# Intermediate Macroeconomics

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ECOS2002 Intermediate Macroeconomics
Week 5:
Christopher Gibbs
University of Sydney
Semester 1, 2021
Agenda
• The stylized facts of the business cycle
• Recap of the Keynesian goods market
• The IS relationship
The long and the short
Long-run model ) potential output, long-run inflation
• Solow-Swan and Romer models give potential output.
• MV = PY quantity theory of money gives long-run
inflation (∆M = π).
Short-run model ) current output, current inflation
• IS-LM (Old Keynesian)
• IS-MP-PC (New Keynesian)
Recessions
Definition (Recession)
Two consecutive quarters of negative real GDP growth.
1 It is also characterized by large increases in the
unemployment rate.
Recessions
-5.0
-2.5
0.0
2.5
5.0
7.5
1960 1970 1980 1990 2000 2010
research.stlouisfed.org
Gross Domestic Product by Expenditure in Constant Prices: Total Gross
Real Gross Domestic Product
(Percent Change from Year Ago)
Recessions
9 8 7 6 5 4 3
10
11
12
1980 1985 1990 1995 2000 2005 2010 2015
research.stlouisfed.org
Civilian Unemployment Rate
Unemployment Rate: Aged 15-64: All Persons for Australia©
(Percent)
How to model short run fluctuations
The long and the short
Definition (Potential Output)
Potential output is the output of the economy when all factors
of productions are fully utilised at their long-run sustainable
trends.
• Recall we assumed L = L¯ and all available K was employed
in our growth models.
The long and the short
• Two ways to think about short-run fluctuations:
– Our textbook likes the idea of long-run trend
Yt = Y¯t + Y^t (1)
where Yt is current output, Y¯t is potential output, and Y^t is
the short run fluctuations.
– Alternative is the plucking model” or the asymmetric
model:
Yt = Y¯t – Gap (2)
The long and the short
The long and the short
Figure: Source: Garrison (1996) EI
The long and the short
• The output gap:
– Note that both of these decompositions can be thought of
as a gap between potential and actual.
output gap = Yt – Y¯t (3)
The long and the short
• How do we measure potential?
– Well in reality we can’t. But, we try:
– Past trend
– Pick a point in the past where we believe we were at
potential, then use characteristics such as labour force
participation, capacity utilization, and demographic
characteristics to infer where we are now in relation to that
time.
– This fact will be very important for policy analysis and one
reason why economists who use the same models can often
disagree on the correct course of action.
• The level of output consistent with full employment
i.e. the natural rate of unemployment.
The Short-Run
• Two short-run relationships in the data:
1. The Phillips Curve – relationship between inflation and the
output gap.
2. Okun’s law – relationship between unemployment and the
output gap.
The Short-Run
The Short-Run
The Short-Run
Figure: Australian Data: Okun’s Law
The Short-Run
The Phillips Curve is also often represented as relationship
between inflation and unemployment rather than inflation and
the output gap.
The Short-Run
Figure: Old version of the Phillips Curve: Phillips Curve is the
relationship between unemployment and inflation.
The Short-Run
Figure: Smith (2008) JMCB
The Short-Run
Figure: Smith (2008) JMCB
The Short-Run
Figure: Smith (2008) JMCB
The Short-Run
• History of the Phillips Curve
– Although, the relationship can be demonstrated as a result
of the AD/AS model. It was first noticed empirically when
analyzing inflation data for the United Kingdom in the
early 1960’s by A.W. Phillips.
– It was then independently confirmed to hold true in the
United States.
The Short-Run
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Unemployment
CPI Inflation
U.S. Phillips Curve 1960 – 1969
Figure: The Phillips Curve – US CPI and Unemployment 1960-1969
The Short-Run
• When this relationship was found, many economists
believed that through government policy, a specific point
on the Phillips curve could be chosen for the economy.
• However, this view proved to be shortsighted.
• The relationship hinges on expected inflation.
The Short-Run
• Milton Friedman predicted that the Phillips Curve relation
would not hold.
– The economy will always tend towards the Natural Rate of
Unemployment (NRU) and if the government attempts to
lower the level of unemployment below the natural rate by
raising inflation, they would only be successful until people
revised their expectations. Once people expected a higher
rate of inflation, the economy would move back to the NRU.
The Short-Run
Figure: Phillips Curve Relation: 1960-2008
The Short-Run
• Our goal over the remaining 7 weeks:
1 Develop a short-run model that can explain those
relationships.
2 Incorporate policy into the model.
3 Analyse the role policy can play in macroeconomic
fluctuations.
A static model of the business cycle
Outline
• We are departing from the textbook for a few lectures.
• Our goal is to develop the static model that underlies the
dynamic model of the business cycle given in the textbook.
• Once we have built the model we will connect it back to
the textbook model.
The IS/LM Model
• This model that roughly depicts the economy described
J.M. Keynes in The General Theory.
• It is a pure demand side model meaning that in its most
economy. We will add this later.
• It was built to think about economies that are depressed.
The IS/LM Model
• Components of the IS/LM model
– Three markets
1 Goods market
2 Money market
3 Bond market
– Price level exogenous
– No supply constraints
Keynesian Cross Review
• A model of the Demand for Goods and Services – The
Demand Side
Y = C + I + G + Nx
= C + I + G + Ex – IM
Y + IM = C + I + G + Ex (4)
– Key Question: What determines GDP?
Keynesian Cross Review
• Consumption (C)
– Disposable Income (Income – Taxes = YD = Y – T)
– The consumption function
C = F(YD) (5)
• Consumption is a function of disposable income
– We assume that there is a positive relationship between
consumption and YD.
– This equation is called a Behavioral Equation
Keynesian Cross Review
• Let’s define the consumption function as a linear
relationship (Note I use a different notation then the book.
I think mine is better. The intuition is the same.)
C = C0 + C1YD (6)
C1: The marginal propensity to consume C0: Autonomous
consumption
Keynesian Cross Review
• For now lets investment, government spending, and taxes
be exogenous
– Investment: I = I¯
– Government spending: G = G¯
– Taxes: T = T¯
– Net exports: Nx = Nx ¯
• So demand for goods and services is
Demand = C0 + C1YD + I¯+ G¯ + Nx ¯
• Equilibrium Condition ) Supply = Demand
Y = C0 + C1YD + I¯+ G¯ + Nx ¯ (7)
Keynesian Cross Review
Solving For Equilibrium
Y = C0 + C1YD + I¯+ G¯ + Nx ¯ (8)
sub in for YD
Y = C0 + C1(Y – T¯) + I¯+ G¯ + Nx ¯ (9)
solve for Y
Y = C0 + C1Y – C1T¯ + I¯+ G¯ + Nx ¯
Y – C1Y = C0 – C1T¯ + I¯+ G¯ + Nx ¯
Y (1 – C1) = C0 – C1T¯ + I¯+ G¯ + Nx ¯
(10)
(11)
(12)
(13)
Y =
1
1 – C1
[C0 – C1T¯ + I¯+ G¯ + Nx ¯ ]
Keynesian Cross Review
• The Determination of GDP/Income
– The Multiplier
1-1C1
– Example: (intuition: One person’s spending is another
person’s income) If C1 = :8 i.e. if someone gives you a
dollar you spend 80 cents of it.
– That 80 cents now becomes another person’s income
– They in turn spend :8 ∗ (\$0:80) = \$0:64
– That 64 cents now becomes another persons income
– They in turn spend :8 ∗ (\$0:64) = \$0:51
GDP “= \$1 + \$0:80 + \$0:64 + \$0:51 + :::
Keynesian Cross Review
• This process can be approximated by well know infinite
series: The Geometric Series
GDP “= \$1 + 0:8(\$1) + 0:82(\$1) + 0:83(\$1) + :::
• What does this add up to?
Keynesian Cross Review
S = 1 + C1 + C12 + C13 + ::: + C1n
S = 1 + C1[1 + C1 + C12 + ::: + C1n-1]
S = 1 + C1[1 + C1 + C12 + ::: + C1n-1 + (C1n – C1n)]
S = 1 + C1[S – C1n]
S = 1 + C1S – C1n+1
S – C1S = 1 – C1n+1
S(1 – C1) = 1 – C1n+1
S = 1 – C1n+1
1 – C1
• Now, as n gets really large, C1n+1 ≈ 0.
Keynesian Cross Review
• Autonomous Spending
– C0 – C1T¯ + I¯+ G¯ + Nx ¯
Y = 1
1-C1 [C0 – C1T¯ + I¯+ G¯ + Nx ¯ ]
* *
Multiplier Autonomous Spending
Keynesian Cross Review
Figure: Comparative Statics
Keynesian Cross Review
Figure: Comparative Statics
The IS Curve
Now let’s expand on the Keynesian Cross
The IS Curve
• Investment (I)
– Investment depends negatively on the real rate of interest
I = I(r)
I = I0 – I1R
The IS Curve
Graph examples and equilibrium with interest rates.
The IS Curve
• The IS (Investment-Saving) curve – relating the real
interest rate, money, and output
• Deriving the IS curve