Dr. Steven Waters
Econ 380
Page 1 of 10
Lecture 1
Math Review & Special Topics
The hardest arithmetic to master is that
which enables us to count our blessings.
Eric Hoffer, Reflections On The Human Condition
This is both a math review and a set of math topics that we will be covering over the
course of the semester. The review is found on pp. 1-4 of this lecture and covers the
basics of logs, exponents, derivatives, and optimization.
We will be using these concepts
early and often in the class.
The topics on pp. 5-10 of this lecture will be introduced
throughout the semester – refer back to this lecture as necessary.
The Economics Outline
1.
Review Syllabus
The Mathematics Outline
1.
Calculus / Math Review
1.1.
Logs & Exponents
1.2.
Derivatives
1.3.
Partial Derivatives
2.
Univariate Optimization Rules
3.
Multivariate Optimization
4.
New Concepts using Existing Skills
4.1.
Young’s Theorem
4.2.
Total Differentials
4.3.
Implicit Functions
4.4.
The Envelope Theorem
Log Rules
Rule
Example
1)
)
ln(
)
ln(
)
ln(
y
x
xy
+
=
)
3
ln(
)
5
ln(
)
3
5
ln(
+
=
⋅
2)
)
ln(
)
ln(
)
ln(
y
x
y
x
−
=
)
3
ln(
)
5
ln(
)
3
5
ln(
−
=
3)
)
ln(
)
ln(
x
A
x
A
=
)
3
ln(
5
)
3
ln(
5
=

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