W3211 Spring 2009 Professor Vogel Review for Midterm #1: Solutions Review Questions and solutions: 1. Consider the following payo matrix: L T x 1 ; y1 B x 3 ; y3 R x 2 ; y2 x 4 ; y4
In the following questions, suppose this is a simultaneous move game: (a)
W3211 Spring 2009 Professor Vogel Homework #2: Due February 10, 2009 Please write your name on the top of every page of your homework (in case they get separated) and please staple all pages together. Where appropriate, you must show all work. If you just
W3211 Spring 2009 Professor Vogel Homework #3: Due Tuesday 02/24/09 Please write your name on the top of every page of your homework (in case they get separated) and please staple all pages together. Where appropriate, you must show all work. If you just
W3211 Lecture 1
Introduction and Mathematical Review Jonathan Vogel
Columbia University
Spring 2009
Jonathan Vogel (Columbia)
W3211 Lecture 1
Spring 2009
1 / 21
Introduction
Two main themes in economics
1. Individual behavior Assumptions:
1
Agents face we
W3211 Spring 2009 Professor Vogel Recitation for the Week of February 02, 2009.
1. (a) M RS = M Ux =M Uy = y:
x;y; 1 x
1=x 1
= 1=x, It is diminishing with x but is independent of 2x 3y)
(b) max L = y + ln x + (12
@L @x @L @y @L @
=
2 =0 3 =0 2x 3y = 0 = 1
Lecture 12: Production Functions
Key Terms in Lecture
Production function Technology Inputs Marginal (physical) product
Diminishing marginal product
Average (physical) product Isoquant Marginal rate of technical substitution
Production Function
The fi
Lecture 12: Production Functions
Key Terms in Lecture
Production function Technology Inputs Marginal (physical) product
Diminishing marginal product
Average (physical) product Isoquant Marginal rate of technical substitution
Production Function
The fi
Lecture 2: Preferences and Utility
Ranking bundles of goods
If we have two real numbers, its easy to say which is larger: e.g. 7 > 5 If you have two products, its often easy to say which you like moree.g. Coke > Pepsi or Pizza > Doritosbut not always Wha
Syllabus, Economics W3211, Spring 2016
Last updated: January 25, 2016
W3211: Intermediate Microeconomics
Instructor:
Professor Qingmin Liu, qingmin.liu@columbia.edu
Office Hours: Friday 1:30pm3:30 pm (1012, International Affairs Building).
Additional of
Lecture 9: Game Theory
Key Terms in Lecture
Subgame and proper subgame Subgame perfect Nash Equilibrium (SPNE) Backward induction
Subgameperfect Nash equilibrium (SPNE) rules out empty threats by requiring strategies to be rational even for contingenci
Lecture 3: Utility Maximization
Optimization Principle
Agents choose to allocate their fixed income in such a way as to maximize their utility. To maximize utility, given a fixed amount of income, an individual will buy the goods and services:
that exha
Lecture 4: Demand Functions
Income and Substitution Effects
Key Terms in Lecture
Demand Function Normal, Inferior, and Giffen goods Substitution effect and Income effect Individuals demand curve
Movement along a demand curve (change in quantity demanded
Lecture 6: Game Theory
Key Terms in Lecture
Game
players actions strategies payoffs
Extensive Form Normal Form Nash Equilibrium Dominant Strategy
Game Theory
In economics we consider an agent choosing actions to maximize its objective function (subje
Lecture 7: Game Theory
Key Terms in Lecture
Mixed strategies Continuum of actions Tragedy of the commons
Mixed Strategies
When a player chooses one action or another with certainty, he is following a pure strategy Players may also follow mixed strategie
W3211 Problem Set #1
Columbia University
January 29, 2016
Abstract
The problem set is due one week from now on 1:00PM, Friday
Feburary 5, 2016. Place your problem sets in one of the three boxes,
#16, #17, or #18, on the 10th of IAB. Late submission will n
W3211 Spring 2009 Professor Vogel Homework #5: Due Tuesday 04/14/09 Please write your name on the top of every page of your homework (in case they get separated) and please staple all pages together. Where appropriate, you must show all work. If you just
W3211 Spring 2009 Professor Vogel Homework #3: Due Tuesday 03/31/09 Please write your name on the top of every page of your homework (in case they get separated) and please staple all pages together. Where appropriate, you must show all work. If you just
W3211 Spring 2009 Professor Vogel Recitation for the Week of February 09, 2009 1. Bob' utility as a function of his wealth, w, is U (w) = w1=2 . Bob' wealth is $16. He is s s given the option to either keep his $16 or to invest his $16 in a new .rm called
W3211 Spring 2009 Professor Vogel Recitation for the Week of February 02, 2009 1. U (x; y) = y + ln x, I = 12, px = 2, and py = 3. (a) Solve for the M RS. Is it deminishing? (b) Solve the the optimal (x ; y ). 2. U (x; y) = y + ln x, and suppose that I >
1. q = 100  3p p = =
100 3
100 3

q 3 100 3

q 3
q  wl  vk =

k l(1) 3
k l(1)  wl  vk
Taking the FOCs: (1) (1) (1) l k = 100  k l 3 k (1) l(1)  k k l(1) = v 3 3 k = 100 k (1) l(1)  2 k (21) l(22) = v 3 3 l = l =
k l v w
 k l(1) 1
W3211 Spring 2009 Professor Vogel Recitation Week of 04/06/09 The rental rate of capital is v > 0 and the wage rate for labor is w > 0. 1. The demand facing Edgar' .rm, Edgaria, is given by q = 100 3p. Suppose Edgaria' s s 1 production function is f (k; l
Solutions to HW 1
Anukriti Sharma February 3, 2009
Question 1. 1. Two possible reasons are: Icelandic banking sector was huge relative to the economy, unlike the US case. As a result, US government could meet its obligations, while Iceland couldn't. Icela