption. That is, if we are considering not
just income but all our resources then we just add our stock of assets
to the income we earn to get the true present value lifetime resources.
Say we denote the present value of our assets as a, then our present
value lifetime resource constraint is Yc+yf(1+r+a)
This means that a y change in the value of our assets or wealth will
have the same impact on our consumption as a change in our income. if
the value of our assets increases ,the present value of lifetime
resources increases, which is shown by a rightward parallel shift of the
budget constraint and if consumption is a normal good ,then we will
consume more both today b and in future. Note that to make it simpler,
we can just think conceptually of future income including both income
earned and also the value our assts which could be sold (this reduces
the number of symbols without changing our results)
7.5 Theories of Aggregate Consumption
1) Absolute Income Hypothesis/Keynesian consumption function
This theory of aggregate consumption was derived by john myriad Keynes
in 1930s.Keyne made some three main assumptions
- 0<MPC< where MPC=DC/DY or the MPC is the amount of extra
consumption out of etra dollar of income - APC increases as Y increases where APC =C/Y ar the APC is the ratio
of total consumption total income - Y is the predominant determinant of C and r has little impact on C.
Given these three assumptions ,the Absolute income hypothesis
can be written as
Ct=C+cYt where C>0 and 0<c<1
Ct—is aggregate consumption
C-is called autonomous consumption
c-is the marginal propensity to consume
Yt-is aggregate disposable income
This model captures the KCF or the AIH because
- The MPC ,c ,is between 0 and 1by assumption
- The interest rate is assumed to have no effect on aggregate
consumption and this is shown by by its being not included in the
aggregate consumption function - The APC falls as income increases which we can show by rearranging
our model;APC=CtYt=CYt+c which tells us that as Yt increases then
Cyt also decreases. the following graph shows what the KCF looks
like and low it relates to consumption
Keynesian Consumption Function
The success of any theory and model is that they are consistent with the
relevant to the real world data. What about the KCF/AIH? Sometimes after
Keynes theory was developed, households were surveyed and it was found
out that
- Richer households consumed more than poor ones. MPC>0
- Richer households saved more than poor ones .MPC<1
- Richer households saved larger fractions of their income which means
that APC increases as Yt increases Consumption C Income Y C Ct=C+cYt
Keynesian Consumption Function - The correlation between income and consumption was found to be very
strong .so this on this evidence the KCF seemed to be consistent
with the available real world data about consumption
The consumption puzzle Unfortunately for Keynes and his KCf, during the
1940s two pieces were produced that were not consistent with the KCF
predictions about how aggregate consumption and savings should behave
SECULAR STAGNATION DID NOT OCCUR
The first anomaly had to do with a theoretical implication of the KCF
that as Y increases, C increases but proportionately less than income.
This means the pool of savings increases more than proportionately as
income rose. Since savings equals investment in equilibrium, investment
increases proportionately more than income. But the problem is that it
does not make sense for firms to want to keep m, investing if people
were buying proportionately smaller levels of consumption goods as
compared to their incomes A long differential of infinite duration
commonly referred to as circular stagnation would then occur. It was
thought that once the 2nd world war ended, thus ending the large
government demand for goods and services that the economy will enter a
period of secular stagnation .But, it did not! What actually happened
conflicted with the theory of Keynes about how aggregate consumption
depended on aggregate income The KCF was not consistent with new time
series data After Keynes developed the KCF, Simon Kuznets created data
from the US national accounts from 1869 to the 1940s on aggregate Y and
C. It showed that C was very stable fraction of Y even as Y increased a
lot. This conflicted with the KCF .The difference arose between this
study and the earlier ones that supported the KCF because the early
studies were cross-sectional in detail(they looked at a snapshot of the
economy at a point)whereas Kuznets study was o a time series nature(It
looked at the economy over many points in time)So the evidence seemed to
indicate that there were two consumption functions: a short-run
consumption function in which the APC was basically constant with
different levels of Y. This an be graphically shown as below
2)The Life Cycle hypothesis
The KCF while able to explain aggregate consumption of the economy at a
point in time was able to explain it over time. This led to the new ways
of trying to explain aggregate consumption. Two theories were developed
at about the same time .i) one theory was developed by Franco Modigliani
,Alberto Ando and Richard Brumberg.in the 1950s.They argued 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. they
hypothesized that the income of the people varies in a known way over
people‘s ;lives and that people use savings to move income from high
income periods to low income periods known now as the life cycle
hypothesis. it is the application of the fisher model
