ECO 120- Macroeconomics

1
ECO 120- Macroeconomics

• Weekend School 1
• 21st April 2007
• Lecturer Rod Duncan
• Previous version of notes PK Basu

2
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)

3
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?

4
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.

5
Kobe, the naughty dog
6
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.

7
Elements of a good story

• All stories have three parts
• Beginning- description of how things are
  initially- the initial equilibrium.
• Middle- we have a shock to the system, and we
  have some process to get us to a new equilibrium.
• End- description of how things are at the new
  final equilibrium- the story stops.
• Equilibrium- a system at rest.

8
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.

9
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.

10
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 dont count sales of milk to
  cheese-makers)
• Goods and services- both count as output

11
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?

12
Measuring GDP

• Population- Australias 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 life-style
  than 1,000 in 2000.

13
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

14
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

15
Some Australian economic history
16
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.

17
Australian business cycle
18
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)

19
Unemployment

• Working age population Labour force Not in
  labour force
• Labour force Employed Unemployed

20
Unemployment
21
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.

22
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

23
Inflation
24
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.

25
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

26
Consumption and savings

• We assume consumption (C) depends on households
  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.

27
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.

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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 lt b lt
  1.

29
A linear consumption function

• C(Y) a b Y, a gt 0 and b gt 0

C(Y)
C(0) a, so even if Y0, C gt 0.
Slope is b gt 0, so C is increasing in Y.
a
Y
30
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.

31
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 lt d lt
  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.

32
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

33
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.

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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.

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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.

36
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.

37
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.

38
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.

39
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.
• An mathematical equation
• A graph
• A table
• For example the consumption function could be
• C 100bn 0.5Y

40
Consumption function

• We can represent this same function with a graph.

C
C(Y) 100bn 0.5Y
150bn
Slope is 0.5
100bn
The MPC is 0.5
Y
100bn
41
Consumption function

• Or we can represent the same function with a
  table.
• Three ways of represent-ing the same function.

Y C(Y) 100 0.5Y C
0 100 0.5 (0) 100
100 100 0.5 (100) 150
200 100 0.5 (200) 200
300 100 0.5 (300) 250
400 100 0.5 (400) 300
500 100 0.5 (500) 350
42
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)

43
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.

44
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.
• Lets use the same simple linear consumption
  function
• C 100 0.5Y
• I 100
• AE C I 100 0.5Y 100 200 0.5Y

45
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
Y
100bn
46
Aggregate expenditure function
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

• But we could also use the table form.

47
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.

48
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
49
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.

50
Equilibrium

• The equilibrium value of Y is where the 45 degree
  line and the AE line cross. Y is at 400bn.

Y
AE 200 0.5Y
400
Y
400
51
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.

52
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 Y- the
  200bn. This portion is called autonomous
  expenditure.
• The other part does depend on the value of Y- the
  0.5Y.
• In our model part of autonomous expenditure is C
  and part is I.

53
Scenario Investment falls
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

• What happens if I drops from 100 to 50 perhaps
  because of uncertainty due to terrorism scares?
• Equilibrium GDP drops to 300.

54
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.

55
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)

56
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

57
Multiplier

• If mpc0.75, 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 0ltMPClt1, our multiplier will be greater
  than 1.
• The larger is the MPC, the larger is our
  multiplier.

58
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.

59
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)

60
Three sector model

• Our new aggregate expenditure function includes
  government purchases of goods and services, so we
  have
• AE C I G
• Lets 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.

61
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

62
Table form
Y C 75 0.5Y I G AE
0 75 100 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
63
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.

64
Equilibrium
Y C 75 0.5Y I G AE
400 275 100 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
65
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

66
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.

67
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.

68
Deriving AD

• So as P?, we expect
• C? (real balances)
• I? (interest rate)
• NX? (foreign-purchases)
• So as P?, we expect
• AE C? I? G NX?
• The AE curve shifts down.
• Equilibrium Y falls.

69
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
70
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

71
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.

72
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?

73
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.

74
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.

75
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.

76
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.

77
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.

78
The LR AS curve

• The LR AS curve is vertical, so long-run Y does
  not depend on prices.
• The long-run Y is determined by
• Labour skills
• Capital efficiency
• Technology
• Labour market rules
• And others

P
LR AS
Low U/E
High U/E
YLR
Y
79
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.

80
Equilibrium

• Equilibrium occurs at a price level where goods
  demand (AD) is equal to goods supply (SR AS).

P
AS
P0
AD
Y0
Y
81
Unemployment
LR AS

• The gap between the natural rate of output and
  current output is called the recessionary gap.
• The level of unemployment depends on the size of
  this gap.

P
AS
P0
Unemployment
AD
Y0
YLR
Y
82
Shift in AD (C? or G? or T? or I? or NX?)
83
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 gt 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.

84
Shift in AD
85
Shift in AS (rise in oil prices)
AS1

• 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 gt AS, so prices rise and
  output falls.

P
AS0
P1
P0
AD
Y1
Y0
Y
86
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.

87
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
Y0
YLR
Y
88
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
89
Sample AD-AS question

• The small country of Speckonamap is in long-run
  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 Speckonmaps
  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.

90
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.

91
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.

92
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 years
  time, R2 in two years time, up to Rn at the
  nth year when the investment ends.
• Net Present Value (NPV) Present Value of Future
  Profits (PV) Investment (I)

93
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?

94
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 years
  time, R2 in two years 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?

95
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?

96
Present value concept

• Not really. The problem is that a 1 today is
  not the same as a 1 in a years 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 friends deal,
  we would compare 10 today to the present value
  of the 20 in a year or 100 years.

97
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)

98
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

99
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 (1i) in one years time.
• Or if you borrow 100 today, you will have to
  repay (1i)100 next year.

100
Interest Rates
101
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, igt0. If I put 1 in the bank today,
  it will grow to be (1 i)1 in one years time,
  will grow to be (1i)(1i)1 (1i)2 in two
  years time and will grow to (1i)n in n years
  time.

102
Bank account
Year Value i.10
0 1 1
1 1(1i) 1.10
2 1(1i)(1i) 1.21
3 1(1i)3 1.33

n 1(1i)n (1.1)n

• If we start with 1 in our bank account, what
  happens to our bank account over time?

103
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/(1i) lt 1
• 1 next year is worth 1/(1 i) today. Since
  igt0, 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/(1i)n (1i)-n
• 1 in n years time is worth 1/(1i)n lt 1 today.

104
PV of 1
Year i0.01 i0.05 i0.10 i0.20
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
105
Net present value

• NPV R1/(1i) R2/(1 i)2 Rn/(1 i)n I
• If NPV gt0, then go ahead and make the
  investment. If NPV lt 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.

106
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 years
  time, R2 in two years time, up to Rn at the
  nth year when the investment ends.

107
Investment decision
Year Benefit Cost PV
0 0 I -I
1 R1 0 R1/(1i)
2 R2 0 R2/(1i)2
3 R3 0 R3/(1i)3

n Rn 0 Rn/(1i)n
108
Net present value

• The NPV of the investment is the sum of the
  values in the far-right column- the PVs.
• NPV R1/(1i) R2/(1 i)2 Rn/(1 i)n I
• If NPV 0, then go ahead and make the
  investment. If NPV lt 0, then the investment is
  not worthwhile.
• Lets look at a more concrete example that we can
  put some numbers to.

109
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)

110
Example of NPV
Year Benefit Cost PV
0 0 I -12,000
1 2,000 0 2,000/(1i)
2 2,000 0 2,000/(1i)2
3 2,000 0 2,000/(1i)3

10 2,000 0 2,000/(1i)10
111
Example of NPV

• NPV -12,000 2,000/(1i) 2,000/(1i)2
  2,000/(1i)3 2,000/(1i)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.

112
Example of NPV

• The NPV varies with the interest rate
• At i0.05, NPV 3,443, so go ahead with
  investment.
• At i0.08, NPV 1,420, so go ahead with
  investment.
• At i0.10, NPV 289, so go ahead with
  investment.
• At i0.12, NPV -700, so dont go ahead with
  the investment.
• Somewhere between a 10 and a 12 interest rate,
  NPV 0. NPV lt 0 for all interest rates greater
  than 12.

113
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?

114
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
Present Value 3443.47 1420.16 289.13 -699.55
115
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.

116
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.

117
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

118
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.

119
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.
• Lets say your home rents for 250 per week.

120
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)/(1i)
• Is very close to
• PV (250 x 52) / i 13,000 / i

121
Housing valuation

• So we get the house values
• At i0.02, PV House 650,000
• At i0.03, PV House 433,000
• At i0.05, PV House 260,000
• At i0.06, PV House 217,000
• At i0.07, 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.

122
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) / (1i)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.

123
Housing price bubbles

• Sometimes the price of housing can vary from this
  PV of housing services price. Some analysts
  argue that todays housing prices is one case-
  these periods are called bubbles.
• Example At 6 interest rates our house was
  worth 217,000. Lets 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.

124
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 years 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.

125
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.

126
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 years time (assume
  that this promise will not be broken)

127
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

128
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).

129
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 dont understand
  Jackson and McIvers 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.

130
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/.