1. Previous version of notes: PK Basu
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 don’t 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 $15.6 billion
Australian GDP in $655.6 billion
What are we forgetting to adjust for?

12. 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 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 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.

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.

28. 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.

29. 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.
Slope is b > 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 < 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.

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.

34. 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.

35. 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(Y) = $100bn + 0.5Y
$150bn
Slope is 0.5
$100bn
The MPC is 0.5 Y
$100bn

41. Consumption function Y C(Y) = 100 + 0.5Y C 100 + 0.5 (0) 100
Or we can represent the same function with a table.
Three ways of represent-ing the same function. Y
C(Y) = Y C
(0)
100
(100)
150
200
(200)
300
(300)
250
400
(400)
500
(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.
Let’s use the same simple linear consumption function:
C = Y
I = 100
AE = C + I = Y = Y

45. Aggregate expenditure function
This equation is a relationship between income (Y) and aggregate expenditure (AE).
AE = Y
$250bn
Slope is 0.5
$200bn Y
$100bn

46. Aggregate expenditure functionY C I AE
100
200
150
250
300
350
400
500
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 100 200
100
200
150
250
300
350
400*
500
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 = Y
400
400 Y

51. Equilibrium
Finally, if you are comfortable with the mathematics, you can solve for the equilibrium value of Y using the equations:
Y* = AE = Y*
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
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
100 50
150
200
250
300*
400
300
350
500

54. Scenario But you could also find the same answer with some algebra:
AE = C + I = Y + 50 = Y
Y* = AE = Y*
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 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.

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
Let’s assume we have the same linear consumption function as before, but now in disposable income:
C = (Y – T)
Let T = G = 50 and let I = 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 = (Y – 50)
AE = Y –
AE = Y
We can also represent this as a table. Our C function with disposable income is:
C = (Y-50) = Y

62. Table form Y
C = Y I G AE 75
100 50
225
125
275
200
175
325
300
375
400
425
500
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 50 425 287.5 437.5 450*
300
475
312.5
462.5
500
325

65. Equilibrium The equilibrium value of Y is 450.
We could find the answer with our equations:
AE = Y
Y* = AE = Y*
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 = (Y - T) + I + G
AE = Y
AE = Y
Solving for Y*, we get:
Y* = AE = Y*
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: The AE curve shifts down.
C↓ (real balances)
I↓ (interest rate)
NX↓ (foreign-purchases)
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
High
U/E
Low
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 > 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)
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. 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
YLR Y0 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 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.

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 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)

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 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?

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?
“Give me $10 today, and I promise to give you $20 in 100 years time.”

96. 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.

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 $(1+i) in one year’s time.
Or if you borrow $100 today, you will have to repay $(1+i)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, 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.

102. Bank account Year Value i=.10 $1 1 $1(1+i) $1.10 2 $1(1+i)(1+i) $1.21$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
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/(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.

104. PV of $1
Year
i=0.01
i=0.05
i=0.10
i=0.20 1
0.99
0.95
0.91
0.83 2
0.98
0.69 3
0.97
0.86
0.75
0.58 10
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/(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.

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 year’s time, R2 in two year’s time, … up to Rn at the nth year when the investment ends.

107. Investment decision Year Benefit Cost PV I -I 1 R1 R1/(1+i) 2 R2I -I 1 R1
R1/(1+i) 2 R2
R2/(1+i)2 3 R3
R3/(1+i)3 … n Rn
Rn/(1+i)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/(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.

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 I -$12,000 1 $2,000 $2,000/(1+i) 2I
-$12,000 1
$2,000
$2,000/(1+i) 2
$2,000/(1+i)2 3
$2,000/(1+i)3 … 10
$2,000/(1+i)10

111. 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.

112. 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%.

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
-12000 1
-10600
-10960
-11200
-11440 2
-9130
-10320 3
-9352 4 5 6 7 8 9
987.06 10
749.94
Present Value
289.13

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.
Let’s 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)/(1+i) + …
Is very close to:
PV = ($250 x 52) / i = $13,000 / i

121. 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.

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) / (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.

123. 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.

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 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.

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 year’s 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 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.

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