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Microfoundations
Consumption and Investment
Learning Objectives
• Understand the difference between the long-run
consumption function and the short-run
consumption function.
• Understand the logic of the permanent income
hypothesis and the life cycle hypothesis.
• Know the implications of the PIH and LCH on
consumption and the business cycle
• Appreciate the strengths and weaknesses of the
PIH and LCH as explanations of consumer
behavior.
Consumption and the Business
Cycle
• Consumer spending cycles are not as
extreme as those of GDP, particularly
during recessions.
– Consumer spending usually declines by less
than GDP.
• In 1990-91, consumption declined by more than
GDP.
Consumption Spending: Selected
Facts
• Durable goods spending increased 2 to 4 times
faster than spending on non-durables and
services in expansions.
• Durable goods spending declined in every
postwar downturn except 1949 and 1953-54.
• Nondurable spending declined in only four of
the last nine recessions.
• Services increased in every recession except
for 1980.
Consumption Spending
• Consumption is defined as all spending
done by the household sector on durables,
non-durables, and services with the
exception of purchases of new housing.
Consumption Spending
• Consumption spending is determined by two
main factors:
– The macroeconomic environment of
employment and inflation.
– Individual consumer purchasing power as
reflected in household income, loans, existing
savings and other wealth.
Early Consumption Theories
• The absolute income hypothesis says that
consumption is directly related to income.
• As income rises, consumption rises but by a
smaller amount. This means we can write:
– C = a0 + bYd
• a0 is subsistence consumption. When Yd = 0, some
positive consumption still occurs.
• The coefficient b is the marginal propensity to
consume (MPC). It tells us by how much
consumption changes when disposable income
changes.
Consumption Function: Review
According to the absolute income
hypothesis, consumption spending is
directly related to disposable income.
C
/\C
The intercept of the consumption function,
a0, represents subsistence consumption.
/\Y
a0
0
The slope of the consumption function,
/\C//\Y, is called the marginal propensity
to consume. The MPC shows by how much
consumption changes as income changes.
Yd
Consumption
• Later, economists collected data to measure
the relationship between consumption and
GDP and to check its validity.
• They discovered that different sets of data
generated very different estimates of the
marginal propensity to consume.
CLR = 0.9Yd
CSR = 0.75Yd
Consumption Conflict
C
CLR = 0.9Yd
CSR = 0.75Yd
a0
0
Y
Consumption Functions
• Long-run consumption function
– When income is zero, subsistence consumption is
zero.
– Consumption rises by $0.90 for every dollar increase
in disposable income.
• Short-run consumption function
– When income is zero, subsistence consumption is
positive.
– Consumption rises by $0.75 for every dollar increase
in disposable income.
Reconciliation
• During the 1940s and 1950s, economists
determined that there are two separate
consumption functions.
– The short run function describes how income
and consumption are related over short periods
of time.
– The long run function describes how income
and consumption are related over longer
periods of time.
Forward Looking Theories of
Consumer Behavior
• Forward-looking expectations are estimates of the
future values of economic variables.
• They are based on the current and past values of
several variables and an economic model that
accounts for their behavior.
– Consumers are assumed to prefer stable patterns of
consumption.
– Consequently, they assess whether a change in income
is permanent or temporary before they spend it.
Two Theories
• Two major theories were developed to
explain the relationship between the two
consumption functions.
– The Permanent Income Hypothesis
• Milton Friedman
– The Life Cycle Hypothesis
• Franco Modigliani
The Permanent Income
Hypothesis
• People simultaneously choose how much to
consume now and how much to consume in
the future.
• To make those decisions, they consider how
much income they earn now and expect to
earn in the future as well as how much
savings they have accumulated.
Permanent Income Hypothesis
• Friedman suggested that people consume a
constant fraction (k) of their expected/permanent
income.
– C = kYP = 0.9($10,000) = $9,000 where k is the
individual’s MPC.
• k depends on individual tastes and on the variability of
income.
– YP = YP-1 + j(Y – YP-1) where j is some fraction of the
amount by which Y differs from YP-1.
– C = kYP-1 + kj(Y – YP-1) = 0.9YP-1 + 0.18(Y – YP-1)
Permanent Income Hypothesis
C = kYP-1 + kj(Y – YP-1) = C = 0.9YP-1 + 0.18(Y-YP-1)
• This equation shows that the PIH is based on a
distinction between two concepts of the MPC.
– The long-run MPC is simply the coefficient (k) of
permanent income or 0.9.
– The short-run MPC is the coefficient of a change in
actual income, kj, which is equal to the product of
the MPC and the fraction of the amount by which
actual income differs from permanent income.
Transitory Income
• Transitory income is the difference between
actual and permanent income and is not expected
to recur.
– Transitory income (Yt) is actual income minus
permanent income.
• Yt = Y – YP = Y – YP-1 – j(Y – YP-1) = (1 – j)(Y – YP-1)
• Friedman assumes that the MPC out of Yt is zero.
– Therefore, C = 0Yt + kYP = kYP.
Reconciling the Consumption Data
• According to the cross section data, highincome people had higher saving ratios than
low income people, but the long-run saving
ratio was nearly constant.
Consumption Reconciliation
CLR
C
CSR
The saving ratio, S/Y is
constant along CLR, but
it differs from S/Y on CSR
at every point except the
intersection of the two
consumption functions.
0
Y
Consumption Reconciliation
CLR
C
CSR
F
C0
CSR
B
A
0
YP-1 YP0
Y0
Y
Consumption Reconciliation
• The ratio C/Y is constant at every point
along CLR..
• At point A, where current income equals the
last period’s permanent income, the longrun consumption-income ratio just equals
the short-run consumption-income ratio and
the functions intersect.
Consumption Reconciliation
• But, if the person’s income rises to Y0, the current
estimate of permanent income (YP) rises above the
last period’s (YP-1) by a fraction (j) of the excess
of actual income over last period’s estimate (YP-1).
– YP = YP-1 + j(Y – YP-1)
• Consumption rises by k times the increase in
permanent income to C0.
– C0 = kYP-1 + kj(Y – YP-1)
Consumption Reconciliation
• At YP0, consumption lies vertically above
point A by the fraction kj times the
horizontal distance between YP-1 and Y0.
• Consumption increases only a small
amount, and at point B most of the short-run
increase in income is saved.
Consumption Reconciliation
CLR
C
CSR
CSR
F
A
0
If the change in income is
maintained, the short-run
consumption function
shifts up along the
long-run function.
Y
The Permanent Income
Hypothesis
• People try to keep their consumption about
the same over their lifetime.
– During years in which income is temporarily
high, they save most of the temporary portion
in case income temporarily dips in the future.
– During years in which income is temporarily
low, they borrow to maintain their level of
spending.
The Permanent Income
Hypothesis
• In the short run, most changes in income
and consumption are transitory or
temporary.
– Therefore, studies that use short run (quarterly)
data pick up the transitory changes in income
and consumption.
• The MPC is low because people are saving most of
the temporarily high income.
The Permanent Income
Hypothesis
• In the long run, most changes in transitory
income and consumption average to zero.
– Therefore, studies that use long run (10 year
averages) data pick up permanent income and
consumption.
• The MPC is high because people have
incorporated the higher income into their
expectations and have increased consumption.
The Life Cycle Hypothesis
• People simultaneously choose how much to
consume now and how much to consume in
the future.
• To make those decisions, they consider how
much income they earn now and expect to
earn in the future as well as how much
savings they have accumulated.
The Life Cycle Hypothesis
• Modigliani argued that people base their
consumption decisions on the present value
of their lifetime income.
• He suggested that consumption, income and
saving vary over a person’s lifetime.
Life Cycle Hypothesis
• During working years people’s income
exceeds consumption and people save and
accumulate assets.
• At retirement, people begin to dissave,
drawing down their accumulated assets.
• At death all assets have been depleted.
Yd
Saving
C
Consumption Dissaving
0 Working Years
W
This picture depicts disposable income,
consumption and saving during a typical
person’s lifetime
Retirement
This picture shows the accumulation of
saving during working years and
decumulation during retirement.
0 Working Years
Retirement
Life Cycle Hypothesis
• No initial assets
– Total lifetime consumption of C0 per year for L
years just equals totally income Y0 per year for
R years.
• C0L = Y0R or C0 = (R/L)Y0
Life Cycle Hypothesis
• The simple version of the LCH explains the
positive association of saving and income.
– A rising GDP per capita, increases both the
saving and income of those of working age
relative to those who are retired.
Life Cycle Hypothesis
• The simple version of the LCH also
explains the long-run constancy of S/Y
– S/Y is constant if the population in each
historical era is divided into the same
proportions of working and retired people, and
if each age group has the same saving behavior.
Life Cycle Hypothesis
• The role of assets
– If a person has an initial endowment of assets,
A, and plans to spend those assets over his or
her lifetime rather than leave an inheritance,
consumption can be higher and saving lower in
any period since the asset endowment provides
more spending power.
– The consumption function becomes:
• C1L = A + Y0R
or C1 = A1/L + R/LY0
Life Cycle Hypothesis
• Modigliani was the first to point out the
importance of assets for consumption
decisions.
– Empirical work indicates that the marginal
propensity to consume out of accumulated
assets is roughly 0.03 to 0.06 cents out of every
$1 increase in wealth.
Consumption and the Business
Cycle
• There are two reasons why consumption
spending is less volatile than GDP.
– The PIH and LCH suggest that consumption
spending does not fully reflect changes in
disposable income.
• When income rises (falls), consumption spending
rises (falls) by less.
Consumption and the Business
Cycle
– Disposable income is less volatile than GDP
because of the automatic stabilization
properties of fiscal policy.
• Progressive taxation and transfers dampen the fall in
disposable income during recessions.
PIH, LCH and Policy
• The PIH and LCH have two policy lessons:
– Permanent policies will have more impact on
the economy than temporary policies.
– Monetary policy, through its effect on the
value of people’s wealth, can affect
consumption.
Summary
• The short run and long run consumption
functions differ.
– The short run consumption function has a
positive intercept and a lower MPC than the
long run function.
– The long run consumption function has no
positive intercept.
Summary
• According to the PIH and LCH, the short
run consumption function has a lower MPC
and a positive intercept because short term
movements in income are dominated by
transitory changes.
Summary
• The PIH and LCH assume that people try to
smooth their consumption over their
lifetime by saving transitory increases in
income and dissaving to maintain
consumption during transitory decreases in
income.
Does the LCH Fit the Facts?
• The LCH suggests the following:
– Elderly people dissave.
– People smooth their consumption over time.
Dissaving among the Elderly
• The retired elderly do dissave on average,
but they do not dissave as much as the life
cycle model predicts. Why?
– A person’s lifespan is uncertain and the elderly
may be hesitant to dissave too quickly and run
out of money.
– The elderly want to leave an inheritance to their
heirs.
• Some research supports this idea; other research
indicates that most inheritances result from sudden
death.
Consumption Smoothing
• People do not tend to smooth their
consumption as much as predicted.
– According to the LCH, the MPC from
transitory income is about 5 to 10 percent as
large as the MPC from permanent income.
– The data show that the MPC from transitory
income is about 30 percent as large as the
MPC from permanent income.
Consumption Smoothing
• The early work on these hypotheses
suggested that people base their estimates of
future income on past income using simple
rules of thumb such as the average income
over the past several years.
• Robert Hall suggested that people form
expectations about future income using
rational expectations.
Rational Expectations and
Consumption
• Rational expectations means that people use
all available information, avoid systematic
mistakes, and know the economic model that is
generating their lifetime income.
• Anticipated changes in income, then, would
not change consumption. Only unexpected
changes in income would affect consumption
decisions as people update their expectations
of their permanent income.
Rational Expectations and
Consumption
• Hall’s theory means that because people are
rational, only random changes in income are
not anticipated.
• Therefore, changes in consumption are also
unexpected and random.
• Hall’s theory does not fit the data.
– Changes in aggregate consumption are not
random.
– When income rises even if it is expected,
consumption also rises.
Rational Expectations and
Consumption
• Hall concluded that either people did not form
expectations about future income rationally or
they are unable to borrow against future
income to finance their present consumption.
• Of the two possibilities, economists favor the
liquidity constraint hypothesis.
– Even if people could perfectly anticipate their
lifetime earnings, it is unlikely that they could
borrow enough from future income to completely
smooth consumption over their lifetimes.
Investment
Learning Objectives
• Understand the relationship between changes in
GDP and changes in investment as hypothesized
by the accelerator model.
• Appreciate the strengths and weaknesses of the
accelerator model.
• Learn how an interaction between the multiplier
and the accelerator can generate a business cycle.
• Know the limitations of the multiplier/accelerator
model.
Investment and the Business
Cycle
• Investment increases more rapidly in
expansions and decreases more rapidly in
recession than other GDP components.
– This volatility is the main cause of cyclical
fluctuations in overall economic activity.
Investment: Selected Facts
• Plant and equipment spending increased
more rapidly than GDP in seven of the nine
expansions.
– Plant and equipment outlays typically
increased 60 to 75 percent faster than GDP.
• In 1980-81 expansion, investment increased 135%
faster. In the 1982-1990 expansion, it was 40%
faster.
Investment: Selected Facts
• Plant and equipment spending declined
more rapidly than GDP in eight of the nine
recessions.
– Plant and equipment investment most
commonly fell by two to three times the rate of
decline in GDP.
Investment and the Business
Cycle
• The sharp cyclical pattern arises because
investment in plant and equipment is
deferrable.
– Firms can make do with existing equipment
although doing so may result in profits below
potential.
• The facilities are less efficient than technology
would permit and are unable to meet sudden surges
in demand.
Investment and the Business
Cycle
• Residential fixed investment increased
faster than real GDP in five of the last nine
recessions, and decreased more than real
GDP in five of the last nine expansions.
The Accelerator Theory of
Investment
• The acceleration principle asserts that net
investment is a function of the rate of
change in final output, not the absolute
level of output.
– Let Y = Output
– Let K = Capital Stock
– Let A = K/Y= Capital-output ratio
The Accelerator Model
• Assumptions:
– Other things remaining the same at full
capacity with no change in technical
conditions, increases in output require
additional capital equipment.
• If the capital-output ratio is $3/$1, then every $1
increase in output requires an additional $3 in
capital equipment.
• A = K/Y = /\K//\Y
The Accelerator Model
• Assumptions:
– A change in capital is the same thing as a
change in investment.
• A = I//\Y
• I = A x /\Y
Substitute I for /\K
Solve for I
The Accelerator Model
• Model:
– I = A x /\Y is the formal algebraic expression of
the acceleration principle.
– It says that there is some coefficient A which,
when multiplied by the change in output, will
yield the required net investment expenditure.
The Accelerator Model
• Logic:
– Given a fixed technical relationship between
capital and output, the amount of investment
will vary directly with the size of the absolute
change in output.
• The acceleration principle means that
investment is a function of the rate of
change in final output.
Acceleration Principle
• The acceleration principle helps to explain
why the output of capital goods fluctuates
much more violently than the output of
goods in general.
• The acceleration principle can also be used
to explain why inventories fluctuate more
violently than the output of goods in
general.
Acceleration Principle: Example
Period
Capital
Stock
1
2
3
4
300.0
Output
Replacement
Demand
100.0
30.0
Demand for Total Demand
New Capital
for Capital
0.0
30.0
Output = 100 units per period and the capital-output ratio is 3.
Capital has an average economic life of 10 periods, so normal
replacement demand for capital equipment is 30 units per period or
10% of the capital stock.
Acceleration Principle: Example
Period
Capital
Stock
1
2
3
4
300.0
330.0
Output
Replacement
Demand
100.0
110.0
30.0
30.0
Demand for Total Demand
New Capital
for Capital
0.0
30.0
30.0
60.0
Period 2:
Demand for final output increases by 10%, causing output to rise to 110.
Given a capital-output ratio of 3/1, demand for new capital increases by 30.
Total demand for capital increases by 60 (new plus replacement).
Acceleration Principle: Example
Period
Capital
Stock
1
2
3
4
300.0
330.0
346.5
Output
Replacement
Demand
100.0
110.0
115.5
30.0
30.0
30.0
Demand for Total Demand
New Capital
for Capital
0.0
30.0
16.5
30.0
60.0
46.5
Period 3:
Demand for final output increases by 5%, causing output to rise to 115.5.
Given a capital-output ratio of 3/1, demand for new capital increases by
16.5.
Total demand for capital increases by 46.5 (new plus replacement).
Acceleration Principle: Example
Period
Capital
Stock
Output
Replacement
Demand
1
2
3
4
300.0
330.0
346.5
346.5
100.0
110.0
115.5
115.5
30.0
30.0
30.0
34.6
Demand for Total Demand
New Capital
for Capital
0.0
30.0
16.5
0.0
30.0
60.0
46.5
34.6
Period 4:
Demand for final output does not increase.
Given a capital-output ratio of 3/1, demand for new capital is zero
Total demand for capital increases by 34.6 (replacement = 10% of capital
stock).
Acceleration Principle: Example
• New investment expenditures increased
only so long as final demand was increasing
at an increasing rate.
• Once final demand stabilized at a new
higher level, new investment expenditures
ceased.
• Total investment rose to a peak and then fell
back to replacement level.
Evaluation of the Accelerator
Principle
• The acceleration principle has been used as
part of the explanation of the business
cycle.
– It helps to explain the accelerated increase in
demand for capital and inventories in the
upswing of a cycle.
Evaluation of the Accelerator
Principle
– It also helps to explain the accelerated
decrease in demand for capital and
inventories in the downturn.
• The downturn may occur because the rate of
increase in the demand for consumer goods has
slowed.
The Multiplier-Accelerator
Interaction Hypothesis
• The multiplier process explains why income
and expenditures rise or fall in a cumulative
process given an autonomous change in
spending.
• The accelerator principle states that some
portion of investment is determined by the
change in output or income.
• The combination of the multiplier and the
accelerator can generate cycles.
Multiplier/Accelerator Example
• Let the consumption function be:
– C = 60 + 0.8Y
• Let the accelerator function be:
– /\I = A(Y1 – Y0) where A = 1
• Let the initial levels in period 0 of Y, C and
I be 800, 700 and 100 respectively.
• Let I rise in period 1 by 10.
Period
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Y
800.0
810.0
828.0
850.4
872.7
890.5
900.2
899.8
889.5
871.2
848.8
826.5
809.0
799.7
800.4
811.1
C
I
700.0
700.0
708.0
722.4
740.3
758.2
772.4
780.1
779.8
771.6
757.0
739.0
721.2
707.2
699.7
700.4
100
110
110
110
110
110
110
110
110
110
110
110
110
110
110
110
/\I=A/\Y
Total I
0
0
10.0
18.0
22.4
22.3
17.8
9.7
-0.36
-10.3
-18.2
-22.5
-22.2
-17.5
- 9.3
0.75
100.0
110.0
120.0
128.0
132.4
132.3
127.8
119.7
109.6
99.7
91.7
87.5
87.7
92.4
100.7
110.8
Multiplier-Accelerator Model
• Given these assumptions about the values of
the MPC and A, the model generates two
turning points.
– In period 6, the model peaks
– In period 13, the model bottoms
Multiplier-Accelerator Model
• Note that investment declines in period 5
and that the increase in output from period 4
to period 5 was less than the increase from
period 3 to 4.
• Similarly, investment increases in period 13
after the decrease in output from period 11
to period 12 was less than the decrease from
period 10 to 11.
Limitations of the Model
• Net investment does not respond instantaneously
to changes in output growth, but rather displays
noticeable lags that are not uniform in length.
• Net investment does not respond to accelerations
and decelerations in real GDP growth with
uniform speed.
• The overall level of net investment relative to real
GDP does not have a consistent long-term
relationship to real GDP growth.
Limitations of the Model
• The acceleration principle is effective only when
an industry or economy is operating at full
capacity.
– Additional capital is needed only if the existing
capacity is fully utilized.
• When an expansion begins, there is usually unused capacity in
an industry so that the first effect of an increase in demand for
consumer goods is a fuller utilization of existing capacity,
followed by the addition of more shifts, and then the purchase
of new capital.
Limitations of the Model
– As the economy approaches full employment of
workers and other resources, prices, especially
those of basic raw materials, are bid up.
• Therefore, the full acceleration principle cannot hold
completely.
Flexible Accelerator
• According to the flexible accelerator
hypothesis, investment spending is linked to
a gap between the desired capital stock and
the actual capital stock.
– The gap is not expected to be wholly closed in
one period.
Flexible Accelerator
• Model:
– I = a(K* – Kt-1)
• a = proportion of the gap between K* and Kt-1
• K* = desired capital stock
• Kt-1 = capital stock in the previous period
• Logic:
– When there is a change in demand that requires
more capital goods, the adjustment will be
spread over a number of periods.
Flexible Accelerator: Determinants
of Gross Investment
• The larger the gap between desired capital and
last period’s actual capital, the more current
investment responds to the change in last period’s
output.
• The higher the response of expected output to
last period’s error in estimating actual output, the
more expected output and investment respond to
any unexpected change in last period’s actual
output.
Flexible Accelerator: Determinants
of Gross Investment
• The proportion of the capital stock that is
replaced each year.
– Long-lived capital investment can be delayed. If it is
delayed until sales are strong, total investment will
respond ever more than the simple accelerator suggests.
• Investment responds more to changes in expected
output in capital intensive industries.
– Thus, faster growth expectations in more capital
intensive industries will spur more investment.