ECON 6021: Optimization 2
July 22, 2016
Optimization with inequality constraints
Content:
the constraint set
Lagrange multipliers
Constraint set
So far we have work on problems of the form
max u(x)
xX
s.t.
px=M
where the constraint is an equality. (Pictur
Term 2 2016
ECON6021
Guillaume Roger
University of Sydney
Practice exercises
These are tutorial, or practice questions, for you to familiarise yourself
with the concepts that we use. Think of them as drills, or scales on the
piano: they are useful to get
ECON 6021
Some basic finance
July 22, 2016
ECON 6021
Basic finance
Content:
Compounding and discounting
Annuities and mortgages
Pricing bonds
ECON 6021
Compounding and discounting
You must have heard of the time value of money.
Later in the course well be
ECON 6021 Optimization
July 22, 2016
Optimization with equality constraints
Content:
the constraint set
Lagrange multipliers
Assumed knowledge:
partial differentiation and its background
vector calculus
some linear algebra
Constraint set
When solving the
Decision making under uncertainty
July 22, 2016
Decision making under uncertainty
Content:
Uncertainty
Expected utility
Risk aversion
Assumed knowledge:
Preference ordering
Basics of probability theory
Uncertainty
Our new Constitution is now established,
Choice under uncertainty
Chapter 12
Thinking about uncertainty
An individual makes a choice before
knowing the state of the world in which
the outcome will occur.
The state of the world will determine the
payoff from the act.
2
Thinking about uncertaint
Term 2 2016
ECON6021
Guillaume Roger
University of Sydney
Exercise set 2
Exercise A: Implicit functions
Consider the problem
max (K, L) = p f (K, L) wL rK
K,L
1. Derive the first-order conditions
2. What can you say of L when w changes? When p changes? Th
ECON 6021: lending and borrowing,
insuring.
July 22, 2016
Insuring, lending and borrowing
Why?
Intertemporal smoothing and insurance
I presume that you mostly studied static problems like
max u(x)
xX
s.t.
g (x) m
There is no tomorrow and there is no uncer
Introduction to General Equilibrium.
Some background material
July 22, 2016
General equilibrium
Why?
General equilibrium
Trade involves exchange.
Who buys? Who sells?
How are prices determined?
How is a consumers income determined?
General equilibrium
Let
Contingent claim economy
July 22, 2016
Contingent claim economy
Why?
We want to formalise the notion of General equilibrium and
pave the way to a Finance Economy.
Two-period contingent claim economy
A more general treatment.
uncertainty:
agents insure eac