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The impact of Expectations on
Consumption and Investment and
the IS/LM Expectations Model
Introduction
The purpose of this Lecture is three-fold:
i.
ii.
iii.
The role expectations play in determining consumption
decisions. We will show that they depend not only on
current income but also on expected future income and
financial wealth;
The role expectations play in determining investment
decisions. We will show that they depend on current and
expected profit and current and expected real interest
rates;
Derive the Expectations IS/LM model and reconsider
the short-run effects on output of changes in monetary
and fiscal policies.
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We have considered the role of expectations in financial
markets.
Now we have to consider the role of expectations in
determining consumption and investment (the two main
components of aggregate demand)
Once this is done we will have the main foundations for
the expanded IS/LM model which we will call the
expectations IS/LM model.
Recall that the basic IS curve assumes that:
1. people determine how much to consume and save on
the basis of current income.
2. Investment depends on current nominal interest rate
and the current level of sales
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These are unsatisfactory assumptions!
We have already argued that investment decisions depend
not on the nominal interest rate but on the real interest
rate. However we have to extend the analysis to reflect
that investment depends not only on the current real
interest rate and current sales but also on the expectations
of future real interest rates and future sales!
Consumption also does not simply depend on current
income but should also depend upon expectations of
future income.
Expectations and
Consumption
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Consumption function that underpins the basic IS/LM
model is:
C = C0 + C1YD
Where C1 is 0 < MPC < 1 and YD is current disposable
income.
Our aim to develop a more realistic consumption function
that takes into account expected future income as well.
To do this we will develop a consumption function that
relies on the “Permanent income theory of consumption”
(Friedman) and “life-cycle theory of consumption”
(Modigliani)
The components of
consumption
 The consumption profile for an individual depends upon
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his total wealth accumulated over his lifetime
Total Wealth = Human Wealth + Non Human Wealth
Human Wealth is his present value of expected after-tax
income
NonHuman Wealth is the sum of his financial wealth and
housing wealth
Therefore the consumer has to decide how much to spend
out of his total wealth at each point in time.
We generally assume that consumers would like to spend
a proportion of total wealth to maintain a similar level of
consumption each year throughout his life, X.
Therefore if X is higher than current income the
consumer will borrow (to smooth consumption)
If X is lower than current income the consumer will save.
Consider a consumption function that
depends completely on total wealth:
 Ct = C(total wealtht)
 Thus consumption at time t depends upon
the sum of nonhuman wealth and human
wealth (expected present value of current
and future disposable income) at time t.

Example: 21 year-old student starting a 3 year university
course. The retirement age is 60 and taxes are 25% of your
income.
 Expect a real wage of £40,000 once you finish university
and to increase 3% p.a. in real terms.
 Assume for simplicity that nonhuman wealth is zero and real
interest rate is zero
 Expected present value is:
V(YeLt – Tet) = (£40,000)(0.75)[1 + (1.03) + (1.03)2 +….+
(1.03)36]
= £1,986,000.
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If you expect to live to the age 76 then you have 56 years of
expected life (76 – 21) in which to smooth consumption as
thus the constant level of consumption per year is £35,464.
Thus you should borrow £35,464 x 3 = £106, 392 over next
3 years while you are a student and save when you start
working!
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Thus the problem with this consumption function is that
is does not take into account the direct restrictions that
you face given your current income.
So the consumption function we will use is:
Ct = C(total wealtht, YLt – Tt )
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Consumption is an increasing function of total wealth and
also an increasing function of current disposable income.
Total wealth component captures the consumers
expectations about future income
Revised consumption function implies:
1. Expectations affect consumption directly through
human wealth since human wealth is computed by the
consumer forming expectations of future labour
income, real interest rates and taxes:
– For example consider how expectations of higher
output in the future affect consumption today:
Increase in expected future output;
Increase in expected labour income;
Increase in Human Wealth;
Increase in Consumption today.
2.
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Expectations affect consumption indirectly through
nonhuman wealth (bonds and stocks!!)
Consumers take the value of these assets as given (i.e.
they don’t compute their values as this has already been
done for them by financial markets).
However we know from earlier that the price of bonds
and stocks, depend upon expectations of future interest
rates and dividends.
Consider how expectations of higher output in the
future affect consumption today
Increase in expected future output;
Increase in expected future dividends;
Increase in stock prices;
Increase in nonhuman wealth;
Increase in consumption today
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Therefore the dependence of consumption on
expectations has two main implications for the
relationship between consumption and income.
The response of consumption to changes in
income depends on whether consumers perceive
such changes as transitory (temporary) or
permanent
Consumption may change even if current income
does not change.
Expectations and Investment
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Investment function that underpins the basic
IS/LM model is:
I = I (Y, i )
i.e. Investment demand I is positively related to
current output Y and negatively related to the
current nominal interest rate i.
Our aim to develop a more realistic investment
equation not only depends upon the real interest
rate but also takes into account expected future
output as well.
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Consider a firm who has to decide whether to make a new
investment e.g. buy a new machine.
The decision to buy a machine depends on the present value
of the profits the firm can expect from having this machine
versus the cost of buying it.
Present value > costs; then the firm should buy the machine.
In order to compute the present value of expected profits for
this investment, the firm must estimate how long the
machine will last
The rate of depreciation, , measures how much usefulness
the machine loses from one year to the next.
e.g. Reasonable values for  are between 4% and 15% for
machines, and between 2% and 4% for buildings and
factories.
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Buy the machine in year t, the machine makes its
first expected profit in year t+1, et+1;
The present value of this expected profit is
1
 e t 1
1  rt
We use real interest rate since we are measuring
profits in real terms.
Expected profit in year t+2 is (1 – ) et+2 the
present value being:
1
e
(1 rt )(1 rt1 )
(1  ) et2
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Therefore the present value of expected profits from
buying the machine in year t, V(et) is:
 
V  te 
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a)
b)
1
1
e
 te1 
(
1


)

t  2  ...
e
1  rt
(1  rt )(1  rt 1 )
Therefore aggregate investment for the whole economy
can be expressed as:
It = I (V(et) )
where It is aggregate investment and t is profit per unit of
capital for the whole economy.
Investment depends positively on the expected present
value of future profits (per unit of capital):
The higher current or expected profit, the higher is V(et)
and thus the higher the level of investment.
The higher current or expected real interest rates, the lower
is V(et) and thus the lower the level of investment.
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To see the intuition behind these results more
clearly lets assume firms operate under static
expectations i.e. they expect the future to be like
the present.
 
e
t 1
e
t 2
 ....   t
rt e1  rt e 2  ....  rt

Then the present value of expected profits is the
ratio of the profit per unit of capital to the sum of
the real interest rate and the depreciation rate
t
V 
rt  
 
e
t

And the investment equation is thus:
 t
I t  I 
 rt  
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


The denominator rt +  is the rental cost of capital
Investment depends on the ratio of profit to the
rental cost of capital
The higher the profit, the higher the level of
investment
The higher the real interest rate, the higher the
rental cost of capital, the lower the level of
investment
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Note the similarity between the present value computation
of the firm and the fundamental value of a stock:
 
1 e
1
e
V 
 t 1 
(
1


)

t  2  ...
e
1  rt
(1  rt )(1  rt 1 )
e
t



Dte1
Dte 2
Qt 

 ....
e
(1  rt ) (1  rt )(1  rt 1 )
A firm’s investment decision depends on expected profit.
Stock Price depends on expected dividends (which are paid
from firms profits) .
Therefore investment decisions and stock market prices
depend on the same factors: expected future profits and
expected future real interest rates.
q Theory of Investment
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A firm can raise the financing it needs to pay for an
investment by issuing shares.
Investors buying the shares expect to earn a return from
dividends.
Stock prices tend to be high when the firm has many
opportunities for profitable investment, because these
profit opportunities mean higher future income for
shareholders. Thus, stock prices reflect the incentives to
invest. i.e. the stock price, in effect tells the firm how
much the stock market values each unit of capital already
in place.
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James Tobin proposed that firms base their
investment decisions on the following ratio:
q
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market value of installed capital
replacemen t cost of installed capital
q > 1 then stock market values installed capital at
more than its replacement cost, so a firm can raise
the market value of its stock by buying more
capital
There is a strong relationship between Tobin’ q and
investment thus highlighting the fact that
investment decisions and stock market prices
depend on similar factors.
Tobin’s q Versus the Ratio
of Investment to Capital—
Annual Rates of Change,
1960-1999
There is a tight relation
between investment and
the value of the stock
market.
It = I (V(et) )
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So far we have constructed a new investment condition that
depends solely on expected future profits.
However empirical evidence also suggests that current profit
also plays an important role in determining whether a firm
invests.
Why? Firms may be reluctant to borrow if current profit is low.
But if current profit is high, the firm may not need to borrow to
finance its investments. It does not need to convince potential
lenders.
Therefore Investment depends upon two factors:
Profitability vs Cash Flow
Profitability is the expected present discounted value of profits
Cashflow is current profit.
Both profitability and cash flow are important for investment
decisions, and are likely to move together.
Changes in
Investment and
Changes in Profit in
the United States,
1960-2000
Investment and
profit move very
much together.
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Therefore the Investment Equation we will
use is:
I t  I (V ( e t ),  t )
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Investment decisions depend both on
expected present value of profits and on
the current level of profits!
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1.
2.
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If investment depends on both current and
expected profit, what determines profit?
Level of sales;
Existing capital stock
If sales are low relative to the capital stock,
profits per unit of capital are likely to be low as
well
Assume that sales and output are the same
(there is no inventory investment)
 Yt
 t  
 Kt
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

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Profit per unit of capital , is an increasing function of the
ratio of output (sales) Y, to the capital stock K.
For a given capital stock, the higher the output the higher
the profit.
For a given level of output, the higher the capital stock the
lower the profit.
Thus we have a link between current output, expected
future output and investment.
Current output affects current profit; expected future output
affects expected future profit; and current and expected
future profits in turn affect investment!
Derivation of the Expectations
IS/LM model;
We have shown over the last two weeks that:
 Expectations affect bond and stock prices;
 Expectations affect consumption and investment
decisions;
We are now ready to consider how the
incorporation of such expectations into the
IS/LM model impact on the effectiveness of
monetary and fiscal policy (in the short-run!)
Consumption
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An increase in current and expected future real disposable
income, or a decrease in current and expected future real
interest rates increases human wealth and leads to an
increase in consumption today;
An increase in current and expected real dividends, or a
decrease in current and expected future real interest rates
increases nonhuman wealth and leads to an increase in
consumption today;
A decrease in current and expected future nominal interest
rates leads to an increase in bond prices which leads to an
increase in nonhuman wealth and leads to an increase in
consumption today;
Investment
An increase in current and expected future
real profits, or a decrease in current and
expected future real interest rates, increase
the present value of real profits and leads to
an increase in investment today.
Expectations and
Spending: The
Channels
Expectations affect
consumption and
investment
decisions, both
directly and
through asset
prices.
IS Curve Revisited
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1.
2.
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Since expectations affect consumption and investment it
is clear that the IS curve will have to be amended.
Recall that the IS curve simply shows goods market
equilibrium.
Since expectations involve the consideration of current
and future periods we will simply the analysis by
assuming that there is only two periods.
A current period (or current year)
A future period (all future years collectively)
This means that we don’t have to keep track of
expectations about each future year.
Recall that the basic IS curve is given by:
Y = C(Y – T) + I(Y, i) + G
 Since investment depends on the real interest rate
we can amend this equation to get:
Y = C(Y – T) + I(Y, r) + G
 To introduce expectations we proceed in 2 steps:
Step 1: Define aggregate private spending
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A(Y , T , r )  C(Y  T )  I (Y , r )
And rewrite the IS equation as:
Y  A(Y , T , r )  G
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Note: nothing intuitively has changed. The properties of
aggregate private spending A, follow from the standard
properties of C and I
Aggregate private spending is an increasing function of
income Y: Higher income increases consumption and
investment
Aggregate private spending is a decreasing function of
taxes T: Higher taxes decrease consumption
Aggregate private spending is a decreasing function of
the real interest rate r: Higher r decreases investment
Step 2: Incorporate expectations by allowing spending to
depend not only on current variables but also on their
expected values in the future period.
Y  A(Y , T , r , Y ' , T ' r ' )  G
e
e
e
(  ,  , +,  ,  )
* Primes denote future values, and e’s expected values.
 The positive and negative signs explain how:
Y or Y ' e   A 
T or T ' e   A 
r or r ' e   A 
Expectations and the IS Curve
The New IS Curve
Given expectations, a
decrease in the real interest
rate leads to a small
increase in output: The IS
curve is steeply downward
sloping. Increases in
government spending, or in
expected future output, shift
the IS curve to the right.
Increases in taxes,
 Yt in
 or in
 t future
  taxes,
expected
 Kt real
the expected future
interest rate shift the IS
curve to the left.
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Notice that the new IS curve is still depicted by taking all
variables as given except current output Y and current real
interest rate r.
The IS curve is still downward-sloping. Why? A decrease in
the current real interest rate leads to an increase in spending,
which through the multiplier effect leads to an increase in
output.
However, this revised IS curve is much steeper that the
original, which means that a large decrease in the current
interest rate is likely to have only a small effect on
equilibrium output. Why?
1.
2.
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a.
b.
c.
A decrease in the current real interest rate does not have
much effect on spending if future expected rates are not
likely to be lower as well.
The multiplier is likely to be small. If changes in
income are not expected to last, they will have a limited
effect on consumption and investment.
Shifts in the IS curve arise through changes in all
variable except current Y and current r.
Increase in current taxes or future taxes shift the IS
curve to the left (consumption falls)
Increase in expected future output or a decrease in
expected future real interest rate shift the IS curve to the
right (consumption increases as consumers feel
wealthier and investment increases as profits increase)
Increase in government spending shifts the IS curve to
the right.
LM Curve Revisited
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The LM relation is not modified because the
opportunity cost of holding money today depends
on the current nominal interest rate, not on the
expected nominal interest rate one year from now.
M
 YL(i )
P
 The interest rate that enters the LM relation is the
current nominal interest rate.
Monetary Policy, Expectations and
Output
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1.
2.
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Expansionary Monetary Policy: Increase in the money
supply results in a fall in the nominal interest rate.
In the baseline IS/LM model there was only one interest
rate, the nominal interest rate i, which entered both
equations.
Now however we have many interest rates!
Nominal interest rate which enters the LM equation;
Real interest rate which enters the IS equation;
Current and expected future real interest rates which
enter the IS equation.
Need to consider the link between changes in the
nominal interest rate and changes in current and
expected future real interest rates
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Recall the Fisher Equation
r = i – πe
Thus the expected future real interest rate is equal
to the expected future nominal interest rate minus
expected future inflation
r’e = I’e – π’e
The effect on current and expected future real
interests to a change in the nominal interest rate
depends upon:
– How financial markets revise their expectations of the
future nominal interest rate, i’e.
– How financial markets revise their expectations of
both current inflation, e, and future inflation, ’e.
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To simply the analysis, assume that expected
current inflation and expected future inflation are
zero.
Therefore both current and expected future
nominal and real interest rates are the same.
e
e
e
IS: Y  A(Y , T , r , Y ' , T ' , r ' )  G
M
LM :
 YL(r )
P
The New IS-LM
The IS curve is steeply
downward sloping:
Other things equal, a
change in the current
interest rate has a
small effect on output.
The LM curve is
upward sloping. The
equilibrium is at the
intersection of the IS
and LM curves.
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Suppose that the economy is in a recession and the
monetary authority adopts an expansionary monetary
policy
Money supply increases, the LM curve shifts downwards
and the current interest rate falls. A  B.
If expectations remain unchanged then the effect of this
policy is a small increase in output
However if expectations change as a result of this change
in monetary policy then what happens?
Suppose that in response to the decrease in current
interest rates, financial markets anticipate lower interest
rates in the future and higher output in the future. Then
the IS curve shifts to the right and we get a much larger
increase in output!
The Effects of an
Expansionary Monetary
Policy
The effects of
monetary policy on
output depend very
much on whether and
how monetary policy
affects expectations.
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Therefore the impact of monetary policy on output
depend crucially on its effects on expectations
The effect of monetary policy on output depends on
whether and how changes in the short-term nominal
interest rate lead to changes in the current and the
expected future real interest rate.
Note the similarity with the effects of monetary policy on
the stock market which we considered before. If changes
in monetary policy is expected, investors, firms and
consumers do not change their expectations and
consequently there is little or no effect on output.
If however policy changes are unexpected then there can
be potentially large effects on output as expectations of
future interest rates come down, stock prices rise, and
output increases.
Fiscal Policy, Expectations and
Output
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Maintain the same assumptions as before, such
that nominal and real interest rates are the same.
We want to consider the short-run impact of a
reduction in the budget deficit (i.e. a fall in
government spending with taxes unchanged)
(G – T) 
Assume that taxes in both current period and
future period are unchanged and that government
spending falls in both periods.
What will happen to current output?
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To motivate the results that we get later, recall
the implications of this policy under the basic
IS/LM model which you consider in the autumn
term.
Short-run: IS curve shifts to the left which results
in lower output
Medium-run: deficit reduction has no effect on
output which returns to its natural rate, but leads
to a lower interest rate and higher investment.
Why? Lower government spending with output
unchanged implies that investment must have
offset the decrease in public expenditure. Thus
the interest rates must be lower for investment to
have increased.
Long-run: Higher investment leads to a higher
capital stock and thus a higher level of output.
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Clearly in our new expectations IS/LM model we
will get the same short-run results if expectations
do not change.
However what should happen to expectations?
Assume agents have Rational Expectations
i.e. expectations are formed in a forward-looking
manner. Individuals, firms and investors form
expectations about the future by assessing the
likely course of future expected policy and then
working out the implications of future activity.
The assumption of rational expectations is one of
the most important (if not the most important!)
developments in macroeconomics in the last 25
years. Designing a policy on the assumption that
people make systematic mistakes in responding to
it would be unwise!
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Assume that the future period consists of the
medium-run and the long-run. If people, firms
and financial market participants have rational
expectations then in response to the
announcement of a reduction in the budget deficit
they will expect that in the future output will
return to its natural rate in the medium-run and
increase in the long-run and future interest rates
to fall.
Thus they will revise their expectation of future
output up and their expectation of future interest
rates down, which results in a shift of the IS curve
to the right!
The Effects of a Deficit
Reduction on Current
Output
When account is taken
of its effect on
expectations, the
decrease in
government spending
need not lead to a
decrease in output.
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Net effect is ambiguous.
Expectations of higher consumption and investment may
offset the decrease in government spending.
Also highlights the difficulties of using fiscal policy for
demand-management purposes.
What we can say is the following: The smaller the
decrease in government spending today the smaller the
adverse effect on output today.
The larger the decrease in government spending in the
future period, the larger the effect on expected future
output and interest rates, thus the larger the favourable
effect on spending today.

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Therefore, small cuts in government spending
today and large expected cuts in the future will
cause output to increase more in the current
period—a concept known as backloading.
Backloading —leaving most of the reduction for
the future, not the present, however, may lead to
a problem with the credibility of the deficit
reduction policy.

To summarize, the short-run impact on output of
a particular fiscal policy crucially depends on:
– The credibility of the program
i.e will spending be cut or taxes increased in the
future as announced?
– The timing of the program
i.e How large are the spending cuts today relative to
the future?
– The composition of the program
i.e. Does the policy remove some distortions in the
economy?
– The state of government finances in the first place.
i.e. What state are they in? What will happen to them
if the policy fails?