Microeconomic Theory II Assignment 5: Game Theory Solutions
March 10, 2007
Problem 1. [MWG 8.D.3] Consider a rst-price sealed-bid auction of an object with two bidders. Each bidder is valuation of the object is vi , which is known to both bidders. Ea
Memorandum to Students EC 206 Microeconomic Theory II Prof. Glenn C. Loury March 16, 2007 Students: I recognize that you have had a lot of material thrown at you lately, without proper motivation or organization. Because I don't want our time and eff
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 8: The Principal-Agent Problem (1) A principal needs to contract with an agent to get a risky project done. The project can either succeed or fail. If it succeeds it generates output with gross va
Microeconomic Theory II Assignment 7: Even more on Game Theory and some Externalities and Public Goods Solutions
April 4, 2007
Problem 1. Consider the following extensive form game of complete information (analogous to the partnership game studied by
Economics 206 Spring 2007 (Prof. G. Loury) A Note on Stochastic Dominance (February 8, 2007) Here are a few observations on stochastic dominance that may help with the material in yesterdays lecture. We will study the partial orderings of probability
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 1: Choice under Uncertainty 1. Concerning the Independence Axiom: L L [0, 1], L : L + (1 )L L + (1 )L
(a) (The Axiom extends to strict preference and to indierence.) Show that the Independen
EC 206 Microeconomics II First Midterm Exam February 28, 2007 Professor Glenn C. Loury Instructions. Please answser each of the three questions below. Use a separate blue book for each question. Be sure to put your name, ID #, and the question # on e
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 3: Applications of Stochastic Dominance 1. Let 0 be a random variable representing a workers true ability. tests of worker ability, i = 1, 2, with test scores t1 and t2 given by: t1 = + and t2
EC 206 Microeconomics II: Second Midterm Exam April 9, 2007 (Professor Glenn C. Loury) Instructions. Please answser each of the three questions below. You do NOT need to use separate blue books for each question, but be sure to put your name and ID #
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 2: Risk and Information 1. Concerning Measures of Risk Aversion: Let ui : , i = 1, 2, be two strictly increasing, strictly concave, twice dierentiable Bernoulli utility functions; and, let F : [
EC 206 Microeconomics II: Final Examination May 4, 2007 (Professor Glenn C. Loury) Answers 1. {50 points} (A Principal-Agent Problem) The value of the project is the maximal net surplus that can be realized by exerting costly eort which raises the ch
Microeconomic Theory II Assignment 5: Game Theory Solutions
March 10, 2007
Problem 1. [MWG 8.D.3] Consider a rst-price sealed-bid auction of an object with two bidders. Each bidder is valuation of the object is vi , which is known to both bidders. Ea
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 8: Signalling Games (1) Consider the following Grade Ination Problem: A professor must issue an evaluation of his student to the market. The professor perfectly observes his students productivity,
Microeconomic Theory II Assignment 4: Using Game Theory Solutions
February 25, 2007
Problem 1. Consider the simple duopoly model with linear demand: Two rms produce a homogeneous good for sale in a market with the inverse demand curve P = Max{d Q, 0
Economics 206 Spring 2007 (Prof. G. Loury) Solution of Racing Problem in Assignment 7 [Racing Game] Let V be the value of the prize, and let C(x) be the cost to a player of taking a step toward the nish line of size x. A player gets to move every sec
Economics 206 Spring 2007 (Prof. G. Loury) Solution of Racing Problem in Assignment 7 [Racing Game] Let V be the value of the prize, and let C(x) be the cost to a player of taking a step toward the nish line of size x. A player gets to move every sec
Microeconomic Theory II Assignment 3: Applications of Stochastic Dominance Solutions
February 21, 2007
Problem 1. Let 0 be a random variable representing a workers true ability. worker ability, i = 1, 2, with test scores t1 and t2 given by: t1 = +
EC 206 Microeconomics II: Second Midterm Exam April 9, 2007 (Professor Glenn C. Loury) ANSWERS 1. {35 points} Three bidders participate in the auction sale of a single object which is worth vi to bidder i , where vi is uniformly distributed on the un
Microeconomic Theory II Assignment 2: Risk and Information Solutions
February 15, 2007
Problem 1. Concerning Measures of Risk Aversion: Let ui : , i = 1, 2, be two strictly increasing, strictly concave, twice dierentiable Bernoulli utility functions
Economics 206 Spring 2007 (Prof. G. Loury) Assignment 8: Signalling Games (1) Solution for the Grade Ination Problem: You were asked to show that there is an equilibrium without grade ination in the Grade Ination Signalling Game if and only if: [H L
Microeconomic Theory II Assignment 1: Choice under Uncertainty Solutions
February 20, 2007
Problem 1. Concerning the Independence Axiom: L L [0, 1], L : L + (1 )L L + (1 )L
1. (The Axiom extends to strict preference and to indierence.) Show th
Economics 206 Spring 2007 (Prof. G. Loury) Answers for Assignment 9: The Principal-Agent Problem (1) This is a simple example of the Principal-Agent problem where the agent's (unobservable) effort level can be any non-negative number, but only two (o