Intermediate Microeconomics Calculus Module
Lecture 2
–
Functions of two (or more) variables.
In this lecture we will discuss calculus and algebra when the function involves more than one
variable. You may use the following reference to supplement these notes:
Larson, Sections 7.4 and 7.5.
You may also use FrankParker Math Module 12, although this module will be too advanced for
the beginning of your course, but should be useful later on:
http://www.mcgrawhill.ca/college/olcsupport/frank4/math/pdf/mod12.pdf
Examples of multivariate functions:
Ex.1
What does this function look like? It is difficult to graph since it has
three
dimensions.
Note that wolframalpha.com is a wonderful free tool which can assist with many math problems.
Simply type in your equation at the prompt.
One useful way of visualizing a three dimensional object is through a
level set
. We get a level set
when we pick a point on the vertical axis, and horizontally slice through the three dimension
object, allowing us to depict the resulting “slice” in two dimensions. Economic examples are
indifference curves
, and
isoquants
.
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Variables vs. Parameters
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 Spring '11
 Okhan
 Economics, Microeconomics, Derivative, Ron Larson

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