Week 1: Introduction to growth theory
(Chapters 1-4)
Aarti Singh
University of Sydney
ECOS2002 Intermediate Macroeconomics
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Brief summary of the course information I
I Objective: Develop a more in-depth analysis of two key aspects
macroeconomics: long run analysis and the short-run analysis
I Prerequisite:ECON1002
I Class structure: Lecture notes, Tutorials, Assignments (4)
I Ed (via canvas): For discussions, clari…cations...
I Consultation time: Thursday 11:30-12:30 (in-person and via zoom)
+ Tutor consultation hours
I Recommended textbook: Macroeconomics by Charles Jones (5th
edition) W.W. Norton & Company, New York CJ
I If you want to buy the book directly from the publisher:
https://www.wileydirect.com.au/buy/macroeconomics-international-
student-edition/
I Assigned readings: Go to Lecture schedule> Tutorial Schedule. You
can access the readings via the "Reading List"
3 / 34
Assessments I
I There are three assessments
I In-semester test (30%): April 7 (Week 7)
I Online task (20%): 4 problem sets (multiple weeks)
I Final exam (50%): Formal exam period
4 / 34
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
General approach I
I General approach
I Document the facts.
I Develop a model.
I Compare predictions of the model with original facts.
I Use the model to make other predictions that will eventually be
tested.
I But what is a model?
I Models simplify the complicated real world into its most relevant
elements.
I A model is useful if it has good predictive power.
I Economic models often involve systems of multiple equations
5 / 34
Parts of an economic model I
6 / 34
Example 1 I
I Labour supply and labour demand
I Behavioral equations: describing how people behave
I Ls = number of hours laborers want to work
I Ls = f (w ) = a¯w + l¯ = 2w + 30
I Ld= number of labor hours …rms want to hire
I Ld = f (w ) = f¯ w = 60 w
I w = wage
I Exogenous variables (input): f¯ , l¯ , a¯
I Equilibrium: Ld = Ls
I Find endogenous variables as functions of exogenous variables
7 / 34
Example 2 I
I Keynesian cross
I C = C¯ + c(Y T )
I I = I¯
I G = G¯
I T = T¯
I Equilibrium: Y = C + I + G
I Y = 11c (C¯ cT¯ + I¯ + G¯ )
I Chapter 1-2 review the material already covered in ECON1002
8 / 34
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Growth basics I
I The growth rate
g =
yt+1 yt
yt
(1)
where yt is per capital income. And rewriting
yt+1 = yt (1+ g) (2)
I Iterating
yt = y0(1+ g)
t (3)
or
g =

yt
y0
1
t 1 (4)
9 / 34
Example I
10 / 34
Using logs I
I Using logs for an approximation
ln(yt ) = ln(y0(1+ g)
t )
ln(yt ) ln(y0)
t
= ln(1+ g) ' g
11 / 34
The ratio (logarithmic) scale I
I Recall the rule of 70: If y grows at a rate of g percent per year, then
the number of years it takes y to double is approximately equal to
70/g
12 / 34
Properties of growth rates I
13 / 34
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Main question of interest I
I This lecture: Why some countries are rich and others poor? In
particular, why Americans are 28 times richer than people
from Ghana?
14 / 34
Facts I
15 / 34
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Model of production I
I Consider the following model:
I Single, closed economy; one consumption good
I Inputs in the production process:
I Labor (L¯) and Capital (K¯ )
I Production function: Shows how much output (Y ) can be produced
given any number of inputs
I Cobb-Douglas production function
Y = F (K ; L) = AK
1
3 L
2
3
16 / 34
Properties of the production function I
I F (K , L) is increasing in both K and L. More inputs yield more
output.
I The production function exhibits constant returns to scale
I If K and L increase by x%, Y also increases by x%
I Decreasing returns to scale in K and L i.e. if one is held constant,
then increasing the other increases production at a decreasing rate.
17 / 34
Allocating resources I
I Market structure: Perfect competition
max
L,K
Π = F (K , L) rK wL
I The rental rate and wage rate are taken as given under perfect
competition.
I Intuitively, hire capital until MPK = r and hire labor until MPL = w .
I For simplicity, the price of the output is normalized to one.
I Optimality conditions
18 / 34
Equilibrium I
I Five endogenous variables: Output (Y ), the amount of capital (K ),
the amount of labor (L), the wage (w), the rental price of capital (r)
I Five equations:
19 / 34
Equilibrium in the factor markets I
20 / 34
Model solution I
21 / 34
Interpreting the solution I
I Recall from the FOC’s
w = 2
3
A¯

K¯
L¯
1
3
=
2
3
Y
L
I In the United States, empirical evidence shows:w
L
Y =
2
3 and
r K
Y =
1
3
I 2/3 of production is paid to labor
I 1/3 of production is paid to capital
I The factor shares of the payments are equal to the exponents on the
inputs in the Cobb-Douglas function.
22 / 34
Labour share: US and Australia (La Cava 2019) I
23 / 34
Equilibrium I
I All income is paid to capital or labour
I Results in zero pro…t in the economy
I Veri…es the assumption of perfect competition
I Also veri…es that production equals spending equals income
wL + rK = Y
I Income = production
24 / 34
Analyzing the Production Model I
I Output per person
y = Y

L = A¯k¯
1
3
where k¯ = K¯/L¯
25 / 34
Answer the question I
I Output per person
y = Y

L = A¯k¯
1
3
where k¯ = K¯/L¯
I So to answer the question, a country is richer or has more output
per person when (i) productivity is higher and (ii) the amount of
capital per person is higher
26 / 34
Prediction of the model I
I If all countries are equally productive
27 / 34
What the production model cannot explain I
I First, its only a partial empirical success
I The model appears to systematically over predict income given the
amount of capital that exists.
I Second: Why Doesn’t Capital Flow from Rich to Poor Countries?
I The key here is the A term.
I A may not be constant across countries.
28 / 34
What is A? I
I The A term is called total factor productivity (TFP).
I TFP can be thought of as how e¢ ciently a countries uses capital and
labour to produce output.
I A limitation: Data on TFP is not collected.
I It can be calculated because we have data on output and capital per
person.
I TFP is referred to as the “residual.”
I A lower level of TFP implies that workers produce less output for
any given level of capital per person.
29 / 34
Understandig TFP di¤erences I
I Output di¤erences between the richest and poorest countries?
I Di¤erences in capital per person explain about one-third of the
di¤erence.
I TFP explains the remaining two-thirds.
I Thus, rich countries are rich because
I they have more capital per person.
I more importantly, they use labor and capital more e¢ ciently.
I Why are some countries more e¢ cient at using capital and labor?
30 / 34
Understandig TFP di¤erences I
I Human Capital
I The model does not capture the resources and expertise brought by
people to the production process.
I We believe that human capital may explain a large portion of the
di¤erence. Indeed countries with higher educations levels have higher
TFP.
I Technology
I Richer countries may use more modern and e¢ cient technologies
than poor countries.
I Increases productivity parameter
I Institutions: Institutions are in place to foster human capital and
technological growth.
I Property rights
I The rule of law
I Government systems
I Contract enforcement
31 / 34
Understandig TFP di¤erences II
I Misallocation: Resources not being put to their best use
I Examples: Ine¢ ciency of state-run resources; Political interference
32 / 34
Summarizing the Production model I
I Per capita GDP will be higher in countries that have more capital
per person and use it more e¢ ciently.
I Diminishing returns to capital are quite strong given the 1/3
exponent on K.
I This implies di¤erences in output per capita across countries cannot
be explained well by capital alone.
I There is a lot the model does not capture. In order to …t the data a
lot of the variation must be pushed into the A term.
33 / 34
Outline
General information about this unit
How do we examine key questions in macroeconomics?
Growth basics
Question
A model of production
Next week
Next week I
I Exogenous growth Solow-Swan growth model
I Readings: CJ Chapter 5
34 / 34