NEKG33 Mathematical methods for economists

Chapter 26 : Day 26

By Lund University

Once we know how to do partial derivatives, optimizing a function of two variables is the next step.

Optimization, two variables

This section is about optimization of a function of two variables. We will look at necessary and sufficient conditions for a local optimum point and optimization of convex and concave functions. The optimization problem is very similar to optimization of a function of one variable, replacing ordinary derivatives with partial derivatives.

Optimizing a function of 2 variables, necessary conditions

Optimizing a function of 2 variables, sufficient conditions

Optimizing a function of 2 variables, additional results

Multivariable optimization, n variables

Optimization: Problems

Exercises on multivariable optimization

Problem: Maximize function of two variables

Problem: Minimize function of two variables

Problem: Maximize profit function

Problem: Second derivative test

Problem: Maximize utility function

Problem: Maximize profit function

Problem: First- and second derivative test

Problem: Classify stationary points

Problem: Find extreme points

Problem: Find maximum and minimum points

Problem: Optimizing function of 2 variables

Problem: open, closed, bounded and compact sets