d. Find a competitive equilibrium for this economy. Is the allocation Pareto efficient? Are there any other competitive equilibrium allocations?
|
|
- Michael Long
- 5 years ago
- Views:
Transcription
1 Answers to Microeconomics Prelim of August 7, 0. Consider an individual faced with two job choices: she can either accept a position with a fixed annual salary of x > 0 which requires L x units of labor per annum, or she can start her own business producing widgets. The technology for producing widgets is given by y = f(l, T ) = L T, where L denotes labor (again per annum) and T denotes the quantity of another input. If she were to start her own business, she would devote her own labor time to production rather than hiring outside labor. Both the market for T and the market for widgets are perfectly competitive. However, while the price of T is known to be t, the price of widgets depends upon the state of the economy: if the economy is good, the price will be p g, and if it is bad, the price will be p b < p g. The probability that the economy will be good is π, and the probability that it will be bad is ( π). The individual must determine T and L before knowing which state occurs. Assume she has the (von Neumann - Morgenstern) utility function u(m, L) = m( L L), where m is money, L is her labor, and L is her endowment of time ( L > L x ). Her only source of money is from the job she chooses. a. Explain precisely how the individual would choose between the two jobs. b. If the individual were to start her own business, determine the optimal quantities of y, T, and L she would choose, as functions of the parameters. c. Discuss how changes in the parameters affect her decision whether to start her own business. Increases in which parameters increase the likelihood that she starts her own business? d. Next, suppose L =, t =, and (x, L x ) = (6, ) Show that if she was certain the economy would be good and if p g = 0, then she would choose to start her own firm; whereas if she was certain the economy would be bad and if p b = 8, then she would rather accept the offer of (x, L x ). For the remainder of the problem, suppose the widget technology is changed to y = L / T /4. e. Now, assume that if she starts her own business, instead of devoting her own labor to production, she hires outside labor at the wage w. Again, she must decide on all input amounts before learning the state of the economy. In this case, her business is her only source of income and she does not work otherwise. Alternatively, she can accept the job with the fixed salary x and labor requirement L x, as before. Set up her decision problem. f. Compare the individual s optimal decisions in part e to what she would choose if she were to maximize expected profit instead of expected utility as the owner of her own business. g. Finally, suppose that if she starts her own business she can both hire outside labor at wage w and supplement this using her own labor. Set up the new decision problem and discuss how this would affect the likelihood of her starting her own business.. Consider an economy with two goods, two consumers, and one firm. The firm produces f(l) = min{5l, 5} units of food when it uses L 0 units of labor as input. It also can dispose of either good without cost. Consumer initially owns units of time (for labor or leisure) and gets utility cl from consuming c 0 units of food and l 0 units of leisure. Consumer owns the firm and, initially, no goods. Consumer cares only about food and wants as much of it as possible. a. Graph the production function of the firm. Describe its returns to scale. b. Is there a Pareto efficient (Pareto optimal) allocation in which consumer consumes no food and no leisure? Explain. c. Find all Pareto efficient allocations in this economy. How do they differ from one another?
2 d. Find a competitive equilibrium for this economy. Is the allocation Pareto efficient? Are there any other competitive equilibrium allocations? Suppose now that there is technical progress. The firm has a new production function g(l) = 8 L for L 0. The rest of the economy remains the same as before. e. Find a competitive equilibrium and compare the allocation and the welfare of the consumers to what they were in the equilibrium of part d. f. Is the allocation in part e Pareto efficient for the economy after there is technical progress? g. Does the technical progress lead to Pareto improvement if the economy is competitive? Explain why or why not. Answers: a. The graph of the production function f(l) has a kink at (3, 5). To the left of this point, the graph is linear with slope 5, joining (3, 5) to (0, 0). To the right of (3, 5), the graph is horizontal. There are constant returns to scale over the input range L [0, 3) and decreasing returns for increases in input from any L > 0 to any L > max{l, 3} since tl = L implies tf(l ) = 5tL > 5 = f(tl ). b. and c. A Pareto efficient allocation must solve max c l s.t. c +c f(l), l +l +L, c i 0, l i 0, i =,, and c c for some c. For feasible L, f(l) = 5L. If, at a solution, c l > 0, then l = 0 and the first two constraints and last constraint bind. Otherwise c l can be raised. At such a solution, the problem can be rewritten as max c l s.t. c = 5( l ) c, which is solved at c = (0 c )/, l = (0 c )/0, L = + ( c /0), f(l) = 5 + ( c /), c = c, l = 0. There are multiple solutions with c l = 0 in the optimization problem above, but for the allocation to be Pareto efficient, c must be maximized subject to feasibility, which implies c = l = l = 0, L =, f(l) = 0 = c. The different efficient allocations differ according to how much food consumer gets. The more food consumer gets, the more consumer works and the less it consumes. d. Let p and w be equilibrium prices of food and time. If p 0, then the consumers have no optimal consumption, so p > 0 in equilibrium. The firm s profit is 5pL wl if L 3, so if w < 5p, the firm demands L = 3, which is not feasible. If w > 5p, then the firm demands L = 0, but consumer demands a positive amount of food, so in equilibrium, w = 5p > 0 and the profit is 0. Consumer has Cobb-Douglas demands c = w/(p) = 5, l = w/(w) =. Consumer has no wealth, so no consumption. The firm demands L = l = and produces f(l) = 5. These conclusions follow from the definition of equilibrium, so there is no other competitive allocation. The allocation is Pareto efficient from part b or, alternatively, from the first welfare theorem since the preferences are locally nonsatiated. e. As in part d, c = w/p, l =. Consumer demands no leisure, so L = l = maximizes the firm s profit 8p L wl. This implies 4p = w, c = 4, g(l) = 8, c = 4, where c can be found using feasibility or the budget constraint of consumer : pc = 8p wl = 8p w. The wage rate in terms of food falls compared to the equilibrium in part d. Consumer works and gets as much leisure as in part d, but consumes less food. The firm produces more and gets more profit and consumer gets more food than in part d. f. The allocation is Pareto efficient by the first welfare theorem. g. The technical progress does not lead to Pareto improvement. The marginal product of consumer at the initial equilibrium labor supply falls as a result of the progress, since the productivity of smaller amounts of labor rises. As a result, the wage rate falls in terms of food and consumer, whose income comes only from labor, is hurt.
3 3. A monopoly firm can hire from a population of qualified workers. Half of the workers are of type and half of type. Type θ workers (θ =, ) produce θ( + t) units of output when they are assigned a job of difficulty type t 0. A worker of type θ who is paid w units of output gets utility w c(t, θ) when working at a job of type t, where c is twice continuously differentiable. Denoting partial derivatives by subscripts, c tt (t, θ) > 0, c tθ (t, θ) <, c(0, θ) = 0, c t (0, θ) = 0, c t (, ) >, for all t > 0 and θ 0. The monopoly can offer workers jobs of any type t 0 and wages depending on the job type. It seeks to maximize its expected profit, where the profit from any particular worker is the value of the worker s output minus the wage the monopoly pays. Workers are free to accept or reject any contracts offered to them. They maximize their utility, getting reservation utility of 0 if they reject all offers. a. Interpret the assumptions about c and its derivatives and describe how the types of workers differ from each other. b. Suppose the monopoly can recognize every worker s type θ before it makes any contract offers. Formulate the monopoly s optimization problem. Find an optimal job difficulty t for each type θ (optimal for the monopoly). Find corresponding wages that are optimal for the monopoly for each of these job types. Show how these optimal contracts can look in a graph. Compare the contracts the two worker types receive, being as specific as possible. c. Suppose now that the monopoly cannot recognize any particular worker s type, but knows all the information given above part a. Formulate the monopoly s optimization problem when it can offer a menu of contracts (job difficulty types and corresponding wages). Characterize the optimal contracts that workers accept and show how they can look in a graph. The graph can be the same one you used in part b. Compare the contracts received by the two types of workers to each other and to those they receive in part b. Be as specific as possible with the given information. Compare the expected profit of the monopoly to what it is in part b. What fraction of the workers in the population does the monopoly want to hire? d. What can be said about the efficiency of the outcomes in parts b and c? If an outcome is Pareto inefficient, could a government that has the same information as the monopoly obtain a Pareto improvement by restricting the set of contracts the monopoly can offer? Explain. Answers: 3a. More difficult jobs are more costly for both types of workers. The marginal cost (cost of a small amount of additional difficulty per unit of difficulty) is near 0 for the more productive worker (type ) when the difficulty is near 0 and the cost and marginal cost are less for the more productive worker than for the other type worker. The marginal cost rises for both worker types as the job difficulty increases and is above for the more productive worker when the difficulty is above. b. The monopoly offers type θ a wage w and job type t to maximize θ( + t) w s.t. w c(t, θ) 0. The optimal t maximizes θ( + t) c(t, θ) and is the unique solution to θ c (t, θ), with equality if t > 0. Denote this t by ˆt θ. The corresponding wage is ŵ θ = c θ (ˆt θ ). Since c (0, ) = 0 and c (, ) >, we have 0 < ˆt <. If ˆt > 0, then implicit differentiation of the first order condition yields dˆt θ /dθ > 0, so the higher productivity worker is assigned a more difficult job. The same conclusion holds if ˆt = 0 since ˆt > 0. As in the graphs, the wage can be higher for type or for type, but type strictly prefers the contract received by type to its own contract if type is paid a positive wage (since the graph of c(t, ) lies above that of c(t, ), except possibly at t = 0, and these graphs are indifference curves of the two types at utility level 0.) Each type gets utility 0 and a wage below its productivity. c. The monopoly cannot do better than to offer two contracts (t θ, w θ ), θ =, to maximize its expected profit ( + t w + + t w )/ from a given worker subject to (Pθ) w θ c(t θ, θ) (participation constraints) and 3
4 4 (Iθ) w θ c(t θ, θ) w θ c(t θ, θ), θ, θ =, (incentive constraints). In the usual way, it is possible to show that maximizing the objective function subject to (P) and (I) alone yields a solution that satisfies the other two constraints and satisfies (P) and (I) with equality. The first order conditions for the monopoly optimization imply = c (t, ) and = c (t, ) c (t, ) > c (t, ), hence t = ˆt and t < ˆt (unless ˆt = 0). Also w = c(t, ) and w satisfies I with equality. It follows that w < ŵ unless ˆt = 0 and that t > t, w > w, w c(t, ) > 0, and w > ŵ. The monopoly expected profit is less than in part b, but it is still positive, so the monopoly wants to hire all the qualified workers. d. If workers of type θ get (t θ, w θ ), then w θ = θ( + t θ ). If w θ is higher, then the firm makes an expected loss on that contract and gets a higher payoff by withdrawing it. If wθ is lower, then a firm whose contract is rejected by type θ can raise its payoff by offering a slightly higher wage and the same job difficulty, an offer that type θ accepts. The same argument shows that (θ, w) maximizes w c(t, ) s.t. w = + t, so t = ˆt. Let ( t, w ) satisfy w = + t and w c(t, ) = w c( t, ) so that type is indifferent between ( t, w ) and (t, w). Since type prefers (t, w) to (t, w) if t < t, type must get its most preferred contract satisfying t t and w = + t. If ˆt < t, then (t, w) = ( t, w ). Otherwise, (t, w) = (ˆt, + ˆt ). In any case, t > t and w > w. Type gets the same job difficulty as in part b (more than in part c unless ˆt = 0) and a higher wage than in both b and c. If ˆt t, then type gets the same job difficulty as in b and c and a higher wage. If ˆt < t, then type gets a more difficult job than in b and c and gets a higher wage., 6 F B N /3 /3 A E 5, 6 D C D C 0, 3 9, 0 0, 3 9, 5 4. Nature (N) and players and play the game represented by the tree above. N plays left with probability /3 and right with probability /3. The payoff of player is listed first at each terminal node. a. List all the pure strategies of player and of player. b. Represent the extensive form game above as a strategic form game in which the payoffs corresponding to strategies of players and are the expected payoffs. c. For the game in part b, find all the Nash equilibria (NE) in which players and play pure strategies. d. Returning to the extensive form game, consider a behavioral strategy profile in which player plays A with probability a, plays B with probability b, and plays C with
5 5 probability c. Let α be the belief probability that player attaches to the node following A. Find all the sequential equilibria in which players and play pure strategies (i.e., where each of a, b, c takes the value of either 0 or ). Compare your results to those in part c. e. There is a sequential equilibrium in which b = but 0 < a < and 0 < c <. Find it and describe it in words. Answers: 4a. Player : AB, AF, EB, EF. Player : C, D. \ C D AB 9, 0/3 0, 3 b. AF 0/3, 6/3 /3, 4 c. The pure NE are {AB, C} and {EF, D}. EB 9/3, 4 0/3, 5 EF 4, 6 4, 6 d. If a and b are both 0, then α can be any number in [0, ]. To show this, we need to construct sequences of totally mixed strategies with probabilities a k and b k of A and B converging to 0 with conditional probabilities of the node after A converging to α. If α (0, ), then the sequences a k = α/k and b k = ( α)/k have this property. If α = 0, then a k = /k and b k = /k work and if α =, then a k = /k and b k = /k do. (/3)a If a and b are not both 0, then α = (/3)a+(/3)b +(/)(b/a) if α > 3/5 if c > 5/9 Player s best response: c = [0, ] if α = 3/5 Player right: a = [0, ] if c = 5/9 0 if α < 3/5 0 if c < 5/9 Player left: b = if c > /9 [0, ] if c = /9 0 if c < /9 Then c = {a =, b = } α = 3 c =. Also c = 0 {a = 0, b = 0} α [0, ]. In order to generate c = 0, α 3. So pure strategy 5 sequential equilibria are: {a =, b =, c = } with α = /3 and {a = 0, b = 0, c = 0} with α 3/5. e. From the answer to part d, if 0 < a, c < in SE, we must have α = 3/5 and c = 5/9. If b =, then 3/5 = α = implies a = 3/4. Thus, {a = 3/4, b =, c = 5/9} +(/)(b/a) with α = 3/5 is a sequential equilibrium. In it, the left type of player chooses to interact with player for sure and the right type of player chooses to interact with player with probability 3/4. If player interacts with player, player believes that it is the right type with probability 3/5 and cooperates (accommodates by choosing C) with probability 5/9.,
Answers to June 11, 2012 Microeconomics Prelim
Answers to June, Microeconomics Prelim. Consider an economy with two consumers, and. Each consumer consumes only grapes and wine and can use grapes as an input to produce wine. Grapes used as input cannot
More informationAnswers to Microeconomics Prelim of August 24, In practice, firms often price their products by marking up a fixed percentage over (average)
Answers to Microeconomics Prelim of August 24, 2016 1. In practice, firms often price their products by marking up a fixed percentage over (average) cost. To investigate the consequences of markup pricing,
More informationUniversity at Albany, State University of New York Department of Economics Ph.D. Preliminary Examination in Microeconomics, June 20, 2017
University at Albany, State University of New York Department of Economics Ph.D. Preliminary Examination in Microeconomics, June 0, 017 Instructions: Answer any three of the four numbered problems. Justify
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2015 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2014 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationAdvanced Microeconomic Theory EC104
Advanced Microeconomic Theory EC104 Problem Set 1 1. Each of n farmers can costlessly produce as much wheat as she chooses. Suppose that the kth farmer produces W k, so that the total amount of what produced
More informationCUR 412: Game Theory and its Applications, Lecture 9
CUR 412: Game Theory and its Applications, Lecture 9 Prof. Ronaldo CARPIO May 22, 2015 Announcements HW #3 is due next week. Ch. 6.1: Ultimatum Game This is a simple game that can model a very simplified
More informationEC202. Microeconomic Principles II. Summer 2009 examination. 2008/2009 syllabus
Summer 2009 examination EC202 Microeconomic Principles II 2008/2009 syllabus Instructions to candidates Time allowed: 3 hours. This paper contains nine questions in three sections. Answer question one
More informationGeneral Examination in Microeconomic Theory SPRING 2014
HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Microeconomic Theory SPRING 2014 You have FOUR hours. Answer all questions Those taking the FINAL have THREE hours Part A (Glaeser): 55
More informationEcon 101A Final Exam We May 9, 2012.
Econ 101A Final Exam We May 9, 2012. You have 3 hours to answer the questions in the final exam. We will collect the exams at 2.30 sharp. Show your work, and good luck! Problem 1. Utility Maximization.
More informationDepartment of Economics The Ohio State University Midterm Questions and Answers Econ 8712
Prof. James Peck Fall 06 Department of Economics The Ohio State University Midterm Questions and Answers Econ 87. (30 points) A decision maker (DM) is a von Neumann-Morgenstern expected utility maximizer.
More informationMicroeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 2017
Microeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 017 1. Sheila moves first and chooses either H or L. Bruce receives a signal, h or l, about Sheila s behavior. The distribution
More informationRamsey s Growth Model (Solution Ex. 2.1 (f) and (g))
Problem Set 2: Ramsey s Growth Model (Solution Ex. 2.1 (f) and (g)) Exercise 2.1: An infinite horizon problem with perfect foresight In this exercise we will study at a discrete-time version of Ramsey
More informationMicroeconomic Theory May 2013 Applied Economics. Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY. Applied Economics Graduate Program.
Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY Applied Economics Graduate Program May 2013 *********************************************** COVER SHEET ***********************************************
More informationEcon 101A Final exam Mo 18 May, 2009.
Econ 101A Final exam Mo 18 May, 2009. Do not turn the page until instructed to. Do not forget to write Problems 1 and 2 in the first Blue Book and Problems 3 and 4 in the second Blue Book. 1 Econ 101A
More informationFinal Examination December 14, Economics 5010 AF3.0 : Applied Microeconomics. time=2.5 hours
YORK UNIVERSITY Faculty of Graduate Studies Final Examination December 14, 2010 Economics 5010 AF3.0 : Applied Microeconomics S. Bucovetsky time=2.5 hours Do any 6 of the following 10 questions. All count
More informationAnswer: Let y 2 denote rm 2 s output of food and L 2 denote rm 2 s labor input (so
The Ohio State University Department of Economics Econ 805 Extra Problems on Production and Uncertainty: Questions and Answers Winter 003 Prof. Peck () In the following economy, there are two consumers,
More informationSupplement to the lecture on the Diamond-Dybvig model
ECON 4335 Economics of Banking, Fall 2016 Jacopo Bizzotto 1 Supplement to the lecture on the Diamond-Dybvig model The model in Diamond and Dybvig (1983) incorporates important features of the real world:
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationChapter 4 Topics. Behavior of the representative consumer Behavior of the representative firm Pearson Education, Inc.
Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-1 Representative Consumer Consumer s preferences over consumption and leisure as represented by indifference
More informationMicroeconomics II. CIDE, MsC Economics. List of Problems
Microeconomics II CIDE, MsC Economics List of Problems 1. There are three people, Amy (A), Bart (B) and Chris (C): A and B have hats. These three people are arranged in a room so that B can see everything
More informationMicroeconomic Theory August 2013 Applied Economics. Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY. Applied Economics Graduate Program
Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY Applied Economics Graduate Program August 2013 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationIntroduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4)
Introduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4) Outline: Modeling by means of games Normal form games Dominant strategies; dominated strategies,
More informationCUR 412: Game Theory and its Applications, Lecture 12
CUR 412: Game Theory and its Applications, Lecture 12 Prof. Ronaldo CARPIO May 24, 2016 Announcements Homework #4 is due next week. Review of Last Lecture In extensive games with imperfect information,
More informationUnraveling 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 October, 2013 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that
More informationProblem Set VI: Edgeworth Box
Problem Set VI: Edgeworth Box Paolo Crosetto paolo.crosetto@unimi.it DEAS - University of Milan Exercises solved in class on March 15th, 2010 Recap: pure exchange The simplest model of a general equilibrium
More informationPAULI MURTO, ANDREY ZHUKOV
GAME THEORY SOLUTION SET 1 WINTER 018 PAULI MURTO, ANDREY ZHUKOV Introduction For suggested solution to problem 4, last year s suggested solutions by Tsz-Ning Wong were used who I think used suggested
More informationECO 352 International Trade Spring Term 2010 Week 3 Precepts February 15 Introduction, and The Exchange Model Questions
ECO 35 International Trade Spring Term 00 Week 3 Precepts February 5 Introduction, and The Exchange Model Questions Question : Here we construct a more general version of the comparison of differences
More informationMONOPOLY (2) Second Degree Price Discrimination
1/22 MONOPOLY (2) Second Degree Price Discrimination May 4, 2014 2/22 Problem The monopolist has one customer who is either type 1 or type 2, with equal probability. How to price discriminate between the
More informationAnswers to Problem Set 4
Answers to Problem Set 4 Economics 703 Spring 016 1. a) The monopolist facing no threat of entry will pick the first cost function. To see this, calculate profits with each one. With the first cost function,
More informationAdvanced Microeconomics
Advanced Microeconomics ECON5200 - Fall 2014 Introduction What you have done: - consumers maximize their utility subject to budget constraints and firms maximize their profits given technology and market
More informationMA200.2 Game Theory II, LSE
MA200.2 Game Theory II, LSE Problem Set 1 These questions will go over basic game-theoretic concepts and some applications. homework is due during class on week 4. This [1] In this problem (see Fudenberg-Tirole
More informationHW Consider the following game:
HW 1 1. Consider the following game: 2. HW 2 Suppose a parent and child play the following game, first analyzed by Becker (1974). First child takes the action, A 0, that produces income for the child,
More informationSection 9, Chapter 2 Moral Hazard and Insurance
September 24 additional problems due Tuesday, Sept. 29: p. 194: 1, 2, 3 0.0.12 Section 9, Chapter 2 Moral Hazard and Insurance Section 9.1 is a lengthy and fact-filled discussion of issues of information
More informationCUR 412: Game Theory and its Applications Final Exam Ronaldo Carpio Jan. 13, 2015
CUR 41: Game Theory and its Applications Final Exam Ronaldo Carpio Jan. 13, 015 Instructions: Please write your name in English. This exam is closed-book. Total time: 10 minutes. There are 4 questions,
More informationAnswer Key for M. A. Economics Entrance Examination 2017 (Main version)
Answer Key for M. A. Economics Entrance Examination 2017 (Main version) July 4, 2017 1. Person A lexicographically prefers good x to good y, i.e., when comparing two bundles of x and y, she strictly prefers
More informationMicroeconomics Comprehensive Exam
Microeconomics Comprehensive Exam June 2009 Instructions: (1) Please answer each of the four questions on separate pieces of paper. (2) When finished, please arrange your answers alphabetically (in the
More informationProblem 3 Solutions. l 3 r, 1
. Economic Applications of Game Theory Fall 00 TA: Youngjin Hwang Problem 3 Solutions. (a) There are three subgames: [A] the subgame starting from Player s decision node after Player s choice of P; [B]
More informationThe Ohio State University Department of Economics Econ 601 Prof. James Peck Extra Practice Problems Answers (for final)
The Ohio State University Department of Economics Econ 601 Prof. James Peck Extra Practice Problems Answers (for final) Watson, Chapter 15, Exercise 1(part a). Looking at the final subgame, player 1 must
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationUniversity of California, Davis Date: June 24, PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE. Answer four questions (out of five)
University of California, Davis Date: June 4, 03 Department of Economics Time: 5 hours Microeconomics Reading Time: 0 minutes ANSWER KEY PREIMINARY EXAMINATION FOR TE Ph.D. DEGREE Answer four questions
More informationECE 586BH: Problem Set 5: Problems and Solutions Multistage games, including repeated games, with observed moves
University of Illinois Spring 01 ECE 586BH: Problem Set 5: Problems and Solutions Multistage games, including repeated games, with observed moves Due: Reading: Thursday, April 11 at beginning of class
More informationLecture 6 Introduction to Utility Theory under Certainty and Uncertainty
Lecture 6 Introduction to Utility Theory under Certainty and Uncertainty Prof. Massimo Guidolin Prep Course in Quant Methods for Finance August-September 2017 Outline and objectives Axioms of choice under
More informationIntroduction to Game Theory
Introduction to Game Theory Part 2. Dynamic games of complete information Chapter 1. Dynamic games of complete and perfect information Ciclo Profissional 2 o Semestre / 2011 Graduação em Ciências Econômicas
More informationModelling Economic Variables
ucsc supplementary notes ams/econ 11a Modelling Economic Variables c 2010 Yonatan Katznelson 1. Mathematical models The two central topics of AMS/Econ 11A are differential calculus on the one hand, and
More informationU(x 1, x 2 ) = 2 ln x 1 + x 2
Solutions to Spring 014 ECON 301 Final Group A Problem 1. (Quasilinear income effect) (5 points) Mirabella consumes chocolate candy bars x 1 and fruits x. The prices of the two goods are = 4 and p = 4
More informationMicroeconomics of Banking: Lecture 2
Microeconomics of Banking: Lecture 2 Prof. Ronaldo CARPIO September 25, 2015 A Brief Look at General Equilibrium Asset Pricing Last week, we saw a general equilibrium model in which banks were irrelevant.
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationGE in production economies
GE in production economies Yossi Spiegel Consider a production economy with two agents, two inputs, K and L, and two outputs, x and y. The two agents have utility functions (1) where x A and y A is agent
More informationLecture Notes on Adverse Selection and Signaling
Lecture Notes on Adverse Selection and Signaling Debasis Mishra April 5, 2010 1 Introduction In general competitive equilibrium theory, it is assumed that the characteristics of the commodities are observable
More informationThe test has 13 questions. Answer any four. All questions carry equal (25) marks.
2014 Booklet No. TEST CODE: QEB Afternoon Questions: 4 Time: 2 hours Write your Name, Registration Number, Test Code, Question Booklet Number etc. in the appropriate places of the answer booklet. The test
More informationProblem Set 2 - SOLUTIONS
Problem Set - SOLUTONS 1. Consider the following two-player game: L R T 4, 4 1, 1 B, 3, 3 (a) What is the maxmin strategy profile? What is the value of this game? Note, the question could be solved like
More informationEconomics 171: Final Exam
Question 1: Basic Concepts (20 points) Economics 171: Final Exam 1. Is it true that every strategy is either strictly dominated or is a dominant strategy? Explain. (5) No, some strategies are neither dominated
More informationECON Chapter 4: Firm Behavior
ECON3102-005 Chapter 4: Firm Behavior Neha Bairoliya Spring 2014 Review and Introduction The representative consumer supplies labor and demands consumption goods. Review and Introduction The representative
More informationChapter 4. Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization. Copyright 2014 Pearson Education, Inc.
Chapter 4 Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization Copyright Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-2 Representative
More informationLecture 6 Dynamic games with imperfect information
Lecture 6 Dynamic games with imperfect information Backward Induction in dynamic games of imperfect information We start at the end of the trees first find the Nash equilibrium (NE) of the last subgame
More informationMarkets with Intermediaries
Markets with Intermediaries Episode Baochun Li Professor Department of Electrical and Computer Engineering University of Toronto Network Models of Markets with Intermediaries (Chapter ) Who sets the prices?
More informationMarkets with Intermediaries
Markets with Intermediaries Part III: Dynamics Episode Baochun Li Department of Electrical and Computer Engineering University of Toronto Required reading: Networks, Crowds, and Markets, Chapter..5 Who
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 2 1. Consider a zero-sum game, where
More informationConsumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization
Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 1 Discussion So far: How to measure variables of macroeconomic
More informationDARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21. Dartmouth College, Department of Economics: Economics 21, Summer 02. Topic 5: Information
Dartmouth College, Department of Economics: Economics 21, Summer 02 Topic 5: Information Economics 21, Summer 2002 Andreas Bentz Dartmouth College, Department of Economics: Economics 21, Summer 02 Introduction
More informationNoncooperative Oligopoly
Noncooperative Oligopoly Oligopoly: interaction among small number of firms Conflict of interest: Each firm maximizes its own profits, but... Firm j s actions affect firm i s profits Example: price war
More informationMicroeconomic Theory II Preliminary Examination Solutions
Microeconomic Theory II Preliminary Examination Solutions 1. (45 points) Consider the following normal form game played by Bruce and Sheila: L Sheila R T 1, 0 3, 3 Bruce M 1, x 0, 0 B 0, 0 4, 1 (a) Suppose
More informationUCLA Department of Economics Ph.D. Preliminary Exam Industrial Organization Field Exam (Spring 2010) Use SEPARATE booklets to answer each question
Wednesday, June 23 2010 Instructions: UCLA Department of Economics Ph.D. Preliminary Exam Industrial Organization Field Exam (Spring 2010) You have 4 hours for the exam. Answer any 5 out 6 questions. All
More informationOligopoly Games and Voting Games. Cournot s Model of Quantity Competition:
Oligopoly Games and Voting Games Cournot s Model of Quantity Competition: Supposetherearetwofirms, producing an identical good. (In his 1838 book, Cournot thought of firms filling bottles with mineral
More informationExercise Chapter 10
Exercise 10.8.1 Where the isoprofit curves touch the gradients of the profits of Alice and Bob point in the opposite directions. Thus, increasing one agent s profit will necessarily decrease the other
More informationEconomics 121b: Intermediate Microeconomics Final Exam Suggested Solutions
Dirk Bergemann Department of Economics Yale University Economics 121b: Intermediate Microeconomics Final Exam Suggested Solutions 1. Both moral hazard and adverse selection are products of asymmetric information,
More informationHonors General Exam PART 1: MICROECONOMICS. Solutions. Harvard University April 2013
Honors General Exam Solutions Harvard University April 201 PART 1: MICROECONOMICS Question 1 The Cookie Monster gets a job as an analyst at Goldman Sachs. He used to like cookies, but now Cookie Monster
More informationEcon 210, Final, Fall 2015.
Econ 210, Final, Fall 2015. Prof. Guse, W & L University Instructions. You have 3 hours to complete the exam. You will answer questions worth a total of 90 points. Please write all of your responses on
More information1 Two Period Exchange Economy
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 2 1 Two Period Exchange Economy We shall start our exploration of dynamic economies with
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 3 1. Consider the following strategic
More informationG5212: Game Theory. Mark Dean. Spring 2017
G5212: Game Theory Mark Dean Spring 2017 Modelling Dynamics Up until now, our games have lacked any sort of dynamic aspect We have assumed that all players make decisions at the same time Or at least no
More informationLecture notes: 101/105 (revised 9/27/00) Lecture 3: national Income: Production, Distribution and Allocation (chapter 3)
Lecture notes: 101/105 (revised 9/27/00) Lecture 3: national Income: Production, Distribution and Allocation (chapter 3) 1) Intro Have given definitions of some key macroeconomic variables. Now start building
More informationComparing Allocations under Asymmetric Information: Coase Theorem Revisited
Comparing Allocations under Asymmetric Information: Coase Theorem Revisited Shingo Ishiguro Graduate School of Economics, Osaka University 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan August 2002
More informationWeb Appendix: Proofs and extensions.
B eb Appendix: Proofs and extensions. B.1 Proofs of results about block correlated markets. This subsection provides proofs for Propositions A1, A2, A3 and A4, and the proof of Lemma A1. Proof of Proposition
More information9. Real business cycles in a two period economy
9. Real business cycles in a two period economy Index: 9. Real business cycles in a two period economy... 9. Introduction... 9. The Representative Agent Two Period Production Economy... 9.. The representative
More informationCUR 412: Game Theory and its Applications, Lecture 11
CUR 412: Game Theory and its Applications, Lecture 11 Prof. Ronaldo CARPIO May 17, 2016 Announcements Homework #4 will be posted on the web site later today, due in two weeks. Review of Last Week An extensive
More informationECONOMICS 723. Models with Overlapping Generations
ECONOMICS 723 Models with Overlapping Generations 5 October 2005 Marc-André Letendre Department of Economics McMaster University c Marc-André Letendre (2005). Models with Overlapping Generations Page i
More information1 Solutions to Homework 3
1 Solutions to Homework 3 1.1 163.1 (Nash equilibria of extensive games) 1. 164. (Subgames) Karl R E B H B H B H B H B H B H There are 6 proper subgames, beginning at every node where or chooses an action.
More informationTime, Uncertainty, and Incomplete Markets
Time, Uncertainty, and Incomplete Markets 9.1 Suppose half the people in the economy choose according to the utility function u A (x 0, x H, x L ) = x 0 + 5x H.3x 2 H + 5x L.2x 2 L and the other half according
More informationMicroeconomics Qualifying Exam
Summer 2018 Microeconomics Qualifying Exam There are 100 points possible on this exam, 50 points each for Prof. Lozada s questions and Prof. Dugar s questions. Each professor asks you to do two long questions
More informationMacroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1
Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1 1.1 (from Romer Advanced Macroeconomics Chapter 1) Basic properties of growth rates which will be used over and over again. Use the
More informationNotes on Macroeconomic Theory. Steve Williamson Dept. of Economics Washington University in St. Louis St. Louis, MO 63130
Notes on Macroeconomic Theory Steve Williamson Dept. of Economics Washington University in St. Louis St. Louis, MO 63130 September 2006 Chapter 2 Growth With Overlapping Generations This chapter will serve
More informationDepartment of Agricultural Economics. PhD Qualifier Examination. August 2010
Department of Agricultural Economics PhD Qualifier Examination August 200 Instructions: The exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationIn Diamond-Dybvig, we see run equilibria in the optimal simple contract.
Ennis and Keister, "Run equilibria in the Green-Lin model of financial intermediation" Journal of Economic Theory 2009 In Diamond-Dybvig, we see run equilibria in the optimal simple contract. When the
More informationA Closed Economy One-Period Macroeconomic Model
A Closed Economy One-Period Macroeconomic Model Chapter 5 Topics in Macroeconomics 2 Economics Division University of Southampton February 21, 2008 Chapter 5 1/40 Topics in Macroeconomics Closing the Model
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2015
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2015 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationOnline Appendix for Debt Contracts with Partial Commitment by Natalia Kovrijnykh
Online Appendix for Debt Contracts with Partial Commitment by Natalia Kovrijnykh Omitted Proofs LEMMA 5: Function ˆV is concave with slope between 1 and 0. PROOF: The fact that ˆV (w) is decreasing in
More informationUncertainty in Equilibrium
Uncertainty in Equilibrium Larry Blume May 1, 2007 1 Introduction The state-preference approach to uncertainty of Kenneth J. Arrow (1953) and Gérard Debreu (1959) lends itself rather easily to Walrasian
More informationChapter 3 Introduction to the General Equilibrium and to Welfare Economics
Chapter 3 Introduction to the General Equilibrium and to Welfare Economics Laurent Simula ENS Lyon 1 / 54 Roadmap Introduction Pareto Optimality General Equilibrium The Two Fundamental Theorems of Welfare
More informationProblem Set 3: Suggested Solutions
Microeconomics: Pricing 3E00 Fall 06. True or false: Problem Set 3: Suggested Solutions (a) Since a durable goods monopolist prices at the monopoly price in her last period of operation, the prices must
More information1. Suppose a production process is described by a Cobb-Douglas production function f(v 1, v 2 ) = v 1 1/2 v 2 3/2.
1. Suppose a production process is described by a Cobb-Douglas production function f(v 1, v 2 ) = v 1 1/2 v 2 3/2. a. Write an expression for the marginal product of v 1. Does the marginal product of v
More informationLecture 2 General Equilibrium Models: Finite Period Economies
Lecture 2 General Equilibrium Models: Finite Period Economies Introduction In macroeconomics, we study the behavior of economy-wide aggregates e.g. GDP, savings, investment, employment and so on - and
More informationAssignment 5 Advanced Microeconomics
LONDON SCHOOL OF ECONOMICS Department of Economics Leonardo Felli S.478; x7525 Assignment 5 Advanced Microeconomics 1. Consider a two consumers exchange economy where the two people (A and B) act as price
More informationEcon 210, Final, Fall 2015.
Econ 210, Final, Fall 2015. Prof. Guse, W & L University Instructions. You have 3 hours to complete the exam. You will answer questions worth a total of 90 points. Please write all of your responses on
More informationAS/ECON 2350 S2 N Answers to Mid term Exam July time : 1 hour. Do all 4 questions. All count equally.
AS/ECON 2350 S2 N Answers to Mid term Exam July 2017 time : 1 hour Do all 4 questions. All count equally. Q1. Monopoly is inefficient because the monopoly s owner makes high profits, and the monopoly s
More informationAdverse Selection: The Market for Lemons
Andrew McLennan September 4, 2014 I. Introduction Economics 6030/8030 Microeconomics B Second Semester 2014 Lecture 6 Adverse Selection: The Market for Lemons A. One of the most famous and influential
More informationGame theory and applications: Lecture 1
Game theory and applications: Lecture 1 Adam Szeidl September 20, 2018 Outline for today 1 Some applications of game theory 2 Games in strategic form 3 Dominance 4 Nash equilibrium 1 / 8 1. Some applications
More informationECO 5341 (Section 2) Spring 2016 Midterm March 24th 2016 Total Points: 100
Name:... ECO 5341 (Section 2) Spring 2016 Midterm March 24th 2016 Total Points: 100 For full credit, please be formal, precise, concise and tidy. If your answer is illegible and not well organized, if
More information