ECO 120- Macroeconomics
Weekend School #1
21st April 2007
Lecturer: Rod Duncan
Previous version of notes: PK Basu
Topics for discussion
• Module 1- macroeconomic variables
• Module 2- basic macroeconomic models
• Module 3- savings and investment
• What will not be discussed
– Answers to Assignment #1 (use the CSU
forum for this)
Forms of economics
• Microeconomics- the
study of individual
decision-making
– “Should I go to college
or find a job?”
– “Should I rob this
bank?”
– “Why are there so
many brands of
margarine?”
• Macroeconomics- the
study of the behaviour
of large-scale
economic variables
– “What determines
output in an
economy?”
– “What happens when
the interest rate
rises?”
Economics as story-telling
• In a story, we have X happens, then Y
happens, then Z happens.
• In an economic story or model, we have X
happens which causes Y to happen which
causes Z to happen.
• There is still a sequence and a flow of
events, but the causation is stricter in the
economic story-telling.
Kobe, the naughty dog
Modelling Kobe
• Kobe likes to unmake the bed.
• Kobe likes treats.
• We assume that more treats will lead to
fewer unmade beds.
(Not a very good) Model:
Treats↑ → Unmaking the bed↓
• We can use this model to explain the past
or to predict the future.
Elements of a good story
•
All stories have three parts
1. Beginning- description of how things are
initially- the initial equilibrium.
2. Middle- we have a shock to the system, and
we have some process to get us to a new
equilibrium.
3. End- description of how things are at the
new final equilibrium- the story stops.
•
“Equilibrium”- a system at rest.
Timeframes in economics
• In economics we also talk in terms of three
timeframes:
– “short run”- the period just after a shock has occurred
where a temporary equilibrium holds.
– “medium run”- the period during which some process
is pushing the economy to a new long run equilibrium.
– “long run”- the economy is now in a permanent
equilibrium and stays there until a new shock occurs.
• You have to have a solid understanding of the
equilibrium and the dynamic process of a model.
What are the big questions?
• What drives people to study macroeconomics?
They want solutions to problems such as:
–
–
–
–
–
–
Can we avoid fluctuations in the economy?
Why do we have inflation?
Can we lower the unemployment rate?
How can we manage interest rates?
Is the foreign trade deficit a problem?
[How can we make the economy grow faster?] Not
taken up in this class. This class focuses on short-run
problems.
Economic output
• Gross domestic product- The total market
value of all final goods and services
produced in a period (usually the year).
– “Market value”- so we use the prices in
markets to value things
– “Final”- we only value goods in their final form
(so we don’t count sales of milk to cheesemakers)
– “Goods and services”- both count as output
Measuring GDP
• Are we 40 times (655/16) better off than
our grandparents?
– Australian GDP in 1960- $15.6 billion
– Australian GDP in 2000- $655.6 billion
• What are we forgetting to adjust for?
Measuring GDP
• Population- Australia’s population was 10
million in 1960 and 19 million in 2000.
– GDP per person in 1960 = $15.6 bn / 10m
= $1,560
– GDP per person in 2000 = $655.6 bn / 19m
= $34,500
• Prices- $1,000 in 1960 bought a better lifestyle than $1,000 in 2000.
Nominal versus real GDP
• So how to correct for rising prices over
time?
– Measure average prices over time (GDP
deflator, Consumer Price Index, Producer
Price Index, etc)
– Deflate nominal GDP by the average level of
prices to find real GDP
Real GDP = Nominal GDP / GDP Deflator
Nominal versus real GDP
• We use prices to value output in
calculating GDP, but prices change all the
time. And over time, the average level of
prices generally has risen (inflation).
– Nominal GDP: value of output at current
prices
– Real GDP: value of output at some fixed set
of prices
Some Australian economic history
Australian GDP 1950-1995
600 000
500 000
Million A$
400 000
GDP
300 000
GDP Change
Real GDP
200 000
100 000
0
1950
1960
1970
1980
1990
2000
Business cycle
• The economy goes through fluctuations over
time. This movement over time is called the
“business cycle”.
– Recession: The time over which the economy is
shrinking or growing slower than trend
– Recovery: The time over which the economy is
growing more quickly than trend
– Peak: A temporary maximum in economic activity
– Trough: A temporary minimum in economic activity.
Australian business cycle
Aust Business Cycle
10
8
6
4
% Ch RGDP
2
0
1950
-2
-4
1960
1970
1980
1990
2000
Unemployment
• To be officially counted as “unemployed”,
you must:
– Not currently have a job; and
– Be actively looking for a job
• “Labour force”- the number of people
employed plus those unemployed
• “Unemployment rate”
– (Number of unemployed)/(Labour force)
Unemployment
• Working age
population = Labour
force + Not in labour
force
• Labour force =
Employed +
Unemployed
Unemployment
Unemployment over the Business Cycle
12
10
Percent (%)
8
6
Unemployment
4
Change in GDP
2
0
1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995
-2
-4
Inflation
• Inflation is the rate of growth of the
average price level over time.
• But how do we arrive at an “average price
level”?
– The Consumer Price Index surveys
consumers and derives an average level of
prices based on the importance of goods for
consumers, ie. a change in the price of
housing matters a lot, but a change in the
price of Tim Tams does not.
Consumer Price Index
• Then the CPI expresses average prices
each year relative to a reference year,
which is a CPI of 100.
CPIt = (Average prices in year t)/(Average
prices in reference year) x 100
• Inflation can then be measured as the
growth in CPI from the year before:
– Inflationt = (CPIt – CPIt-1) / CPIt-1
2.0
0.0
-2.0
Sep-04
Sep-02
Sep-00
Sep-98
Sep-96
Sep-94
Sep-92
Sep-90
Sep-88
Sep-86
Sep-84
Sep-82
Sep-80
Sep-78
Sep-76
Sep-74
Sep-72
Sep-70
Inflation
Consumer Price Inflation
20.0
18.0
16.0
14.0
12.0
10.0
8.0
6.0
4.0
Inflation
Calculating GDP
• Gross domestic product- The total market value
of all final goods and services produced in a
period (usually the year).
• Alternates methods of calculating GDP
– Income approach: add up the incomes of all members
of the economy
– Value-added approach: add up the value added to
goods at each stage of production
– Expenditure approach: add up the total spent by all
members of the economy
• The expenditure approach forms the basis of the
AD-AS model.
Expenditure approach
• GDP is calculated as the sum of:
– Consumption expenditure by households (C)
– Investment expenditures by businesses (I)
– Government purchases of goods and services
(G)
– Net spending on exports (Exports – Imports)
(NX)
Aggregate Expenditure: AE = C + I + G + NX
Consumption and savings
• We assume consumption (C) depends on
household’s disposable income:
– Disposable income YD = (Income – Taxes)
• The consumption function shows how C
changes as YD changes.
• Household savings (S) is the remainder of
disposable income after consumption.
• The savings function shows how S
changes as YD changes.
Properties of a consumption
function
• What assumptions are we going to make about
aggregate consumption of goods and services in
an economy?
– An aggregate consumption function is simply adding
up all consumption functions of all individuals in
society.
– If personal income is 0, people consume a positive
amount, through using up savings, borrowing from
others, etc, so C(0) should be greater than 0.
– As personal income rises, people spend more, so the
slope of C(Y) should be positive.
Consumption function
• Consumption is a function of YD or C =
C(YD). We assume that this relationship
takes a linear (straight-line) form
C = a + b YD
where a is C when YD is zero and b is the
proportion of each new dollar of YD that is
consumed.
• We assume that C is increasing in YD, so 0
< b < 1.
A linear consumption function
• C(Y) = a + b Y, a > 0 and b > 0
C(Y)
C(0) = a, so
even if
Y=0, C > 0.
a
Slope is b > 0,
so C is
increasing in Y.
Y
Graphing a function in Excel
• This subject use a lot of “quantitative data”
(which means lists of numbers measuring
things).
• Students will need to develop their quantitative
skills– Graphing data
– Using data to support an argument
– Modelling in Excel
• We will be using Excel during this subject. You
must become familiar with Excel.
Savings function
• Household savings is a function of YD or S =
S(YD). We assume
S = c + d YD
where c is S when YD is zero and d is the
proportion of each new dollar of YD that is saved.
• We assume that S is increasing in YD, so 0 < d <
1.
• But also households must either consume or
save their income, so C + S = YD. This can only
be true if c = -a and b +d = 1.
More terms
• Average Propensity to Consume (APC)
is consumption as a fraction of YD:
APC = C / YD
• Average Propensity to Save (APS) is
savings as a fraction of YD:
APS = S / YD
• Since all disposable income is either
consumed or saved, we have:
APC + APS = 1
More terms
• Marginal Propensity to Consume (MPC) is the
change in consumption as YD changes:
MPC = (Change in C) / (Change in YD)
• Marginal Propensity to Save (APS) is the
change in savings as YD changes:
MPS = (Change in S) / (Change in YD)
• For our linear consumption and savings
functions, MPC = b and MPS = d. If YD
changes, then consumption and savings must
change to use up all the change in YD , so
MPC + MPS = 1.
Graphing the functions
• When YD = 0, C + S = 0,
so at point A, the
intercept terms are both
just below 2 and of
opposite sign.
• The 45 degree line in the
top graph shows the level
of YD. At point D, C is
equal to YD, so S = 0.
• MPC = 0.75 is the slope
of the C function.
• MPS = 0.25 is the slope
of the S function.
What else determines C?
• Household consumption will also depend
on:
– Household wealth
– Average price level of goods and services
– Expectations about the future
• Changes in these factors will produce a
shift of the whole C and S functions.
Shifts of C and S functions
• A rise in household
wealth will increase C
for every level of YD,
so C shifts up.
• A rise in average
prices will lower the
real wealth of
households and so
lower C for every
level of YD, so C shifts
down.
Example: Alice and Sam
• Question: Alice and Sam are a typical
two-income couple who live for ballroom
dancing. Their combined salaries come to
$1,400 per week after tax. They spend:
•
•
•
•
$300 per week on rent,
$300 per week on car payments,
$200 per week on ballroom dancing functions and
$200 per week on everything else.
• (a) Calculate their APC, APS, MPC and
MPS.
Example: Alice and Sam
• Sam injures his back and is forced to take a
lighter work-load, so their combined incomes
drop to $1,000 per week. Due to the back injury,
Alice and Sam are forced to stop their ballroom
dancing, however their spending in the
‘everything else’ category rises to $300.
• (b) Calculate their APC, APS, MPC and MPS.
Create graphs to show this information.
Consumption function
•
•
The consumption function relates the level of
private household consumption of goods and
services (C) to the level of aggregate income
(Y).
We can represent the consumption function in
three different and equivalent ways.
1. An mathematical equation
2. A graph
3. A table
•
For example the consumption function could
be:
–
C = $100bn + 0.5Y
Consumption function
• We can represent this same function with
a graph.
C
C(Y) = $100bn + 0.5Y
$150bn
Slope is 0.5
The MPC is 0.5
$100bn
$100bn
Y
Consumption function
• Or we can
represent
the same
function with
a table.
• Three ways
of
representing the
same
function.
Y
C(Y) = 100 + 0.5Y
C
0
100 + 0.5 (0)
100
100
100 + 0.5 (100)
150
200
300
100 + 0.5 (200)
100 + 0.5 (300)
200
250
400
500
100 + 0.5 (400)
100 + 0.5 (500)
300
350
Exogenous variables
• Exogenous variables are variables in a
model that are determined “outside” the
model itself, so they appear as constants.
• For the aggregate expenditure model, we
treat as exogenous:
– Investment (I)
– Government consumption (G)
– Taxes (T)
– Net Exports (NX)
Aggregate expenditure
• In a closed (no foreign trade) economy:
AE = C(Y) + I + G
• In an open economy:
AE = C(Y) + I + G + NX
• Changes in a or the exogenous variables
(I, G, T or NX) will shift the AE curve. A
change in b will tilt the AE curve.
• Equilibrium occurs when goods supply, Y,
is equal to goods demand, AE.
Two sector model
• Aggregate expenditure (AE) in the two sector
model is composed of consumption (C) and
investment (I).
AE = C + I
• In this model, we treat I as exogenous, so it is a
constant.
• Let’s use the same simple linear consumption
function:
C = 100 + 0.5Y
I = 100
AE = C + I = 100 + 0.5Y + 100 = 200 + 0.5Y
Aggregate expenditure function
• This equation is a relationship between
income (Y) and aggregate expenditure
(AE).
AE = 200 + 0.5Y
$250bn
Slope is 0.5
$200bn
$100bn
Y
Aggregate expenditure function
• But we
could
also use
the table
form.
Y
0
100
C
100
150
I
100
100
AE
200
250
200
300
200
250
100
100
300
350
400
500
300
350
100
100
400
450
Equilibrium in two sector model
• Equilibrium in a model is a situation of “balance”.
In our AE model, equilibrium requires that
demand for goods (AE) is equal to supply of
goods (Y).
Y = AE = C + I
• For the equilibrium we are looking for the value
of GDP, Y*, such that goods demand and goods
supply are equal.
• In our two sector AE model that means that we
can look up our AE table and find where AE = Y.
• The equilibrium value of Y will be our prediction
of GDP for our AE model.
Equilibrium
• The
equilibrium
value of
GDP is
$400bn.
Y
C
I
AE
0
100
100
200
100
150
100
250
200
200
100
300
300
250
100
350
400*
300
100
400*
500
350
100
450
Equilibrium
• We could accomplish the same by using
our graph of the AE function.
– The AE line shows us the level of goods
demand for each value of Y.
– The 45 degree line represents the value of Y
or supply of goods.
– Equilibrium will occur when the 45 degree line
and the AE line cross. At the crossing, goods
demand is equal to goods supply for that level
of Y.
Equilibrium
Y
AE = 200 + 0.5Y
400
400
Y
• The equilibrium
value of Y is
where the 45
degree line and
the AE line
cross. Y* is at
$400bn.
Equilibrium
• Finally, if you are comfortable with the
mathematics, you can solve for the
equilibrium value of Y using the equations:
Y* = AE = 200 + 0.5Y*
Y* – 0.5Y* = 200
0.5Y* = 200
Y* = 400
• You arrive at the same answer no matter
which way you use to derive it.
Autonomous expenditure
• In our model we have two part of
aggregate expenditure:
AE = $200bn + 0.5Y
– One part does not depend on the value of Ythe $200bn. This portion is called
“autonomous expenditure”.
– The other part does depend on the value of Ythe 0.5Y.
• In our model part of autonomous
expenditure is C and part is I.
Scenario: Investment falls
• What happens if I
drops from 100
to 50 perhaps
because of
uncertainty due
to terrorism
scares?
• Equilibrium GDP
drops to 300.
Y
C
I
AE
0
100
50 150
100
150
50 200
200
200
50 250
300*
250
50 300*
400
300
50 350
500
350
50 400
Scenario
• But you could also find the same answer
with some algebra:
AE = C + I = 100 + 0.5Y + 50 = 150 + 0.5Y
Y* = AE = 150 + 0.5Y*
Y* – 0.5Y* = 150
0.5Y* = 150
Y* = 300
• Find the answer in the way you feel most
comfortable.
Multiplier
• So a $50bn drop in investment (or
autonomous expenditure) leads to a
$100bn drop in equilibrium GDP.
• The ratio of the change in GDP over the
change in autonomous expenditure is
called the multiplier:
Multiplier = (Change in GDP)/(Change in I)
Expenditure multiplier
• Imagine the government
wishes to affect the
economy. One tool
available is government
consumption, G, or
government taxes, T.
This is called “fiscal
policy”.
• Any change in G (∆G) in
our AE model will
produce:
1
ΔY 
ΔG
1 - mpc
Multiplier
• If mpc=0.75, then the
multiplier is (1/0.25) or 4,
so $1 of new G will
produce $4 of new Y.
• Our multiplier is equal to
1/(1-MPC).
• Since 0<MPC<1, our
multiplier will be greater
than 1.
• The larger is the MPC,
the larger is our multiplier.
Three sector AE model
• Now we make our model slightly more
complicated by bringing in the government. The
government has two effects on our model:
– The government raises tax revenues (T) by taxing
household incomes.
– The government purchases some goods and services
for government consumption (G).
• We treat the levels of T and G as exogenous to
our AE model. Government policy determines
what T and G will be, and policy is not affected
by the equilibrium level of GDP.
Three sector model
• Household consumption depended on
household income, Y, in our two sector model.
• In the three sector model, the income that
households have available to spend or save is
now income net of taxes, Y – T. We call this
amount “disposable income”, YD.
• The consumption function will now depend on
disposable income, not income.
C = C(Y – T) = C(YD)
Three sector model
• Our new aggregate expenditure function
includes government purchases of goods and
services, so we have:
AE = C + I + G
• Let’s assume we have the same linear
consumption function as before, but now in
disposable income:
C = 100 + 0.5 (Y – T)
• Let T = G = 50 and let I = 100. We can follow
the same steps as before to find our AE function
and then to find equilibrium GDP.
Aggregate expenditure function
• Our AE function is:
AE = C(Y – T) + I + G
AE = 100 + 0.5(Y – 50) + 100 + 50
AE = 100 + 0.5Y – 25 + 100 + 50
AE = 225 + 0.5Y
• We can also represent this as a table. Our
C function with disposable income is:
C = 100 + 0.5(Y-50) = 75 + 0.5Y
Table form
Y
C = 75 +
0.5Y
0
75
I
G
AE
100
50
225
100
125
100
50
275
200
175
100
50
325
300
225
100
50
375
400
275
100
50
425
500
325
100
50
475
Equilibrium
• If we want to find equilibrium GDP in our three
sector model, we need to find the level of GDP,
Y*, for which goods demand (AE) is equal to
goods supply (Y).
• If we look at our table, we see that for an income
level of Y of 400, AE is 425 which exceeds Y. At
an income level of Y of 500, AE is 475 which is
less than Y.
• We would guess that the equilibrium value of Y
lies between 400 and 500.
• We construct a new table of values of Y between
400 and 500.
Equilibrium
Y
C = 75 +
0.5Y
400
275
I
G
AE
100
50
425
425
287.5
100
50
437.5
450*
300
100
50
450*
475
312.5
100
50
462.5
500
325
100
50
475
Equilibrium
• The equilibrium value of Y is 450.
• We could find the answer with our
equations:
AE = 225 + 0.5Y
Y* = AE = 225 + 0.5Y*
Y* - 0.5Y* = 225
0.5Y* = 225
Y* = 450
Scenario: Investment falls
• What happens if we have the same drop in
investment in the three sector model? So I drops
from 100 to 50?
• Using our equations:
AE = 100 + 0.5(Y - T) + I + G
AE = 75 + 0.5Y + 50 + 50
AE = 175 + 0.5Y
• Solving for Y*, we get:
Y* = AE = 175 + 0.5Y*
Y* = 350
• Our multiplier = 100/50 = 2 as before.
Deriving aggregate demand
• How do average prices affect demand for goods and
services?
– Real balances effect: higher prices means our assets have less
value so people are poorer and consume less.
– Interest-rate effect: higher prices drive up the demand for
money and so drive up interest rates, at higher interest rates,
investment falls (see later)
– Foreign-purchases exports: at higher Australian prices, foreign
goods are cheaper, so net exports falls (see later)
• As the average price level rises, demand for goods and
services should fall, with all else held constant.
Deriving AD
• So as P↑, we expect:
– C↓ (real balances)
– I↓ (interest rate)
– NX↓ (foreignpurchases)
• So as P↑, we expect:
AE = C↓ + I↓ + G + NX↓
• The AE curve shifts
down.
• Equilibrium Y* falls.
Aggregate demand
• We would like to have
a relationship
between the demand
for goods and
services and the price
level. We call this the
“aggregate demand”
(AD) curve.
• The AD curve is
downward-sloping in
aggregate price.
P0
P1
AD
Y0
Y1
Y
Shifts of the AD curve
• Factors that affect the AE curve will affect the AD
curve. For example, if household wealth rose,
then C would increase for all levels of
disposable income. Demand would be higher
for all levels of prices, so the AD curve shifts to
the right.
– C: household wealth, household expectations about
the future
– I: interest rates, business expectation about the
future, technology
– G and T: changes in fiscal policy
– NX: the currency exchange rate, change in output in
foreign countries
AD and the multiplier
• A change in I will shift
the AE curve up. This
will produce a shift to
the right of the AD
curve.
• The shift in the AD
curve will be the
change in I times the
multiplier.
Aggregate supply
• The aggregate demand curve showed the
relationship between goods demand and the
average level of prices.
• The aggregate supply (AS) curve shows the
relationship between goods supply and the
average level of prices.
• By goods supply, we are thinking about all of the
goods and services provided by all the
producers in the economy.
• How does the aggregate price level affect the
aggregate level of goods and services supply?
Deriving the AS curve
• We will differentiate between goods supply in the
short-run (SR) and in the long-run (LR).
• The crucial difference between the two time
periods is that we will assume that nominal
wages for employees are fixed in the SR.
Workers’ money wages do not change in the
SR. But workers’ wages are free to move in
the LR.
• So we will have two different AS curves- the SR
AS and the LR AS curves.
Fixed nominal wages
• How can we defend the assumption that wages
are fixed in the SR?
– All wages in a modern economy are set either via
contracts between employers and employees or via a
labour agreement between unions and employers.
– These contracts specify well in advance (a few
months to several years) what the wages of a worker
will be in nominal terms.
– These contracts are usually very difficult to change.
Supply of an individual firm
• So what effect will this assumption of fixed
wages have? To think about this, we will think
about the supply of a small firm in our economy.
• Intuition: If the output price for a firm rises, but
the cost of labour stays the same, a firm will
want to increase profits by producing more
output. But if the output price and the cost of
labour both rise by the same amount, a firm will
not increase output.
Deriving the SR AS curve
• In the short-run (“SR”), since wages are
fixed, a rise in P will have no affect on W,
so individual firms will find it profitable to
increase output.
• As all firms are raising output, aggregate
supply will increase in the SR if aggregate
prices rise.
• So the SR AS curve is upward-sloping in
aggregate prices.
Deriving the LR AS curve
• We assume that workers are interested in their
real wages (wages relative to prices W/P).
• If P rises, workers will demand a compensating
W rise, so as to keep real wages the same as
before.
• In the LR, real wages are unchanged by
changes in P, so output is not affected by
changes in P.
• The LR AS curve is vertical at the “natural rate of
output”.
The LR AS curve
P
• The LR AS curve is
vertical, so long-run Y
does not depend on
prices.
• The long-run Y is
determined by:
LR AS
Low
U/E
High
U/E
YLR
Y
–
–
–
–
–
Labour skills
Capital efficiency
Technology
Labour market rules
And others…
Review: Aggregate supply
• There will be a short-run AS curve which is
upward-sloping in prices.
• The SR AS (or usually just “AS”) is
used to model scenarios.
• The long-run AS curve is vertical at the
level of potential output, since wages will
change proportionately to price changes.
• The LR AS is used (mostly) to talk
about unemployment.
Equilibrium
• Equilibrium occurs at
a price level where
goods demand (AD)
is equal to goods
supply (SR AS).
P
AS
P0
AD
Y0
Y
Unemployment
LR AS
P
P0
Y0
YLR
• The gap between the
“natural rate of
AS
output” and current
output is called the
“recessionary gap”.
Unemployment• The level of
unemployment
AD
depends on the size
Y
of this gap.
Shift in AD (C↑ or G↑ or T↓ or I↑ or
NX↑)
Shift in AD
• We start with an economy of $10tr and a price
level of 110.
• A change in autonomous expenditure causes
the AE curve to shift from AE0 to AE1. We move
to a new AD curve at AD1.
• At the old price level of 110, AD > AS by $2tr, so
prices rise, pushing AD down and AS up until we
reach out new equilibrium.
• Our new equilibrium will have higher P and Y
than when we started.
Shift in AD
Shift in AS (rise in oil prices)
AS1
P
AS0
P1
P0
AD
Y1
Y0
Y
• A rise in oil prices
raises the cost of
production for all
producers and shifts
the SR AS curve up/to
the left.
• At the old prices, AD
> AS, so prices rise
and output falls.
Business cycle
• Over the business cycle, we will have periods of
high output (booms) and periods of low output
(recessions).
• In booms, output is high and unemployment is
low, while in recessions, output is low and
unemployment is high.
• The “natural rate of unemployment” is the level
of unemployment in a “normal” period of the
economy. This is achieved when output is at
full-employment or the LR AS level.
A “Boom” in the Economy
LR AS
• An economy in a
boom is an economy
with an output level
higher than the
natural rate of output.
• Unemployment is
below the natural rate
in a boom.
P
AS
P0
AD
YLR
Y0
Y
A “Recession”
LR AS
• An economy in a
recession is an
economy with an
output level below the
natural rate of output.
• Unemployment is
above the natural rate
in a recession.
P
AS
P0
AD
Y0
YLR
Y
Sample AD-AS question
• The small country of Speckonamap is in longrun equilibrium with its aggregate demand (AD)
and short-run aggregate supply (AS) curves
intersecting on the long-run aggregate supply
curve (ASLR). The dot-com bubble in
Speckonmap’s industry bursts. Business
investment drops.
• a. Explain the short- and long-term
consequences of this bursting bubble using the
AD-AS diagram. Be as clear and complete as
you can.
Sample AD-AS question
• b. What policies could the government of
Speckonamap pursue to counter the
collapse of business investment? Think of
two different ways that the government
could shift the AD-AS curves.
Investment
• Investment can refer to the purchase of new
goods that are used for future production.
Investment can come in the form of machines,
buildings, roads or bridges. This is called
“physical capital”.
• Another type of investment is called “human
capital”. This is investment in education,
training and job skills.
• Usually when we talk about investment, we
mean investment in physical capital, but
investment should include all forms of capital.
Investment decision-making
• How to determine profitability of investment?
• Example: An investment involves the current
cost of investment (I). The investment will pay
off with some flow of expected future profits.
The future stream of profits is R1 in one year’s
time, R2 in two year’s time, … up to Rn at the nth
year when the investment ends.
• Net Present Value (NPV) = Present Value of
Future Profits (PV) – Investment (I)
Investment decision-making
• What determines investment?
– Businesses or individuals make an investment if they
expect the investment to be profitable.
• Imagine we have a small business owner who is
faced with an investment decision.
• The small business owner will make the
investment as long as the investment is
profitable.
• How to determine profitability of investment?
Profitability of an investment
• Example:
– An investment involves the current cost of investment (I).
– The investment will pay off with some flow of expected future
profits.
– The future stream of profits is R1 in one year’s time, R2 in two
year’s time, … up to Rn at the nth year when the investment
ends.
• Imagine you are the business owner. How do we decide
whether to make the investment? Can we simply add up
the benefits (profits) and subtract the costs (investment)?
Profits today = R1 + R2 + … + Rn – I?
• What is wrong with this calculation?
Present value concept
• Imagine our rule about future values was simply to add
future costs and benefits to costs and benefits today.
• Scenario: A friend offers you a deal:
– “Give me $10 today, and I promise to give you $20 in 1 years
time.”
• If we subtract costs ($10) from benefits ($20), we get a
positive value of $10. Does this seem like a sensible
decision?
• Scenario: A friend offers you a deal:
– “Give me $10 today, and I promise to give you $20 in 100 years
time.”
• If we subtract costs ($10) from benefits ($20), we get a
positive value of $10. Does this seem like a sensible
decision?
Present value concept
• Not really. The problem is that a $1 today is not the
same as a $1 in a year’s time or 100 years’ time.
• We can not directly add these $1s together since they
are not the same things. We are adding apples and
oranges.
• We need a way of translating future $1s into $1s today,
so that we can add the benefits and costs together.
• The conversion is called “present value”.
• In making the decision about our friend’s deal, we would
compare $10 today to the present value of the $20 in a
year or 100 years.
Present value concept
• An investment is about giving up something
today in order to get back something in the
future.
• So an investment decision will always involve
comparing $1s today to $1s in the future.
• Investment decisions will always involve present
values. If we subtract the present value of future
profits from costs today, we get net present
value.
Net Present Value (NPV) = Present Value of Future
Profits (PV) – Investment (I)
Net present value
• The investment rule will be to invest if
and only if:
NPV ≥ 0
• Or
Present Value of Future Profits (PV) –
Investment (I) ≥ 0
Interest rates
• Interest rates are a general term for the
percentage return on a dollar for a year:
– that you earn from banks for saving
– that you pay banks for borrowing or investing
• For example, the interest rate might be
10%, so if you put $1 in the bank this year,
it will become $(1+i) in one year’s time.
• Or if you borrow $100 today, you will have
to repay $(1+i)100 next year.
Interest Rates
18.00
16.00
14.00
12.00
10.00
Bank Interest Rates
8.00
6.00
4.00
2.00
Jan-03
Jan-00
Jan-97
Jan-94
Jan-91
Jan-88
Jan-85
Jan-82
Jan-79
Jan-76
Jan-73
Jan-70
0.00
Discounting future values
• How do we place a value today on $1 in t years’
time?
• This is called “discounting” the future value.
One way to think about this question is to ask:
– “How much would we have to put in the bank now to
have $1 in t years’ time?”
– Money in the bank earns interest at the rate at the
rate i, i>0. If I put $1 in the bank today, it will grow to
be $(1+ i)1 in one year’s time, will grow to be
$(1+i)(1+i)1 = $(1+i)2 in two years’ time and will grow
to $(1+i)n in n years’ time.
Bank account
• If we start
with $1 in
our bank
account,
what
happens to
our bank
account
over time?
Year
Value
i=.10
0
$1
$1
1
$1(1+i)
$1.10
2
$1(1+i)(1+i)
$1.21
3
$1(1+i)3
$1.33
…
…
…
n
$1(1+i)n
$(1.1)n
How much is a future $1?
• In order to have $1 next year, we would have to
put x in today:
$1 = (1+ i) $x
$x = 1/(1+i) < 1
• $1 next year is worth 1/(1 + i) today. Since i>0,
$1 next year is worth less than $1 today.
• In order to have $1 in n years’ time, we would
have to put x in today:
x = 1/(1+i)n = (1+i)-n
• $1 in n years’ time is worth 1/(1+i)n < 1 today.
PV of $1
Year
i=0.01
i=0.05
i=0.10
i=0.20
0
1
1
1
1
1
0.99
0.95
0.91
0.83
2
0.98
0.91
0.83
0.69
3
0.97
0.86
0.75
0.58
10
0.91
0.61
0.39
0.16
n
(1.01)-n
(1.05)-n
(1.10)-n
(1.20)-n
Net present value
• NPV = R1/(1+i) + R2/(1+ i)2 + … + Rn/(1+ i)n – I
• If NPV >=0, then go ahead and make the
investment. If NPV < 0, then the investment is
not worthwhile.
• As i rises, the PV of future profits will drop, so
the NPV will fall. If we imagine that there are
thousands of potential investments to be made,
as i rises, fewer of these potential investments
will be profitable, and so investment will fall.
• We expect then that I falls as i rises.
Investment decision
• Imagine we are the small business owner
we were discussing before. We have a
new project which we might invest in:
– An investment involves the current cost of
investment (I).
– The investment will pay off with some flow of
expected future profits.
– The future stream of profits is R1 in one year’s
time, R2 in two year’s time, … up to Rn at the
nth year when the investment ends.
Investment decision
Year
Benefit
Cost
PV
0
1
2
3
0
R1
R2
R3
I
0
0
0
-I
R1/(1+i)
R2/(1+i)2
R3/(1+i)3
…
…
…
…
n
Rn
0
Rn/(1+i)n
Net present value
• The NPV of the investment is the sum of
the values in the far-right column- the PVs.
NPV = R1/(1+i) + R2/(1+ i)2 + … + Rn/(1+ i)n – I
• If NPV ≥ 0, then go ahead and make the
investment. If NPV < 0, then the
investment is not worthwhile.
• Let’s look at a more concrete example that
we can put some numbers to.
Example of NPV
• Example: A small business in Bathurst
that owns photo store is considering
installing a state-of-the-art developing
machine for digital photographs.
– Cost = $12,000 (after selling current machine)
– Future benefits = $2,000 per year in extra
business every year for 10 year life-span of
machine (assume benefits start next year)
Example of NPV
Year
Benefit
Cost
PV
0
0
I
-$12,000
1
$2,000
0
$2,000/(1+i)
2
$2,000
0
$2,000/(1+i)2
3
$2,000
0
$2,000/(1+i)3
…
…
…
…
10
$2,000
0
$2,000/(1+i)10
Example of NPV
• NPV = -$12,000 + $2,000/(1+i) + $2,000/(1+i)2 +
$2,000/(1+i)3 + … + $2,000/(1+i)10
• Our NPV then depends upon the interest rate, i,
facing the small business.
• For a small business, the relevant interest rate
would be the rate that it cost raise the money,
say by taking out a bank loan.
• So the interest rate would be the bank small
business loan rate.
Example of NPV
• The NPV varies with the interest rate:
– At i=0.05, NPV = $3,443, so go ahead with
investment.
– At i=0.08, NPV = $1,420, so go ahead with
investment.
– At i=0.10, NPV = $289, so go ahead with investment.
– At i=0.12, NPV = -$700, so don’t go ahead with the
investment.
• Somewhere between a 10% and a 12% interest
rate, NPV = 0. NPV < 0 for all interest rates
greater than 12%.
Example of NPV
• Another way of thinking about this problem
is to ask “Can I repay the loan and still
make money?”
• The small business owner borrows
$12,000 from the bank and uses the
$2,000 in extra business each year to
repay the loan.
• Would the business owner repay the loan
before the machine needs to be replaced?
Example of NPV- bank loan
Year
0.05
0.08
0.1
0.12
0
-12000
-12000
-12000
-12000
1
-10600
-10960
-11200
-11440
2
-9130
-9836.8
-10320
-10812.8
3
-7586.5
-8623.74
-9352
-10110.3
4
-5965.83
-7313.64
-8287.2
-9323.58
5
-4264.12
-5898.74
-7115.92
-8442.41
6
-2477.32
-4370.63
-5827.51
-7455.49
7
-601.19
-2720.28
-4410.26
-6350.15
8
1368.75
-937.91
-2851.29
-5112.17
9
3437.19
987.06
-1136.42
-3725.63
10
5609.05
3066.03
749.94
-2172.71
3443.47
1420.16
289.13
-699.55
Present
Value
Example of a NPV- bank loan
• So for interest rates of 10% and below, the bank
loan is repaid before the machine wears out, so
the investment is worthwhile.
• For interest rates of 12% and above, the bank
loan is not repaid by the time the machine needs
to be replaced, so the investment is not
worthwhile.
• The bottom line shows that the remainder in the
bank account at the end of 10 years is the NPV
of the investment decision.
• So another way to think of NPV is as the money
left in an account at the end of a project.
Investment demand
• Instead of thinking about a single small
business, think of a whole economy of
businesses and individuals making investment
decisions.
• Some of these investment decisions will be very
good ones and some will be very poor ones.
There is a whole range.
• As i rises, the PV of future profits will drop, so
the NPV will fall. If we imagine that there are
thousands of potential investments to be made,
as i rises, fewer of these potential investments
will be profitable, and so investment will fall.
Investment demand
• If we graphed the investment demand for goods
and services (I) against interest rates, it would
be downward-sloping in i. The higher is i, the
lower is investment demand.
• What can shift the I curve? Factors that affect
current and expected future profitability of
projects:
– New technology
– Business expectations
– Business taxes and regulation
Shifts in investment demand
• Example: An increase in business
confidence/expectations raises the
expected future profits for businesses.
• At the same interest rates as before, since
the Rs are higher, the NPVs of all
investment projects will be higher.
• The investment demand curve is shifted to
the right. I is higher for all interest rates.
Uses of PV concept
• Housing valuation: We can use the PV
concept to estimate what house prices should
be.
• What do you have when you own a home? You
have the future housing services of that home
plus the right to sell the home.
• Value of housing services should be the price
people pay to rent an equivalent home. Rent is
the price of a week of housing services.
• Let’s say your home rents for $250 per week.
Housing valuation
• If you stayed in your home for 50+ years,
your house is worth the PV of 50 years of
52 weekly $250 payments plus any sale
value at 50 years. How do we calculate
the PV of such a long stream of numbers?
• Trick: For very long streams, the sum:
• PV = ($250 x 52) + ($250 x 52)/(1+i) + …
• Is very close to:
• PV = ($250 x 52) / i = $13,000 / i
Housing valuation
• So we get the house values:
–
–
–
–
–
At i=0.02, PV House = $650,000
At i=0.03, PV House = $433,000
At i=0.05, PV House = $260,000
At i=0.06, PV House = $217,000
At i=0.07, PV House = $186,000
• At a house price above this price, you are better
off selling your house and renting for 50 years.
At a house price below this price, you are better
off owning a house.
Housing valuation
• You can also see how sensitive house prices are
to the interest rate. When i rose from 6% to 7%,
the value of the house dropped $31,000.
• You can see why home owners care so much
about the home loans rates.
• But what about the resale price at 50 years?
– The PV of the house sale in 50 years time is (Sale
Price) / (1+i)50, which for most values of i is going to
be a very small number- 8% of Sale Price at 5%
interest and 3% of Sale Price at 7% interest.
Housing price bubbles
• Sometimes the price of housing can vary from
this PV of housing services price. Some
analysts argue that today’s housing prices is one
case- these periods are called “bubbles”.
• Example: At 6% interest rates our house was
worth $217,000. Let’s say Sam bought the
house for $300,000 in order to sell the house
one year from now.
• In order to be able to repay the $300,000, Sam
has to gain $18,000 (6% of $300,000) by holding
the house for a year.
Housing price bubbles
• Since Sam gets $13,000 worth of housing
services from the house, the value of the house
has to rise $5,000 to $305,000 in next year’s
sale for a total gain of $18,000.
• Even though the house is unchanged, the
“overpayment” for the house has to rise- the
house is still only worth $217,000 in housing
services- but it now sells for $305,000.
• So in a “bubble”, if people are overpaying for a
house, the overpayment has to keep rising.
Eventually people realize that the house only
generates $217,000 in services.
Housing price bubbles
• Example: In Holland in 1636, the price of some
rare and exotic tulip bulbs rose to the equivalent
of a price of an expensive house. People paid
that much in plans to resell at even higher
prices.
• In 1637, prices for tulips crashed and by 1639,
tulip bulbs were selling for 1/200th of the peak
prices.
• Bubbles tend to crash fast and dramatically.
Example: Bond Valuation
You can save money at the bank and earn a
10% yearly return on your savings. What
is the most you would be willing to pay for
(include your calculations and explain
carefully):
a. a promise of a $1 in one year’s time
(assume that this promise will not be
broken);
Example question
b. a 10 year $100 savings bond (the bond
will pay you $100 in the year 2015, where
2015 is known as the ‘maturity date’) and
do a graph of the value of the 10 year
$100 maturity in 2015 savings bond as we
get closer to the maturity date; and
Example question
c. a 10 year $100 savings bond that also
pays you $5 per year for every year that
you hold the bond (including the 10th
year).
Resources
• There are many resources available to you.
Often students hurt themselves by not taking
advantage of the resources they have.
• Books: There are plenty of macroeconomics
principles books. If you don’t understand
Jackson and McIver’s coverage, get to a library
and read a different textbook. There is also a
study guide by Bredon and Curnow referenced
in the subject outline.
• Online: There is an enormous amount of
material on the Web. Just use a search engine
and look around.
Resources
• Forum: Get into a habit of reading the CSU
forums once a week. Post questions on the
forum and join in the discussion.
• Official websites: Have a look at the websites for
government agencies like the Reserve Bank of
Australia or the Australian Bureau of Statistics.
• CSU help: Student Services at CSU has a lot of
help it can provide students with problems- look
at http://www.csu.edu.au/division/studserv/.