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Mathematical Methods in Economics

Course description: This class will cover the mathematics you need to succeed in
Intermediate Macroeconomics, Intermediate Microeconomics, and upper level electives in
Economics. We start with the basics: algebra , solving equations, and graphing. Other
topics include differentiation , functions and financial mathematics. We will make extensive
use of examples in Economics to solidify the concepts. These include equilibrium in various
markets, elasticities, comparative statics, and optimization.

Course prerequisites: There are no prerequisites for this class

Class meetings: This class will meet Mondays and Wednesdays from 10:35-11:50 am.

Office Hours: TBA.

Textbook: The required text for this class is: Essential Mathematics for Economics and
Business, third edition, by Teresa Bradley. It is available at the Columbia University Book Store.

Evaluation: Your grade in this class will depend on your performance on: 2 midterm
exams (each 25%), a cumulative final (40%), and weekly problem sets (10%). Late problem
sets will not be accepted. The lowest problem set grade will be dropped. There will be no
make-up exams given. The dates of the midterms are below. The final exam will be on the
date determined by the official schedule. Please note that after I submit final grades, I will
not respond to emails regarding them.

Teaching assistant: TBA.

Honor code: I value Barnard’s Honor Code for the integrity it fosters. All exams and
assignments in this class are to be completed in accordance with the Barnard Honor Code.
Columbia students commit themselves to the Honor Code upon registering for a Barnard
course. The codes says, in part:

“We consider it dishonest to ask for, give, or receive help in examinations or
quizzes, to use any papers or books not authorized by the instructor in examinations,
or to present oral work or written work that is not entirely our own,
unless otherwise approved by the instructor. We consider it dishonest to remove
without authorization, alter, or deface library and other academic materials.”

(Rough) Schedule of Topics to be Covered
(Chapter numbers in (.) )
(Check courseworks intro page regularly for updates)

WEEK 1: Sept 3:

• Preliminaries (1)
 — Arithmetic operations and fractions
 — Solving equations and inequalities
 — Working with percentages

WEEK 2: Sept 8, 10:

Graphing Linear Equations (2)
 — The equation of the line
 — Graphs
 — Applications: supply and demand, elasticity

WEEK 3: Sept 15, 17:

Simultaneous equations (3)
 — Two equations in two unknowns
 — Three equations in three unknowns
 — Applications: equilibrium and its implications

WEEK 4: Sept 22, 24:

• Non- linear equations (4)
 — Polynomial , exponential and logarithmic functions
 — Applications: demand and supply, growth
 — Hyperbolic functions

WEEK 5: Sept 29, Oct 1

• October 1: Rosh Hashanah, no class
• Differentiation (6)
 — Definition and rules
 — Higher derivatives

WEEK 6: Oct 6, 8:

• Applications of Derivatives (6)
 — Marginal and average functions
 — Optimization

WEEK 7: Oct 13, 15:

• October 13: Midterm exam 1
• Applications of Derivatives cont’d (6)
 — Maximums and minimums: profits
 — Curvature and second derivatives: costs

WEEK 8: Oct 20, 22:

• Applications of Derivatives cont’d (6)
 — Derivatives of functions
 — More rules

WEEK 9: Oct 27, 29:

• Applications of Derivatives cont’d (6)
 — Elasticity and functions

WEEK 10: Nov 3, 5:

• November 3: Election Day Holiday
• Functions of several variables (7)
 — Partial derivatives
 — Applications: marginal values, returns to scale, elasticities

WEEK 11: Nov 10, 12:

• Functions of several variables cont ’d (7)
 — Unconstrained optimization
 — Applications: profit and revenue

WEEK 12: Nov 17, 19:

• November 17: Midterm exam 2
• Functions of several variables cont’d (7)
 — Constrained optimization
 — Applications: utility, cost, budget constraints

WEEK 13: Nov 24, 26:

• November 26: Thanksgiving Holiday
• Financial Mathematics (5)
 — Arithmetic and geometric series
 — Simple and compound interest
 — Net present value and internal rate of return

WEEK 14: Dec 1, 3

• Financial Mathematics cont ’d (5)
 — Annuities, repayments
 — Bond prices

WEEK 15: Dec 8:

• Catch-up and Review

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