Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
Simple Linear Regression
An Economics Model
Economists are interested in studying relationships between economic
variables
For example, economic theory tells us that expenditure on goods
depends on income
Expenditure on goods is the dependent variable
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
ECON8026: Macroeconomics Diploma
Research School of Economics, ANU
Solutions to Problem Set 1,
PART I
1. Method 1: Consider doubling labour between t and t+1 while keeping
capital and technology fixed.
At+1 = At ; Kt+1 = Kt
Yt+1 = At+1 Kt+1
L1
t+1
Yt+1 =
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
Macroeconomics Diploma ECON8026 Week 3+4
Solow Swan again and RamseyKoopmanCass Growth Model with Consumption
Patrick Beiner
August, 2016
Patrick Beiner
Macroeconomics Diploma ECON8026 Week 3+4
[1em]
Solow
August,
Swan
2016 again
1 / 74
and
SolowSwan
1
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
Macroeconomics Diploma ECON8026 Week 5+6
Application of Ramsey Model and Theory of Real Business Cycles
Patrick Beiner
August, 2016
Patrick Beiner
Macroeconomics Diploma ECON8026 Week 5+6
[1em]
Application
August, 2016of Ramsey
1 / 37
Objectives
Consumpti
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
ECON8013 Assignment 1 Solutions
1. Exercises [30 marks]
a) Let Hf =
2 2
be the Hessian matrix for some function f : R2 R.
2 3
i) We know that if f is concave, then any stationary point is a global maximum. So
we need to show that f is concave. Consider th
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
The Multiple Regression Model
In most economic models there are more than one explanatory variables
 When we turn an economic model with more than one explanatory
variable into its corresponding econometric model, we refer to it as a
multiple regression
Analysis 3: Functional Analysis, Spectral theory and Applications
MATH 6214

Spring 2014
13
MULTIVARIABLE
OPTIMIZATION
At first sight it is curious that a subject as pure and
passionless as mathematics can have anything useful to say
about that messy, illstructured, chancy world in which we live.
Fortunately we find that whenever we comprehe