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 points in the interior of the region isnt too bad
in gener
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 functions they
face.
o Understanding demand functions
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 are working more for less.
We begin with a model of labo
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 function is
Recall that
To raise equal revenues under a
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 , and since is a constant, there seems to be no reason to
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 function is quasiconcave if for any (,) and ( and any ;
,
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 simply the elasticity of demand
Elasticity, , is calcula
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 for work in economics as a whole.
The Basic Model of Con
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 by singlevariable, unconstrained problems. Consider a d
Brute Force Method of Optimization
Assumptions about U:

Represents preferences

Defined as any positive real number

Twice continuously differentiable

Strictly increasing

Quasiconcave
Optimization

Third basic ingredient in our model of behavior.
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 for the demand function of , vice versa if youre
solving