Econ6003, Semester 2, 2022
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Econ6003, Semester 2, 2022
Midterm Exam Info & Preparation Advice
Replica of Instructions to appear on the Question Paper.
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Instructions 1. Duration: 2 hours (120 minutes) The above is only the working time for the exam. The Exams Office adds additional buffer time to submit the exam which will be shown on Canvas Exam site. Do NOT treat the buffer time as extra writing time. Manage your time carefully. All your attempts to submit the exam are logged, hence not being able to upload your answers by the deadline will be grounds for granting a Special Consideration only in very rare cases. 2. There are seven questions (with sub-parts) on two pages. 3. Each question is worth 5 points. The exam is worth 35 points in total. 4. Your answers must be handwritten, and submitted online in PDF format only.
5. Please do not write essays 6. Submission deadline instructions are on Canvas. |
Examinable Material.
Only the material covered up to and including Linear Algebra (Ch 10, Ch 11) of Simon & Blume, i.e. until Week 6 excluding the discussion of 
The Shapley Value
. You are responsible for all the topics covered in class (excluding 
The Shapley Value
).
Study Resources
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text were indicated during the term.
(http://www.math.louisville.edu/~lee/) This is alternative to SB. I wish I knew of this source earlier, it appears to be nicely done, concise and covers a lot of precisely what we have done until Linear Algebra. Below, I indicate against each topic which parts of this book cover relevant material. Direct Download Link: http://www.math.louisville.edu/~lee/RealAnalysis/I -ntro R Aealnal.pdf.
IRA also has a number of end of chapter exercises. I do not have a solution manual, nor can I say a priori which of those exercises are
for the most part are excellent. In fact I quite often use them as a quick reference during the course of my own research. |
Preparation Advice
Surely, each of you will have your own preparation style for exams. For this course, the questions in the various assignments and the Quiz are good predictors for the style of questions. You need to have a good understanding of the concepts. I esspecially urge you to keep a 
big stock
of examples/counter examples connecting various definitions. (For example, if I were to say f + g must be continuous whenever f is continuous, you should have a ready counter-example to show this is not true, to save yourself time. Likewise for statements relating to open/closed sets, limits, etc. etc. You will notice that this was highlighted thoughout the problem sets.) Proofs where required in the Exam are not hard, but rely on a good understanding of the concepts.
Below is a list of keywords that can serve you as a guide in your preparation.
1. Basics of Set Theory: Universal Set, ; (the empty set), Given a pair of sets, S ; T, the set operations of union (S [T), intersection (S \T), set minus (S nT) and complement (Sc). An understanding the extension of these operations to more than two sets. De Morgan's laws that 
the union and intersection interchange under complementation
, i.e. (S [T)c = Sc \Tc etc.
2. Functions, domain, range, different types of functions (into, onto, subjective, injective, inverse image of a function.
(In IRA mostly in 
Ch 1, Sections 4.1 - 4.4).
3. Real Sequences: The idea that sequences is xn is a real valued function on N. Bounded vs. Convergent sequences. Concept of the limit of a sequence, Uniqueness of the limit. Monotonic sequences, Cauchy sequences, Different approaches to compute the limit including using the algebra of limits for convergent sequences, Use of monotonicity,
showing sequences are Cauchy, other techniques (the nested property for instance). (In IRA, good idea to work through entire Chapter 3.)
4. Rn 
notion of distance; Interior points; Boundary points; Open sets,; Closed sets, Didifferent equivalent definitions of these concepts: (i) S is closed if and only if Sc is open and (ii) S is closed if for any sequence for xn ! x0 and xn 2 S for all n, then the limit x02 S .; The two definitions of an open set 
(i) S is open if and only if Sc is closed and (ii) S is open if and only if every one of its points is an interior point. Compact set 
a set that is closed and bounded.
Infimum and Supremum vs. Minimum and Maximum in R.
(We covered all of this in fair detail. The explanations in class should mostly be ade- quate. In IRA, this stuff is in Ch 5).
5. Continuous Functions: Definition of continuity at a point, using limits. The algebra of continuous functions (i.e. continuity of the sum, product, ratio and composition of functions). Two definitions for continuous functions 
one using limits and the other involving ", 
etc.
(In IRA, this is covered very well in Ch. 6).
6. Make sure you 
hit
all the following keywords as well, relating to continuous functions during your preperation:
Intermediate Value Theorem, Weierstrass Extreme Value Theorem, Debreu's Utility Representation Theoremand their implications. Brouwer's Fixed Point Theorem.
7. Convex sets, Concave and Quasi-concave functions and existence of unique maxima.
(Similarly Quasi-convex and convex functions and their role in unique minima). (Stuff from class, a good understanding of Problem Set 3 should be enough.)
8. Linear Algebra: Vectors; Norm and Inner Product; Linear combinations of vectors, Linear Span; Linearly Independent vs. Linearly dependent sets of vectors; Basis for Rn . (Chapter 10,11 of SB.)
2022-04-06