ECN 606: Microeconomic Analysis | Kristy Buzard

Logistics

Tue, 04 Jun 2024 00:00:00 +0000

Course schedule

For Fall 2025, ECN 606 meets from 9:30 – 11:00 a.m. on Mondays, Wednesdays, and Fridays from 9:30 – 11:30 a.m. in Eggers 018. I plan to teach entirely in person.

Syllabus

The syllabus for Fall 2023 is here.

Course website

All course materials are on Syracuse University’s Blackboard. Students gain access to the website by enrolling in the course.

Note on course numbering

Until Fall 2018, ECN 606 was numbered as ECN 601.

Textbooks

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Required text

I have listed one textbook as required for the course, mainly because it is nearly encyclopedic in its coverage of microeconomic theory and is the gold standard in the field; also because your other professors will require it:

Mas-Colell, Whinston and Green (1995), “Microeconomic Theory,” Oxford University Press [MWG].

Square brackets indicate abbreviated references. Because MWG is very terse, I urge you to have at least one additional graduate level microeconomic text at your disposal.

Additional graduate-level texts

Some other graduate-level texts with which I am familiar and that I believe may be useful are:

Jehle and Reny (2011), “Advanced Microeconomic Theory,'' Prentice Hall, Third Edition [J&R].
Kreps (1990), “A Course in Microeconomic Theory,'' Princeton University Press [Kreps].
Kreps (2013), ``Microeconomic Foundations I,'' Princeton University Press [KrepsNew].
- The newer Kreps text is inexpensive (especially the electronic versions), but some of the terminology is non-standard and the development is sometimes overly technical for our purposes. Solutions to many of its problems are available in the free Student’s Guide and the math appendices are great; these features alone may make it worth the purchase price.
Muñoz-Garcia (2017), ``Advanced Microeconomic Theory,'' MIT Press [Muñoz-Garcia].
Varian (1992), “Microeconomic Analysis,'' Norton [Big Varian].

The bookstore no longer keep textbooks on its shelves, but you can order textbokks through them.

Relevant chapters

This table is a rough guide to the places in each book that refer to the broad topics we will cover in ECN 606:

Topic	MWG	Big Varian	Kreps	J&R	Kreps New	Muñoz-Garcia
Preferences & Utility Functions	Ch. 1, 2.A-C, 3.A-C	7.1	2.1	1.1-1.2	Chs. 1-2	Ch. 1
Utility Maximization & Demand	2.D, 3.D	7.2-7.5	Ch. 2	1.3	Ch. 3, 10	Ch. 2
Comparative Statics of Demand	2.E-F, 3.E-F	Chs. 8,9	—	1.4-1.5	Ch. 4, 11	Ch. 3
Production and Cost	Ch. 5	Chs. 1,4,5,6	7.1	3.1-3.4	Ch. 9	4.1-4.3
Profit Maximization and Supply	Ch. 5	Chs. 2,3	Ch. 7	3.5	Ch. 9	4.4-4.10
Uncertainty	Ch. 6	Ch. 11	Ch. 3	2.4	Ch. 5	Ch. 5
Intertemporal Choice	20.A-D	Ch. 19	—	—	Ch. 7	—

Undergraduate texts

I recommend you have a good undergraduate intermediate microeconomics text for developing intuition. I use the 4th edition of Varian’s undergraduate text (“Baby Varian”), but the 7th edition is what has been on reserve.

Varian (2006), “Intermediate Microeconomics : A Modern Approach,” Norton, 7th Edition [Baby Varian].

Math references

For math references, I find the appendices of MWG often inaccessible and am not aware of others that are comprehensive. I do, however, like KrepsNew’s appendices on Real Analysis and Convexity. I am a huge fan of the book listed below on optimization by Dixit as well as Simon and Blume’s math for economists book. I will integrate parts of Binmore’s and Velleman’s books in class and suggest them as background preparation for anyone without a background in Real Analysis. I have made available a list of Math topics from Corbae et al. with which you should endeavor to be familiar. Corbae et al. presents the material in a more complex way than what is needed for our purposes, so the list is useful as a reference but I don’t suggest using this as a text to learn the concepts.

Dixit (1990), “Optimization in Economic Theory,” Oxford University Press, Second Edition.
Simon and Blume (1994), “Mathematics for Economists,” Norton.
Binmore (1982), “Mathematical Analysis: A Straightforward Approach,'' Cambridge University Press, Second Edition.
Velleman (2019), “How to Prove it: A Structured Approach,"' Cambridge University Press, Third Edition.
Corbae, Stinchcombe and Juraj (2009), “An Introduction to Mathematical Analysis for Economic Theory and Econometrics,'' Princeton.

There are hard copies of most of these texts on reserve at Bird Library, and electronic versions are available for a few of them at https://catalog.syr.edu/vwebv/enterCourseReserve.do.

Math preparation

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This page contains my recommendations for being well-prepared for ECN 606 from the point of view of math background. Success in ECN 605 is a necessary condition for success in ECN 606, but it is not sufficient. If you have previously succeeded in a rigorous proof-based math course such as real analysis, I suggest you simply review the topics (from a book of your choice) on the Math topics page and brush up on your proof-writing.

If you are not yet comfortable with mathematical proofs, the best thing you can do is to become more comfortable with writing proofs. I give my suggestions below, after a few caveats

Very few people could accomplish this task in a short period of time, no matter how intensively they work. If you devote one hour per weekday for eight weeks, you will accomplish FAR more than you would in five eight-hour days.
This kind of sophisticated thinking requires the brain to remodel itself, and that takes both struggle and recovery time between sessions and especially overnight, as the brain does a large part of consolidating new learning while you sleep. If you’re not getting enough sleep, you brain can’t properly consolidate the new learning (see these new findings on the effects of sleep deprivation).
If you were to start this work on the first day of fall classes, you would be at least halfway through the semester before it really starts to bear fruit. But you need to use this kind of sophisticated thinking from day one. Start NOW.

“How to Prove It” by Velleman

If you have little or no experience with writing mathematical proofs, start with the first five chapters of Velleman (except sections 3.7, 5.4 and 5.5, which I suggest you skip).

This will teach you step-by-step how to write proofs at the same time as it covers the majority of the topics under Logic and Set Theory on the Math topics list.

In order to make an impact, you must actually work the examples. As long as you can work the large majority of the examples for a given section, I suggest you skip the exercises for that section, at least for now.

What I mean by work is: Read the statement of the example. Cover up the answer. Do your best to generate the answer on your own. If you can’t figure it out, take a break and then try again. Perhaps ask a classmate for a hint. Think hard. Wrestle with it.

If you’ve done all this and still don’t know what to do, THEN:

Go back, review, and do the exercises in the previous section.
Try the example on which you were stuck again.
If you can figure it out now, move forward in the book.
If you’re still stuck, repeat Step 1, but go back an additional section. Repeat 2-3. If you’re still stuck, go back one more section. And so on.

“Mathematical Analysis” by Binmore

Binmore is aimed more at giving a concise treatment of the essential concepts than teaching you how to actually prove the results. This should be fine once you’ve completed the Velleman chapters. I you work from start to back in Binmore, focusing on the sections below. Again, if you can do all the proofs in the examples yourself (without looking at the provided proofs), then you can probably skip the exercises.

All of Chapter 1
2.2 – 2.10 (do the exercises in 2.10)
3.7 – 3.11 or Velleman 6.1 on induction proofs would be nice, but not top priority if you’re pressed for time
4.2 – 4.24
I think you can skip Chapter 5 and 6 for the purposes of 606; I’d like to hear from people if this turns out not to be true, or if you need it for other classes (series are used a lot in econometrics)
You’ve likely seen everything in Ch. 7; it’s a good idea to skim over it if you’re not sure
All of Chapter 8
All of Chapter 9, and it’s very important
Chapter 10 is likely review. Make sure to look at 10.6.
11.1 – 11.7
All of Chapter 12 except 12.11
Chapter 13: We will use a little bit of integration, but I assume you will get more than we need in math camp / metrics
Chapter 14 should be covered in undergraduate calculus; refresh if you need to
For 606, I don’t think you need power series (Ch. 15), and I’m sure you don’t need trig (Ch. 16) or the gamma function (Ch. 17)
18.1 – 18.16, 18.21 – 18.23, 18.26 – 18.39
Chapter 19 is perhaps useful as reference if you get caught in a proof about partial derivatives, but probably otherwise mostly a more complicated version of what you’ll go over in math camp.

Other resources

See the Math references section of the Textbook page for further suggestions.

Math topics

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Chapter and section references are from Corbae, Stinchcombe and Juraj (2009), “An Introduction to Mathematical Analysis for Economic Theory and Econometrics.'' I only recommend you follow Corbae et al. if you are already comfortable with highly-technical math. Otherwise, use this list of topics as guidance while using one of the recommended sources on the Textbooks page and following the guidance on the Math preparation page.

Logic

Chapter 1 in Corbae, Stinchcombe and Juraj (2009)

Topic	Reference	Background	Proofs	Direct/General
Statements, Sets, Subsets, Implication	Section 1.1	X	X	X
Ands, Ors, Nots	Section 1.2.a	X	X	X
Implies, Equivalence	Section 1.2.b	X	X	X
Vacuous Statements	Section 1.2.c	X	X	X
Indicators	Section 1.2.d	X	X
Logical Quantifiers	Section 1.4	X	X
Taxonomy of Proofs	Section 1.5	X	X	X

Set Theory

Chapter 2 in Stinchcombe and Juraj (2009)

Topic	Reference	Background	Proofs	Direct/General
Notation for sets	2.2.2, top pg. 21	X	X
Useful theorems on sets	2.2.4, 2.2.6		X?
Cartesian Product	2.3.1	X	X	X
Relation	2.3.4, 2.3.5	X
Function	2.3.8	X	X	X
Correspondence	2.3.12	X	X	X
Image	2.3.16, 2.6.1, 2.6.4	X	X
Cardinality	2.3.17	X	X	X
Equivalence Class	2.4.1, 2.4.5	X	X	X
Partition	2.4.9	X	X?
Inverse, Inverse Image	2.6.7, 2.6.10, 2.6.13	X	X	X
Level Sets of Functions	2.6.12	X	X	X
One-to-One / Injection	2.6.15	X	X
Onto / Surjection / Bijection	2.6.17	X	X
Composite Functions	2.6.20, 2.6.23, 2.6.26	X	X

The Space of Real Numbers

Chapter 3 in Stinchcombe and Juraj (2009)

Topic	Reference	Background	Proofs	Direct/General
The `Why'	Section 3.1 and 3.10	X
Algebraic Properties of $\mathbb{Q}$	3.2.3	X	X
Distance in $\mathbb{Q}$	3.3.1, 3.3.2	X	X
Sequence	3.3.3	X	X	X
Subsequence	3.3.5	X	X
Cauchy	3.3.7, 3.4.8	X
Bounded	3.3.12, 3.3.13, 3.6.1	X	X	X
Real Numbers	3.3.19	X
Algebraic Properties of $\mathbb{R}$	3.3.23	X	X
Distance in $\mathbb{R}$	3.4.1, 3.4.2, 3.4.3	X	X
Convergence	3.4.9, 3.4.10, 3.4.15	X	X	X
Completeness of $\mathbb{R}$	3.4.16	X
Supremum / Infimum	3.6.2, 3.6.5	X	X	X

The Finite-Dimensional Metric Space of Real Vectors

Chapter 4 in Stinchcombe and Juraj (2009)

Topic	Reference	Background	Proofs	Direct/General
Metric Space	4.1.1	X
Convergence, Limit	4.1.4	X	X	X
Complete	4.1.6, 4.4.5	X	X
Open ball	4.1.9		X
Open	4.1.10, 4.1.11	X	X
Open neighborhood	4.1.12		X
Open cover	4.1.18		X
Compact	4.1.19, 4.7.15		X	X
Connected	4.1.21		X	X
Continuous	4.1.22, 4.7.20, 4.85	X	X	X
Vector Space	4.3.1	X?		X
Normed Vector Space	4.3.7	X?
Inner / Dot Product	4.3.9	X	X	X
Cauchy-Schwartz Inequality	4.3.10		X
\textit{p}-Norms	Section 4.3.c		X?	X
Characterizing Closed Sets	Section 4.5.a	X	X
Closure of a Set	4.5.4	X
Boundary of a Set	4.5.5	X	X
Accumulation / Cluster / Limit Point	4.5.7	X	X
Closure and Completeness	4.5.12, 4.5.13	X	X
Bounded	4.7.8	X	X	X
Applications of Compactness	Section 4.7.f	X	X	X
Basic Existence Result	4.8.11, 4.8.16		X	X
Upper Hemicontinuity	4.10.20	X	X
Theorem of the Maximum	4.10.22, 6.1.31		X	X
Upper Semicontinuity	4.10.29	X	X?
Connected	4.1.12, 4.12.3, 4.12.4	X	X	X
Interval	4.12.1, 4.12.2	X	X	X
Intermediate Value Theorem	4.12.5	X	X	X

Finite-Dimensional Convex Analysis

Chapter 5 in Stinchcombe and Juraj (2009)

Topic	Reference	Background	Proofs	Direct/General
Convex Combination	5.1.2	X	X	X
Convex Preferences and Technologies	Section 5.1.c			X
Returns to Scale	5.1.13			X
Convex Hull	5.4.6		X
Upper Contour Set	5.4.23	X	X	X
Affine Combination	5.6.16	X
Interior	5.5.1, 5.5.2	X
Concave Function	5.6.1, 5.6.2	X	X	X
Affine Function	5.6.6	X	X
Quasi-Concave	5.6.12	X	X	X
Single-Peaked	5.6.13	X
Implicit Function Theorem	Sections 2.8.a and 5.9.b		X	X
Envelope Theorem	Section 5.9.c		X	X

Sections 5.8 - 5.10 contain results on optimization. The facts and results that you need should already be familiar from math camp so I do not list them separately.

Week 1 Preparation

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Purpose

This note substitutes until the week before classes start for an announcement on Blackboard–the usual way of telling you what to prepare for each class. This is to allow time for everyone to register and be added to Blackboard.

What follows is an overview of what you should prepare for the first portion of producer theory, which I anticipate we will cover in our first 2-3 lectures (August 28, August 30 and perhaps September 6).

Topic list

You will find the Production Topic List in the Production folder once you access Blackboard. It has notations for the primary text source for each topic. These topic lists are the key to guiding your preparation and studying in each section of the course.

Economic concepts

We begin with production sets, production functions, and properties of technologies (MWG 5.B). You should have a basic understanding of the difference between production sets and production functions as well as familiarity with the properties of technologies listed on the topic list before our first class on Monday, August 28.

We will quickly check in to answer any questions about these commonly-assumed properties of production sets from the reading; then we’ll see which of these properties we can identify/falsify in the isoquant representation of technologies. You should be familiar with isoquants from math camp. When this is done, we’ll move on to important properties associated with isoquants such as the marginal rate of technical substitution and related concepts such as marginal product, marginal rate of transformation and elasticity of substitution in the production context.

Math concepts

You should prepare/review the following math concepts:

Level curves: Section C of the Math Handout (Content/Math on Blackboard)
Sets: Binmore 1.1 to 1.6
Functions: Binmore 7.1 to 7.8
“Cardinal vs. Ordinal” handout (Content/Math on Blackboard)
Convexity/concavity/quasiconvexity/quasiconcavity
- Binmore 12.13
- KrepsNew, Appendix sections A3.1, A3.4 and A3.5 contain a useful treatment of the whole suite of ideas around convexity
- In Content/Math on Blackboard, I’ve posted a document that compiles several definitions of quasiconvexity / quasiconcavity as well as scans of the pages from several of the books from which definitions were taken
Elasticity: Section B of the Math Handout

If you have not taken a proof-based math course such as Real Analysis, you should work through the Binmore sections–especially the examples–even if the concepts are familiar.

By “work through,” I do not mean to just read the section. I mean that you should also try to solve the examples before looking at the answers that are given in the text and then complete the related exercises in the last section of the chapter
- The solutions to the Binmore exercises begin on page 251.
You do not learn to structure your arguments clearly and precisely (as in proofs, and in general in the way that economists are expected to argue) by looking at proofs.
- That’s just not the way the human brain works.
- You learn to structure your arguments clearly and precisely by actually trying to structure your arguments clearly and precisely.
  - If you start with simple enough arguments, you will eventually succeed and then build on that success by gradually attempting to make increasingly complex arguments clear and precise.

Questions?

Email me if you have any questions.