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以下内容为MIT本科经济学课程大纲及期末试卷： 课程大纲：Syllabus 希望对大家有用
DescriptionThis half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered.
PrerequisitesPrerequisites for this course include 14.04 Intermediate Microeconomic Theory, 18.02 Multivariable Calculus, and 18.06 Linear Algebra.
Enrollment in this course is limited and permission of the instructor is required. Permission can be obtained by attending the first class meeting and providing information about previous coursework in mathematics and economics. The course assumes that students have taken undergraduate intermediate microeconomics classes. It also assumes that students are comfortable with multivariable calculus and linear algebra and have had some exposure to real analysis. Historically, many students from outside the economics department have had difficulty with the course. The enrollment limit may result in well-qualified students being turned away.
Textbooks Mas-Collel, Andreu, Michael D. Whinston, and Jerry R. Green. Microeconomic Theory. New York, NY: Oxford University Press, 1995. ISBN: 9780195073409.
Some students have also found the following books helpful:
Jehle, Geoffrey, and Philip Reny. Advanced Microeconomic Theory. 2nd ed. Reading, MA: Addison Wesley, 2000. ISBN: 9780321079169.
Kreps, David. A Course in Microeconomic Theory. Upper Saddle River, NJ: Financial Times Prentice Hall, 1990. ISBN: 9780745007625.
Varian, Hal. Microeconomic Analysis. 3rd ed. New York, NY: W.W. Norton, 1992. ISBN: 9780393957358.
The final exam will be held two days after the last lecture
期末试卷：
14.121 Microeconomic Theory I: Waiver Exam
Prof. Parag Pathak Fall 2008
Instructions. Your grade on this exam does not matter for anything except the decision about whether you need to take (or re-take) the class, so do not panic. You have 90 minutes to complete the exam.
In the following, you are asked to “prove” certain statements. In doing so, you may rely on any results from mathematics you wish, but you should clearly state the steps of your argument and the theorems you reference, if appropriate. Results from economics should be proven unless noted. Partial credit will be given for clear logic and careful reasoning.
1) Consumer Theory
a) A consumer has a preference relation A that is transitive (A stands for “at least as good as”). Define the strict preference relation Aand prove that is transitive.
b) Define the indirect utility function v(p,w) for a consumer. Show that i) v is homogenous of degree 0, ii) strictly increasing in w, iii) nonincreasing in pl for any l, iv) quasi-convex (that is, the set {(p,w)|v(p,w) ≤ v¯} is convex for any ¯v. [You may assume that the consumer’s direct utility function u is suitably well behaved.] Why is v nonincreasing rather than strictly decreasing in pl?
2) Demand Aggregation
Suppose there are two consumers with utility functions u1(x1,x2)= x1 +4√x2 and u2(x1,x2)=4√x1 + x2. The consumers have identical wealth levels w1 = w2 = w/2.
a) Calculate the individual demand functions and the aggregate demand function. b) Compute the individual Slutsky matrices Si(p,wi) for i =1, 2 and the aggregate Slutsky matrix S(p,w). Does aggregate demand satisfy the weak axiom? Justify your answer. c) Let p1 = p2 = 1. Compute the matrix that is the difference between the sum of the individual Slutsky matrices and the aggregate Slutsky matrix:
C(p,w)=�Si(p,wi) − S(p,w).4)
Consider a pure exchange economy with two goods, h =1, 2 and two consumers, i =1, 2 with utility functions u1 and u2 respectively. The total endowment is e =(e1,e2) where e1,e2 - 0.
For each of the following cases, determine which of the Pareto-efficient allocations can be decentralized as competitive equilibria with lump sum transfers.
Briefly describe the equilibrium prices and transfers for each Pareto-efficient allocation.
a) u1(x,y)= α ln(x) + (1 − α)ln(y) and u2(x,y)= β ln(x) + (1 − β)ln y, where α<β and ln x is the natural logarithm of x. b) u1 = u2 is strictly concave, smooth, and homothetic. c) For i =1, 2, ui(x,y)= x + g(y), where g is an increasing and strictly concave function. d) u1(x,y) = max{x, 2y}, u2(x,y) = max{2x,y} and e1 = e2.
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