Constrained Optimization (Lagrange Multipliers)
In the previous section we optimized (i.e. found the absolute extrema) a function on a region that
contained its boundary. Finding potential optimal poi
Lecture 3: Demand Functions
Objective:

Analysis of the demand function
Demand Functions


Provide a convenient description of behavior
o It is important for firms to have a good idea of the demand
Lecture 6: Labor Supply
Labor Supply

Our basic question is: what determines labor supply?
o
In particular, if wages increase, will people work more or less?

The popular perception is that people a
Utility Maximization Method
Here is an alternative derivation, though this one requires us to know the utility
function. Suppose utility is given by:
The demand functions are
and the indirect utility
The Cost Minimization Approach

To make sense of this, let us introduce the expenditure minimization problem:
Note that the objective is to minimize expenditure . We might think of
expenditure as , a
Lecture 5: Maximizing Utility
Objective:

Transition lecture
We will fill in some details concerning the techniques to maximize utility, and will start
on applications.
Quasiconcave Functions

A fun
Lecture 4: Elasticity
Objective:

Build familiarity with the idea of utility maximization and to add some economic content
to the technical analysis.
The Price Elasticity of Demand


Often called s
Lecture 1: Modeling Choice; Preferences and Constraints
Objective:

Introduce the basic model of choice that serves as the foundation for all our work this
semester, and that serves as a foundation f
Lecture 2: The Mathematics of Optimization
Objective:

Review the basic calculus of optimization
SingleVariable Optimization

The basic intuition for solving maximization problems is well captured
Brute Force Method of Optimization
Assumptions about U:

Represents preferences

Defined as any positive real number

Twice continuously differentiable

Strictly increasing

Quasiconcave
Optimiza
Lagrangian Method
1) Formulate utility maximization problem
2) Write Lagrange equation
3) Formulate firstorder conditions
4) Solve system of linear equations
5) Isolate for
a. Only if youre solving f