# Midterm March (a) Consumer i s budget constraint is. c i b i c i H 12 (1 + r)b i c i L 12 (1 + r)b i ;

Save this PDF as:

Size: px
Start display at page:

Download "Midterm March 2015. (a) Consumer i s budget constraint is. c i 0 12 + b i c i H 12 (1 + r)b i c i L 12 (1 + r)b i ;"

## Transcription

1 Masters in Economics-UC3M Microeconomics II Midterm March 015 Exercise 1. In an economy that extends over two periods, today and tomorrow, there are two consumers, A and B; and a single perishable good, consumption. The state of nature tomorrow can either be H or L: Both consumers are endowed with twelve units of the good in each period, and their preferences over consumption today and tomorrow are represented by the utility functions u A (c A 0 ; c A H ; ca L ) = ln ca 0 + ln c A H and ub (c B 0 ; c B H ; cb L ) = ln cb 0 + ln c B L, respectively. (a) (15 points) Suppose that the only market is a credit market. Calculate how much will each person i fa; Bg borrow or save, b i ; as a function of the interest rate, r: Calculate the competitive equilibrium interest rate and allocation. Is this allocation Pareto optimal? (b) (15 points) Now suppose that in addition to the credit market there is a market for a security that pays return (one unit of the good) only in state H. Calculate how much will each person borrow or save and how many units of the security will buy or sell as a function of the interest rate and the security price, p. Calculate the competitive equilibrium interest rate and security price, as well as the allocation. Is this allocation Pareto optimal? (a) Consumer i s budget constraint is c i b i c i H 1 (1 + r)b i c i L 1 (1 + r)b i ; where b is the number of units she borrows today, and r is the interest rate. Since u A is increasing in c A 0 and c A H ; then ca 0 = 1 b i and c A H = 1 + (1 + r)ba. Likewise, since u B is increasing in c B 0 and c B L ; then cb 0 = 1 + b i and c B L = 1 (1 + r)bb. Hence consumer i fa; Bg chooses the amount she borrows in order to solve max br ln 1 + bi + ln 1 (1 + r) b i Thus, both consumers solve the same problem, and therefore their solutions coincide, i.e., b A (r) = b B (r): Hence in a competitive equilibrium there is not borrowing or lending, i.e., b A (r) + b B (r) = 0 only if b A (r) = b B (r): Hence the competitive allocation is just the initial endowment, (c A 0 ; c A H; c A L) = (c B 0 ; c B H; c B L ) = (1; 1; 1) Obviously, this allocation is not Pareto optimal. For example, the allocation is Pareto superior. (c A 0 ; c A H; c A L) = (1; 4; 0); (c B 0 ; c B H; c B L ) = (1; 0; 4)

2 (b) Normalize the price of the security to one. consumer i s budget constraint is With the credit and security markets c i b i y i c i H 1 (1 + r)b i + y c i L 1 (1 + r)b i ; where y i is the number of units of the security consumer i buys. Consumer B only cares about her consumption today and tomorrow in state L; c B 0 and c B L : By selling security and borrowing ( y B ; b B < 0); she can increase her consumption tomorrow in state L: Of course, she has to balance her budget in state H, i.e., 1 (1 + r)b B + y B 0: (1) If r 0, then by setting y B = b B = M; she maintains her consumption today at c B 0 = 1, increases her consumption tomorrow in state L to c B L = 1 (1+r)( M), and is able balance her budget in state H since 1 (1 + r) ( M) + ( M) = 1 + rm > 0: Thus, when r 0 Consumer A will want to sell an in nite amount of security and borrow an in nite amount. Therefore in a competitive equilibrium the interest rate is negative. Let us assume henceforth that r < 0. Consumer B sets up y B to solve equation (1), i.e., y B = 1 + (1 + r)b B, and chooses her demand of credit b B to solve max b B R ln 1 + b B 1 + (1 + r)b B + ln 1 (1 + r) b B : An interior solution to this problem satis es the rst order condition Solving for b B we get r 4 rb B (1 + r) 1 (1 + r) b B = 0; b B (r) = 0r + 16 r(1 + r) : Likewise, Consumer A by buying security nanced with credit is able to increase her consumption in state H, e.g., by choosing y A = b A = M > 0 is able to maintain her consumption today at c A 0 = 1 and increase her consumption tomorrow in state H to c B H = 1 rm: (recall that r < 0). Since the utility of consumer A is strictly increasing in c A H, she would like to exploit this possibility as much as possible, but is constrained as she has to payback her credit when the state is L; that is, she is limited by the constraint 0 1 (1 + r)b A :

3 Therefore, Consumer A will borrow as much as possible, that is, b A (r) = r ; and choose y A to solve max y A R ln r y A 1 + ln 1 (1 + r) 1 + r + ya : An interior solution to this problem satis es the rst order condition r y A + y A = 0: Solving for y A we get The market clearing condition is y A (r) = 8( + r) r + 1 : () b A (r) + b B (r) = 0: Solving, we obtain r = 1= and b A (r ) = b B (r ) = 4. Using equation ( ) we get y A (r ) = 4; and using equation ( 1 )y B (r ) = 4; so that, as implied by Walras Law, the security market clears for r also. The competitive allocation is therefore (c A 0 ; c A H; c A L) = (1; 4; 0); (c B 0 ; c B H; c B L ) = (1; 0; 4); which is Pareto optimal.

4 Exercise. A coastal city is considering building a small arti cial beach. It is known that some residents value this public project in v = monetary units, whereas other residents have no value for it (that is, v = 0). In order to make a decision, the city council is going to conduct a survey asking each resident whether his/her value is v. If a majority of residents answer yes, then the beach will be built and its cost will be shared equally by those who answered yes that is, those who answered no will be exempted from paying. (a) (5 points) Describe the Bayesian game faced by the residents of the city. Assume that the residents values are independent realizations of a random variable that takes values are v and v with probabilities q (0; 1) and 1 q, respectively. (b) (15 points) Assume that there are 3 residents, and that the cost of the project is 3 monetary units. Determine the set of values of q for which sincere voting is a Bayesian Nash equilibrium. Is the sincere BNE e cient? (c) (10 points) For the values of q for which sincere voting is not a BNE, is there a (mixed strategy) symmetric BNE? In this BNE e cient? (a) The Bayesian game played by the residents, following ingredients: = (N; T; A; u; p); is described by the N = f1; :::; ng T = fv; vg n A = f0; 1g n, where 0 (respectively 1) represents answering no (yes) u i : A T! R is de ned as 8 0 if P n j=1 a j < n= >< 0 if P n j=1 a j n=; t i = v and a 1 = 0 u i (a; t) = 3= P n j=1 a j if P n j=1 a j n=; t i = v and a 1 = 1 if P n j=1 >: a j n=; t i = v and a 1 = 0 3= P n j=1 a j if P n j=1 a j n=; t i = v and a 1 = 1: For each t T; p(t) = Q n j=1 (t i); where (v) = q and (v) = 1 q.

6 Exercise 3. Consider the contract design problem of a Principal whose revenue is a random variable taking values x 1 = 4 and x = 18 with probabilities that depend on whether or not the Agent exerts e ort, e f0; 1g; speci cally, p 1 (0) = p (0) = 1=; whereas p 1 (1) = 1=4 and p (1) = 3=4. The Agent s reservation utility is u = 1, and his cost of e ort is v(1) = 1 > 0 = v(0). (a) (0 points) Assuming that the Principal is risk-neutral and the preferences of the Agent are represented by the von Neumann-Morgenstern utility function u(x) = p x; determine the optimal contract when e ort is veri able. (b) (10 points) Under the assumptions in (a), determine the optimal contract when e ort is not veri able. (c) (10 points) Assuming that the Principal is risk averse and the Agent is risk-neutral, determine the optimal contract when e ort is veri able and when it is not veri able. (a) The optimal contract not requiring the Agent exerting e ort, i.e., e = 0; involves paying the Agent a xed wage w(0) = 1; which is obtained solving the participation constraint with equality, Eu( w(0)) = u + v(0), p w(0) = 1 + 0: Pro t is y(0) = E(X(0) 1) = 10: The optimal contract requiring the Agent exerting e ort (i.e., e = 1) involves paying the Agent a xed wage w(1) = 4; which is obtained solving the participation constraint with equality, Eu( w(1)) = u + v(1), p w(1) = 1 + 1: Pro t is y(1) = E (X(1)) 4) = 10:5: Hence when e ort is veri able the optimal contract is (e ; w(e )) = (1; 4) : (b) If e ort is not veri able, then the contract (0; w(0)) continues to satisfy the participation and incentive constraints. However, if the Principal wants the Agent to exert e ort, then the wage contract W (1) = (w 1 (1); w (1)) must satisfy the participation and incentive constraint with equality, that is, 1 w1 (1) + 4p 3 p w (1) = 4 1 w1 (1) + 4p 3 w (1) 1 = 4p 1 w1 (1) + p 1 p w (1) Unfortunately, this system does not have a real solution. (I am sorry, I did not plan this it is just a mistake.)

7 If we assume that the minimum wage the Principal can pay is w = 0; then the most favorable contract is w 1 (1) = 0 and 3p w (1) 4 1p w (1) 1; 4 that is, w (1) = 16: The Principal s pro t with this contract is 1 3 E (X(1)) E(W (1)) = (4) + (18 16) = < 10: Hence the optimal contract is (e ; W (e )) = (0; 1; 1): (c) In this case the optimal contract involves a franchise, i.e., a xed payment to the Principal y given by y = max E(X(e)) v(e) u: ef0;1g If we normalize the Agent s utility function to be u(x) = x, and maintain his reservation utility at the level u = 1; then our calculations in part (a) yield y = 1:5; corresponding to optimal level of e ort e = 1:

### Class Notes, Econ 8801 Lump Sum Taxes are Awesome

Class Notes, Econ 8801 Lump Sum Taxes are Awesome Larry E. Jones 1 Exchange Economies with Taxes and Spending 1.1 Basics 1) Assume that there are n goods which can be consumed in any non-negative amounts;

### UCLA. Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory

UCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory (SPRING 2011) Instructions: You have 4 hours for the exam Answer any 5 out of the 6 questions. All questions are weighted equally.

### EconS 503 - Advanced Microeconomics II Handout on Cheap Talk

EconS 53 - Advanced Microeconomics II Handout on Cheap Talk. Cheap talk with Stockbrokers (From Tadelis, Ch. 8, Exercise 8.) A stockbroker can give his client one of three recommendations regarding a certain

### Introduction. Agents have preferences over the two goods which are determined by a utility function. Speci cally, type 1 agents utility is given by

Introduction General equilibrium analysis looks at how multiple markets come into equilibrium simultaneously. With many markets, equilibrium analysis must take explicit account of the fact that changes

### Name. Final Exam, Economics 210A, December 2011 Here are some remarks to help you with answering the questions.

Name Final Exam, Economics 210A, December 2011 Here are some remarks to help you with answering the questions. Question 1. A firm has a production function F (x 1, x 2 ) = ( x 1 + x 2 ) 2. It is a price

### Adverse Selection. Chapter 3

Chapter 3 Adverse Selection Adverse selection, sometimes known as The Winner s Curse or Buyer s Remorse, is based on the observation that it can be bad news when an o er is accepted. Suppose that a buyer

### The Real Business Cycle Model

The Real Business Cycle Model Ester Faia Goethe University Frankfurt Nov 2015 Ester Faia (Goethe University Frankfurt) RBC Nov 2015 1 / 27 Introduction The RBC model explains the co-movements in the uctuations

### Intermediate Microeconomics (22014)

Intermediate Microeconomics (22014) I. Consumer Instructor: Marc Teignier-Baqué First Semester, 2011 Outline Part I. Consumer 1. umer 1.1 Budget Constraints 1.2 Preferences 1.3 Utility Function 1.4 1.5

### Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania

Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically

Advanced Microeconomics Static Bayesian games Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics / 7 Part E. Bayesian games and mechanism design Static Bayesian

### 4. Only one asset that can be used for production, and is available in xed supply in the aggregate (call it land).

Chapter 3 Credit and Business Cycles Here I present a model of the interaction between credit and business cycles. In representative agent models, remember, no lending takes place! The literature on the

### Chapter 7. Sealed-bid Auctions

Chapter 7 Sealed-bid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)

### Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that

### Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model

Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Recall that the price of an option is equal to

### Optimal Auctions. Jonathan Levin 1. Winter 2009. Economics 285 Market Design. 1 These slides are based on Paul Milgrom s.

Optimal Auctions Jonathan Levin 1 Economics 285 Market Design Winter 29 1 These slides are based on Paul Milgrom s. onathan Levin Optimal Auctions Winter 29 1 / 25 Optimal Auctions What auction rules lead

### Climate-Change Treaties: A Game-Theoretic Approach Roy Radner Stern School, New York University

Climate-Change Treaties: A Game-Theoretic Approach Roy Radner Stern School, New York University A Project Progress Report in collaboration with Prajit K. Dutta, Columbia University Sangwon Park, Korea

### Module 7: Debt Contracts & Credit Rationing

Module 7: Debt Contracts & Credit ationing Information Economics (Ec 515) George Georgiadis Two Applications of the principal-agent model to credit markets An entrepreneur (E - borrower) has a project.

### 2. Information Economics

2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many

### Work incentives and household insurance: Sequential contracting with altruistic individuals and moral hazard

Work incentives and household insurance: Sequential contracting with altruistic individuals and moral hazard Cécile Aubert Abstract Two agents sequentially contracts with different principals under moral

### Cournot s model of oligopoly

Cournot s model of oligopoly Single good produced by n firms Cost to firm i of producing q i units: C i (q i ), where C i is nonnegative and increasing If firms total output is Q then market price is P(Q),

### Prizes and patents: using market signals to provide incentives for innovations

Prizes and patents: using market signals to provide incentives for innovations V.V. Chari, Mikhail Golosov, and Aleh Tsyvinski March 1, 2009 Abstract Innovative activities have public good characteristics

### Games Played in a Contracting Environment

Games Played in a Contracting Environment V. Bhaskar Department of Economics University College London Gower Street London WC1 6BT February 2008 Abstract We analyze normal form games where a player has

### 7. EXTERNALITIES AND PUBLIC GOODS

7. EXTERNALITIES AND PUBLIC GOODS In many economic situations, markets are not complete. Certain actions of a rm or a consumer may a ect other economic agents welfare but are not market transactions. These

### Paid Placement: Advertising and Search on the Internet

Paid Placement: Advertising and Search on the Internet Yongmin Chen y Chuan He z August 2006 Abstract Paid placement, where advertisers bid payments to a search engine to have their products appear next

### Financial Markets. Itay Goldstein. Wharton School, University of Pennsylvania

Financial Markets Itay Goldstein Wharton School, University of Pennsylvania 1 Trading and Price Formation This line of the literature analyzes the formation of prices in financial markets in a setting

### Modeling Insurance Markets

Modeling Insurance Markets Nathaniel Hendren Harvard April, 2015 Nathaniel Hendren (Harvard) Insurance April, 2015 1 / 29 Modeling Competition Insurance Markets is Tough There is no well-agreed upon model

### Federal Reserve Bank of New York Staff Reports

Federal Reserve Bank of New York Staff Reports Monetary Policy Implementation Frameworks: A Comparative Analysis Antoine Martin Cyril Monnet Staff Report no. 313 January 2008 Revised October 2009 This

### Oligopoly markets: The price or quantity decisions by one rm has to directly in uence pro ts by other rms if rms are competing for customers.

15 Game Theory Varian: Chapters 8-9. The key novelty compared to the competitive (Walrasian) equilibrium analysis is that game theoretic analysis allows for the possibility that utility/pro t/payo s depend

### CPC/CPA Hybrid Bidding in a Second Price Auction

CPC/CPA Hybrid Bidding in a Second Price Auction Benjamin Edelman Hoan Soo Lee Working Paper 09-074 Copyright 2008 by Benjamin Edelman and Hoan Soo Lee Working papers are in draft form. This working paper

### the transmission channels of monetary policy the fragility of the nancial system the existence of nancial cycles

1 The macroeconomic consequences of nancial imperfections the transmission channels of monetary policy the fragility of the nancial system the existence of nancial cycles the real eects of nancial intermediation

### Price Discrimination: Exercises Part 1

Price Discrimination: Exercises Part 1 Sotiris Georganas Royal Holloway University of London January 2010 Problem 1 A monopolist sells in two markets. The inverse demand curve in market 1 is p 1 = 200

### A Welfare Criterion for Models with Distorted Beliefs

A Welfare Criterion for Models with Distorted Beliefs Markus Brunnermeier, Alp Simsek, Wei Xiong August 2012 Markus Brunnermeier, Alp Simsek, Wei Xiong () Welfare Criterion for Distorted Beliefs August

### Voluntary Voting: Costs and Bene ts

Voluntary Voting: Costs and Bene ts Vijay Krishna y and John Morgan z November 7, 2008 Abstract We study strategic voting in a Condorcet type model in which voters have identical preferences but di erential

### 1 Present and Future Value

Lecture 8: Asset Markets c 2009 Je rey A. Miron Outline:. Present and Future Value 2. Bonds 3. Taxes 4. Applications Present and Future Value In the discussion of the two-period model with borrowing and

### Lecture 1: current account - measurement and theory

Lecture 1: current account - measurement and theory What is international finance (as opposed to international trade)? International trade: microeconomic approach (many goods and factors). How cross country

### CAPM, Arbitrage, and Linear Factor Models

CAPM, Arbitrage, and Linear Factor Models CAPM, Arbitrage, Linear Factor Models 1/ 41 Introduction We now assume all investors actually choose mean-variance e cient portfolios. By equating these investors

### Lecture 2 Dynamic Equilibrium Models : Finite Periods

Lecture 2 Dynamic Equilibrium Models : Finite Periods 1. Introduction In macroeconomics, we study the behavior of economy-wide aggregates e.g. GDP, savings, investment, employment and so on - and their

### Can a Lump-Sum Transfer Make Everyone Enjoy the Gains. from Free Trade?

Can a Lump-Sum Transfer Make Everyone Enjoy te Gains from Free Trade? Yasukazu Icino Department of Economics, Konan University June 30, 2010 Abstract I examine lump-sum transfer rules to redistribute te

### ECON 40050 Game Theory Exam 1 - Answer Key. 4) All exams must be turned in by 1:45 pm. No extensions will be granted.

1 ECON 40050 Game Theory Exam 1 - Answer Key Instructions: 1) You may use a pen or pencil, a hand-held nonprogrammable calculator, and a ruler. No other materials may be at or near your desk. Books, coats,

### Dynamics and Stability of Political Systems

Dynamics and Stability of Political Systems Daron Acemoglu MIT February 11, 2009 Daron Acemoglu (MIT) Marshall Lectures 2 February 11, 2009 1 / 52 Introduction Motivation Towards a general framework? One

### UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON4310 Intertemporal macroeconomics Date of exam: Thursday, November 27, 2008 Grades are given: December 19, 2008 Time for exam: 09:00 a.m. 12:00 noon

### Financial Economics Lecture notes. Alberto Bisin Dept. of Economics NYU

Financial Economics Lecture notes Alberto Bisin Dept. of Economics NYU September 25, 2010 Contents Preface ix 1 Introduction 1 2 Two-period economies 3 2.1 Arrow-Debreu economies..................... 3

### Game Theory: Supermodular Games 1

Game Theory: Supermodular Games 1 Christoph Schottmüller 1 License: CC Attribution ShareAlike 4.0 1 / 22 Outline 1 Introduction 2 Model 3 Revision questions and exercises 2 / 22 Motivation I several solution

### FINAL EXAM, Econ 171, March, 2015, with answers

FINAL EXAM, Econ 171, March, 2015, with answers There are 9 questions. Answer any 8 of them. Good luck! Problem 1. (True or False) If a player has a dominant strategy in a simultaneous-move game, then

### Real Business Cycle Theory. Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35

Real Business Cycle Theory Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Introduction to DSGE models Dynamic Stochastic General Equilibrium (DSGE) models have become the main tool for

### Costly Voting when both Information and Preferences Di er: Is Turnout Too High or Too Low?

Costly Voting when both Information and Preferences Di er: Is Turnout Too High or Too Low? Sayantan Ghosal and Ben Lockwood University of Warwick October, 2008 Abstract We study a model of costly voting

### Oligopoly. Chapter 10. 10.1 Overview

Chapter 10 Oligopoly 10.1 Overview Oligopoly is the study of interactions between multiple rms. Because the actions of any one rm may depend on the actions of others, oligopoly is the rst topic which requires

### Midterm Exam:Answer Sheet

Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the

### .4 120 +.1 80 +.5 100 = 48 + 8 + 50 = 106.

Chapter 16. Risk and Uncertainty Part A 2009, Kwan Choi Expected Value X i = outcome i, p i = probability of X i EV = pix For instance, suppose a person has an idle fund, \$100, for one month, and is considering

### Market Power, Forward Trading and Supply Function. Competition

Market Power, Forward Trading and Supply Function Competition Matías Herrera Dappe University of Maryland May, 2008 Abstract When rms can produce any level of output, strategic forward trading can enhance

### No-Betting Pareto Dominance

No-Betting Pareto Dominance Itzhak Gilboa, Larry Samuelson and David Schmeidler HEC Paris/Tel Aviv Yale Interdisciplinary Center Herzlyia/Tel Aviv/Ohio State May, 2014 I. Introduction I.1 Trade Suppose

Advanced Microeconomics General equilibrium theory I: the main results Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 52 Part F. Perfect competition

### 14.451 Lecture Notes 10

14.451 Lecture Notes 1 Guido Lorenzoni Fall 29 1 Continuous time: nite horizon Time goes from to T. Instantaneous payo : f (t; x (t) ; y (t)) ; (the time dependence includes discounting), where x (t) 2

### Chapter 21: The Discounted Utility Model

Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal

### Problem 1 (Issuance and Repurchase in a Modigliani-Miller World)

Problem 1 (Issuance and Repurchase in a Modigliani-Miller World) A rm has outstanding debt with a market value of \$100 million. The rm also has 15 million shares outstanding with a market value of \$10

### Discussion of Self-ful lling Fire Sales: Fragility of Collateralised, Short-Term, Debt Markets, by J. C.-F. Kuong

Discussion of Self-ful lling Fire Sales: Fragility of Collateralised, Short-Term, Debt Markets, by J. C.-F. Kuong 10 July 2015 Coordination games Schelling (1960). Bryant (1980), Diamond and Dybvig (1983)

### Cheap Talk : Multiple Senders and Multiple Receivers

Corso di Laurea in Economia indirizzo Models and Methods of Quantitative Economics Prova finale di Laurea Cheap Talk : Multiple Senders and Multiple Receivers Relatore Prof. Piero Gottardi Laureando Arya

### IS LABOR MOBILITY A PREREQUISITE FOR AN OPTIMAL CURRENCY AREA? LABOR MOBILITY AND FISCAL POLICY IN A CURRENCY UNION

XXV CONFERENZA LA FINANZA PUBBLICA NEI SISTEMI MULTILIVELLO COORDINAMENTO, CONCORRENZA E DISCIPLINA FISCALE Pavia, Aule Storiche dell Università, 26-27 settembre 203 IS LABOR MOBILITY A PREREQUISITE FOR

### Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.

Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry

### An example of externalities - the multiplicative case

An example of externalities - the multiplicative case Yossi Spiegel Consider an exchange economy with two agents, A and B, who consume two goods, x and y. This economy however, differs from the usual exchange

### Our development of economic theory has two main parts, consumers and producers. We will start with the consumers.

Lecture 1: Budget Constraints c 2008 Je rey A. Miron Outline 1. Introduction 2. Two Goods are Often Enough 3. Properties of the Budget Set 4. How the Budget Line Changes 5. The Numeraire 6. Taxes, Subsidies,

### Tiered and Value-based Health Care Networks

Tiered and Value-based Health Care Networks Ching-to Albert Ma Henry Y. Mak Department of Economics Department of Economics Boston Univeristy Indiana University Purdue University Indianapolis 270 Bay State

### Covert Networks and the Antitrust Policy

Covert Networks and the Antitrust Policy Flavia Roldán Universidad ORT Uruguay and Public-Private Sector Research Center, IESE Business School June, 2011 Abstract This article studies the e ectiveness

### CONTRACTUAL SIGNALLING, RELATIONSHIP-SPECIFIC INVESTMENT AND EXCLUSIVE AGREEMENTS

CONTRACTUAL SIGNALLING, RELATIONSHIP-SPECIFIC INVESTMENT AND EXCLUSIVE AGREEMENTS LUÍS VASCONCELOS y Abstract. I analyze a simple model of hold-up with asymmetric information at the contracting stage.

### Applied cooperative game theory:

Applied cooperative game theory: Firms and markets Harald Wiese University of Leipzig April 2010 Harald Wiese (Chair of Microeconomics) Applied cooperative game theory: April 2010 1 / 30 Overview part

### Economics 200B Part 1 UCSD Winter 2015 Prof. R. Starr, Mr. John Rehbeck Final Exam 1

Economics 200B Part 1 UCSD Winter 2015 Prof. R. Starr, Mr. John Rehbeck Final Exam 1 Your Name: SUGGESTED ANSWERS Please answer all questions. Each of the six questions marked with a big number counts

### 2. Suppose two Cournot duopolist rms operate at zero marginal cost. The market demand is p = a bq. Firm 1 s best-response function is

Econ301 (summer 2007) Quiz 1 Date: Jul 5 07 Instructor: Helen Yang PART I: Multiple Choice (5 points each, 75 points in total) 1. In the long run, a monopolistically competitive rm (a) operates at full

### Corporate Income Taxation

Corporate Income Taxation We have stressed that tax incidence must be traced to people, since corporations cannot bear the burden of a tax. Why then tax corporations at all? There are several possible

### Central Bank Lending and Money Market Discipline

Central Bank Lending and Money Market Discipline Marie Hoerova European Central Bank Cyril Monnet FRB Philadelphia November 2010 PRELIMINARY Abstract This paper provides a theory for the joint existence

### Optimal insurance contracts with adverse selection and comonotonic background risk

Optimal insurance contracts with adverse selection and comonotonic background risk Alary D. Bien F. TSE (LERNA) University Paris Dauphine Abstract In this note, we consider an adverse selection problem

### Pricing Cloud Computing: Inelasticity and Demand Discovery

Pricing Cloud Computing: Inelasticity and Demand Discovery June 7, 203 Abstract The recent growth of the cloud computing market has convinced many businesses and policy makers that cloud-based technologies

### The E ect of Trading Commissions on Analysts Forecast Bias

The E ect of Trading Commissions on Analysts Forecast Bias Anne Beyer and Ilan Guttman Stanford University September 2007 Abstract The paper models the interaction between a sell-side analyst and a risk-averse

### In ation Tax and In ation Subsidies: Working Capital in a Cash-in-advance model

In ation Tax and In ation Subsidies: Working Capital in a Cash-in-advance model George T. McCandless March 3, 006 Abstract This paper studies the nature of monetary policy with nancial intermediaries that

### Short Run Market Equilibrium. The market supply curve is found by horizontally adding the supply curves of individual rms. If there are m rms, we have

Short Run Market Equilibrium The market supply curve is found by horizontally adding the supply curves of individual rms. If there are m rms, we have X s (p x )= mx j=1 x j (p x ): Just as we can talk

### Internet Advertising and the Generalized Second Price Auction:

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords Ben Edelman, Harvard Michael Ostrovsky, Stanford GSB Michael Schwarz, Yahoo! Research A Few

### On the optimality of optimal income taxation

Preprints of the Max Planck Institute for Research on Collective Goods Bonn 2010/14 On the optimality of optimal income taxation Felix Bierbrauer M A X P L A N C K S O C I E T Y Preprints of the Max Planck

### ECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015

ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1

### Four Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com

Four Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com In this Note we derive the Black Scholes PDE for an option V, given by @t + 1 + rs @S2 @S We derive the

### 2. Efficiency and Perfect Competition

General Equilibrium Theory 1 Overview 1. General Equilibrium Analysis I Partial Equilibrium Bias 2. Efficiency and Perfect Competition 3. General Equilibrium Analysis II The Efficiency if Competition The

### Economic Principles Solutions to Problem Set 1

Economic Principles Solutions to Problem Set 1 Question 1. Let < be represented b u : R n +! R. Prove that u (x) is strictl quasiconcave if and onl if < is strictl convex. If part: ( strict convexit of

### Problem Set 9 Solutions

Problem Set 9 s 1. A monopoly insurance company provides accident insurance to two types of customers: low risk customers, for whom the probability of an accident is 0.25, and high risk customers, for

### Labor Economics, 14.661. Lecture 3: Education, Selection, and Signaling

Labor Economics, 14.661. Lecture 3: Education, Selection, and Signaling Daron Acemoglu MIT November 3, 2011. Daron Acemoglu (MIT) Education, Selection, and Signaling November 3, 2011. 1 / 31 Introduction

### ARE STOCK PRICES PREDICTABLE? by Peter Tryfos York University

ARE STOCK PRICES PREDICTABLE? by Peter Tryfos York University For some years now, the question of whether the history of a stock's price is relevant, useful or pro table in forecasting the future price

### Cooperation with Network Monitoring

Cooperation with Network Monitoring Alexander Wolitzky Microsoft Research and Stanford University July 20 Abstract This paper studies the maximum level of cooperation that can be sustained in sequential

### The Real Business Cycle model

The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian

### The Market-Clearing Model

Chapter 5 The Market-Clearing Model Most of the models that we use in this book build on two common assumptions. First, we assume that there exist markets for all goods present in the economy, and that

### Economics II: Micro Fall 2009 Exercise session 5. Market with a sole supplier is Monopolistic.

Economics II: Micro Fall 009 Exercise session 5 VŠE 1 Review Optimal production: Independent of the level of market concentration, optimal level of production is where MR = MC. Monopoly: Market with a

### 10. Fixed-Income Securities. Basic Concepts

0. Fixed-Income Securities Fixed-income securities (FIS) are bonds that have no default risk and their payments are fully determined in advance. Sometimes corporate bonds that do not necessarily have certain

### Working Paper Series

RGEA Universidade de Vigo http://webs.uvigo.es/rgea Working Paper Series A Market Game Approach to Differential Information Economies Guadalupe Fugarolas, Carlos Hervés-Beloso, Emma Moreno- García and

### Competition and Fraud in Online Advertising Markets

Competition and Fraud in Online Advertising Markets Bob Mungamuru 1 and Stephen Weis 2 1 Stanford University, Stanford, CA, USA 94305 2 Google Inc., Mountain View, CA, USA 94043 Abstract. An economic model

### Margin Requirements and Equilibrium Asset Prices

Margin Requirements and Equilibrium Asset Prices Daniele Coen-Pirani Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA Abstract This paper studies

### Intertemporal approach to current account: small open economy

Intertemporal approach to current account: small open economy Ester Faia Johann Wolfgang Goethe Universität Frankfurt a.m. March 2009 ster Faia (Johann Wolfgang Goethe Universität Intertemporal Frankfurt

### Lecture 11: The Design of Trading Platforms (Alos-Ferrer et al. 2010)

Lecture 11: The Design of Trading Platforms (Alos-Ferrer et al. 2010) 1. Introduction Lecture 10: selection between exogenously given market institutions now: emergence of new institutions 2 possibilities

### 1 Directional Trading Strategies

Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Directional Trading Strategies 1 Directional Trading Strategies With options you can pro t from correctly predicting

### ECON 305 Tutorial 7 (Week 9)

H. K. Chen (SFU) ECON 305 Tutorial 7 (Week 9) July 2,3, 2014 1 / 24 ECON 305 Tutorial 7 (Week 9) Questions for today: Ch.9 Problems 15, 7, 11, 12 MC113 Tutorial slides will be posted Thursday after 10:30am,

### AFM 472. Midterm Examination. Monday Oct. 24, 2011. A. Huang

AFM 472 Midterm Examination Monday Oct. 24, 2011 A. Huang Name: Answer Key Student Number: Section (circle one): 10:00am 1:00pm 2:30pm Instructions: 1. Answer all questions in the space provided. If space

### The Stock Market, Monetary Policy, and Economic Development

The Stock Market, Monetary Policy, and Economic Development Edgar A. Ghossoub University of Texas at San Antonio Robert R. Reed University of Alabama July, 20 Abstract In this paper, we examine the impact

### Choice under Uncertainty

Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory