Solutions to problem set x C F = $50:000 + x x = $50: x = 10 9 (C F $50:000)
|
|
- Phyllis Sparks
- 5 years ago
- Views:
Transcription
1 Econ 30 Intermediate Microeconomics Prof. Marek Weretka Problem (Insurance) a) Solutions to problem set 6 b) Given the insurance level x; the consumption in the two states of the world is Solving for x from the second equation gives and plugging it into the rst one C NF = $0:000 0 x C F = $:000 + x 0 x = $: x x = 0 9 (C F $:000) C NF = $0:000 0:x = $0: $:000 9 C F = 5:560 The two extreme points are (0; 5:560) and (45:000) 9 C F c) Consumer with such Bernoulli utility function is risk averse. To see consider two lotteries (4:0) and (; ) and assume equally likely states. Observe that the two lotteries have the same average payo, but the rst one involves risk. We show on the graph that the risk makes it less attractive and hence agent is risk averse. d) MRS is given by MRS = 0: p C F = p CNF p = r CNF 0:9 p 9 CF 9 C C F F and hence at the endowment point! = (:000; 0:000) MRS = r CNF = p 0 = 0: C F 9
2 Note that the MRS is di erent from the slope of the budget set equal to =9 e) First we nd optimal consumption levels: First secret of happiness implies that MRS is equal to the slope of the budget set. Therefore r CNF = 9 C F 9 ) r CNF C F = ) C NF C F = ) C NF = C F We can see that agent insures fully. Plugging it into the budget constraint and slowing for C F gives But then using the formula for x C F = 5:560 9 C F C F = C NF = 9 5:560 = 455:000 0 x = 0 9 (C F $:000) = = 0 (455:000 $:000) = therefore he covers 4000 f) With such premium the slope of the budget set is slope = 0: 0: = 4 hence budget line becomes steeper. Consequently optimal consumption is not on a 45 o degree line. Problem (Risk aversion and certainty equivalence) a) Yes, he is risk averse b) The expected value from the lottery is (see mark in graph above) c) The expected utility from this lottery is E (L) = = U (L) = p p = 5
3 d) Certainty equivalent CE is the amount of "sure" cash that makes Frank indi erent to the lottery. Lottery (CE; CE) is associated with utility U (CE) = p p p CE + CE = CE By de nition it must be equal to the utility of the original lottery U (L) = 5 hence p CE = 5 ) CE = 5 Therefore Frank is indi erent between $5 for sure, and risky lottery ($00; $0) e) He should choose $40 or more generally anything exceeding $5 f) Expected value of the lottery is unchanged and expected utility from this lottery is E (L) = = U (L) = = Utility from sure cash CE is given by U (CE) = CE which is in turn equal to : Consequently CE = itself. Frank should take the lottery. g) Expected value of the lottery is and expected utility is U(L) = (00) + 0 = 00 Utility from sure cash CE is hence U(CE) = CE (CE) = 00 ) CE = p 00 = 70: 7 Frank should take the lottery. Problem 3 (Standard Edgeworth Box) a) The total resources are! = (00; 0) b) The allocation! E = (0; 0) and! M = (90; 0) is not Pareto e cient. One way to see it is that the endowment is o the contract curve (see point c) 3
4 or c) In Pareto e cient allocation the slopes of indi erence curves must coincide. Therefore MRS E = MRS M x M 5x M = xe 5x E Elvis consumes x E = 00 x M and x E = 0 x M therefore we can write x M x M = 0 xm 00 x M Multiplying both sides by x M 00 x M gives x M 00 x M which can be reduced to = x M 0 x M or nally 00x M = 0x M x M = 0 xm Which de nes a straight line in the Edgeworth box d) Ce nition of Equilibrium: It is an allocation x E ; x E ;and x M ; x M and prices (p ; p ) such that ) for each consumer x i ; x i is optimal given prices (p ; p ) ) (p ; p ) are such that markets clear Remark: Equilibrium is our prediction of what we will observe in markets, when they are not a ected by any distortion. We nd it in a di erent way than the Contract curve. Later we show, however that the equilibrium allocation, among many others, is Pareto e cient and hence it is located on a contrct curve. Equilibrium determines only a relative price, therefore we can normalize p =. We also focus on market for good. (You can verify that market for good will clear automatically). With Cobb-Douglass utility functions, we nd optimal choices using magic formula (shortcut) rather than by deriving it from secrets of happiness. The optimal demand for MP 3 is given by x i = a m i a + b p where a = and b = 5 (they are the same for both traders Elvis and Miriam). Income m i is m E = p w E + p w E = p = 0p + 0 m M = p w M + p w M = p = 90p Consequently the demands for x are x E = 0p p x M = 90p 6 p By the second equilibrium condition prices assure markets clearing, that is the total demand for MP3, x E +x M is equal to the total supply w E + w M = 00. More formally 00 = x E + x E = 0p p 6 p 6 p 4
5 Multiplying both sides by 6p or At such prices the optimal consumption is 600p = 0p p = p p = x E = 0p p = 85 x M = 90p = 5 6 p The consumption of DVD is (again we use magic formulas and equilibrium prices p = ; p = ) x E = 5 0p p = 5 6 (0p + 0) = 8 x M = 5 90p = 5 90p = 6 p 6 p Hence allocation x E = (85; 8 ) and xm = (5; ) and prices (p ; p ) = ( ; ) is an equilibrium e) Any price system that is associated with the relative price equal to supports the same allocation as an equilibrium. For example (p ; p ) = (; ) or (p ; p ) = (; 00) f) Yes, they are e cient. To see it observe that MRS for Elvis and Miriam at equilibrium is equal to MRS E = xe 5x E MRS M = xe 5x E = = and hence their indi erence curves are tangent, so the allocation is Pareto e cient. g) Remark: In this case all allocations in Edgeworth box are Pareto e cient. Equilibrium: For any relative price p p < MRS i = 5 both trader spend their total income on x and no income on x - This results in excess demand for x. For p p > MRS i = 5 both traders spend their income on x and hence there is excess demand for x : Therefore markets can clear only for relative price p p = 5 But then all allocations on the budget set are optimal for each trader therefore any of them is an equilibrium allocation. 5
6 Problem 4 (Uncertainty and Asset Pricing) Endowment allocation is not Pareto e cient. It is also risky as it is associated with di erent payments in two states of the world. b) Equilibrium: Given the Cobb -Douglass preferences the optimal demand of each of the traders is x J = x B = a m J = p 00 + p 0 = a + b p p a m B = p 0 + p 00 = p a + b p p p We normalize p to one so that p =. The market clearing on the market for x requires that which gives a price x J + x B = 00 + p p = + p = 00 ) p = Hence the equilibrium prices are p = p = : Given the prices the equilibrium allocations are x J = ; x J = b m = a + b p and hence consumption of Benjamin is what is left on the market c) MRS for both traders is p 00 p = x B = 00 = x J = 00 = MRS J = MRS B = = = hence indi erence curves are tangent - the allocation is Pareto e cient. The equilibrium allocation is also not risky as the wealth is the same in the two states of the world (this is true for J and for B). Problem 5 (Irving Fisher Determination of Interest Rate) a) No, the initial allocation is not Pareto e cient. b) Given Cobb -Douglass preferences, the optimal demand for consumption "today" is 6
7 C J = C W = a m J = p 0 + p 000 a + b p + = 000p p 3 p a m B = p p 0 a + b p + = p We normalize p to one so that p =. The market clearing for C requires that which gives a price C J + C W = p = 000 ) p = Hence the equilibrium prices are p = and p = : Given the prices the equilibrium allocations are and hence consumption of William is The interest rate is hence c) Yes equilibrium allocation is Pareto e cient as C J = 000p = 000 = 333:333 3 p 3 C J b m = = 000 = 333:333 a + b p 3 C B = :333 = 666:666 C B = :333 = 666:666 + r = p p = r = 00% MRS J = CJ C J MRS B = CB C B = 333: :333 = 666: :666 = = and hence the indi erence curves of two traders are tangent. d) Now the optimal consumptions are C J = C W = a m J = p 0 + p 000 = 000p a + b p + p p a m B = p p 0 = a + b p + p 000 Again normalize p to one so that p =. The market clearing on the market for C requires that which gives a price C J + C W = p 000 = 000 ) p = Hence the equilibrium prices are p = p = ; therefore the interest rate is + r = p p = 7
8 hence r = 0% With greater patients the willingness to save increases and the willingness to borrow goes down. In order to equilibrate the market the interest must go down. e) The demands now are C J = C W = a m J = p 0 + p 000 a + b p + = 000p p 3 p a m B = p p 0 a + b p + = p We normalize p to one so that p =. The market clearing on the market for C requires that which gives a price C J + C W = p = 000 ) p = 4 Hence the equilibrium prices are p = 4 and p = : The interest rate is + r = p p = 4 hence r = 300% Intuition: Jane s have large endowment tomorrow and therefore because she wants to use it today she needs to borrow more. In order to equilibrate the savings market interest must go up. This partially reduces her willingness to borrow and also encourages William to lend. 8
(a) Ben s affordable bundle if there is no insurance market is his endowment: (c F, c NF ) = (50,000, 500,000).
Problem Set 6: Solutions ECON 301: Intermediate Microeconomics Prof. Marek Weretka Problem 1 (Insurance) (a) Ben s affordable bundle if there is no insurance market is his endowment: (c F, c NF ) = (50,000,
More informationMidterm 2 (Group A) U(C; R) =R 2 C. U i (C 1 ;C 2 ) = ln (C 1 ) + ln (C 2 ) p 1 p 2. =1 + r
Econ 30 Intermediate Microeconomics Prof. Marek Weretka Midterm 2 (Group A) You have 70 minutes to complete the exam. The midterm consists of 4 questions (25+35+5+25=00 points) + a bonus (0 "extra" points).
More informationU(x 1. ; x 2 ) = 4 ln x 1
Econ 30 Intermediate Microeconomics Prof. Marek Weretka Final Exam (Group A) You have h to complete the exam. The nal consists of 6 questions (5+0+0+5+0+0=00). Problem. (Quasilinaer income e ect) Mirabella
More informationMidterm 2 (Group A) U (x 1 ;x 2 )=3lnx 1 +3 ln x 2
Econ 301 Midterm 2 (Group A) You have 70 minutes to complete the exam. The midterm consists of 4 questions (25,30,25 and 20 points). Problem 1 (25p). (Uncertainty and insurance) You are an owner of a luxurious
More informationFinal Exam (A) You have 2h to complete the exam and the nal consists of 6 questions ( =100).
Econ 301 Intermediate Microeconomics Prof. Marek Weretka Final Exam (A) You have 2h to complete the exam and the nal consists of 6 questions (15+10+25+15+20+15=100). Problem 1. (Consumer Choice) Jeremy
More informationFinal. You have 2h to complete the exam and the nal consists of 6 questions ( =100).
Econ 3 Intermediate Microeconomics Prof. Marek Weretka Final You have h to complete the exam and the nal consists of questions (+++++=). Problem. Ace consumes bananas x and kiwis x. The prices of both
More informationFinal Exam (Group A)
Econ 30 Intermediate Microeconomics Prof. Marek Weretka Final Exam (Group A) You have h to complete the exam. The final consists of 6 questions (5+0+5+5+0+5=00). Problem. (Choice with Cobb-Douglas preferences)
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 informationMidterm 1 (A) U(x 1, x 2 ) = (x 1 ) 4 (x 2 ) 2
Econ Intermediate Microeconomics Prof. Marek Weretka Midterm (A) You have 7 minutes to complete the exam. The midterm consists of questions (5+++5= points) Problem (5p) (Well-behaved preferences) Martha
More informationFinal. You have 2h to complete the exam and the nal consists of 6 questions ( =100).
Econ 3 Intermediate Microeconomics Prof. Marek Weretka Final You have h to complete the exam and the nal consists of 6 questions (+++++=). Problem. Ace consumes bananas x and kiwis x. The prices of both
More informationProblem Set 1 Answer Key. I. Short Problems 1. Check whether the following three functions represent the same underlying preferences
Problem Set Answer Key I. Short Problems. Check whether the following three functions represent the same underlying preferences u (q ; q ) = q = + q = u (q ; q ) = q + q u (q ; q ) = ln q + ln q All three
More informationFundamental Theorems of Welfare Economics
Fundamental Theorems of Welfare Economics Ram Singh October 4, 015 This Write-up is available at photocopy shop. Not for circulation. In this write-up we provide intuition behind the two fundamental theorems
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 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 informationMoney in OLG Models. Econ602, Spring The central question of monetary economics: Why and when is money valued in equilibrium?
Money in OLG Models 1 Econ602, Spring 2005 Prof. Lutz Hendricks, January 26, 2005 What this Chapter Is About We study the value of money in OLG models. We develop an important model of money (with applications
More informationEconS Substitution E ects
EconS 305 - Substitution E ects Eric Dunaway Washington State University eric.dunaway@wsu.edu September 25, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 14 September 25, 2015 1 / 40 Introduction Last time,
More informationGeneral Equilibrium and Economic Welfare
General Equilibrium and Economic Welfare Lecture 7 Reading: Perlo Chapter 10 August 2015 1 / 61 Introduction Shocks a ect many markets at the same time. Di erent markets feed back into each other. Today,
More informationECON Micro Foundations
ECON 302 - Micro Foundations Michael Bar September 13, 2016 Contents 1 Consumer s Choice 2 1.1 Preferences.................................... 2 1.2 Budget Constraint................................ 3
More informationSuggested Solutions to Problem Set 3
Econ154b Spring 2005 Suggested Solutions to Problem Set 3 Question 1 (a) S d Y C d G Y 3600 2000r 0.1Y 1200 0.9Y 4800 2000r 600 2000r (b) To graph the desired saving and desired investment curves, remember
More informationDepartment of Economics Shanghai University of Finance and Economics Intermediate Macroeconomics
Department of Economics Shanghai University of Finance and Economics Intermediate Macroeconomics Instructor Min Zhang Answer 3 1. Answer: When the government imposes a proportional tax on wage income,
More informationEconS Constrained Consumer Choice
EconS 305 - Constrained Consumer Choice Eric Dunaway Washington State University eric.dunaway@wsu.edu September 21, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 12 September 21, 2015 1 / 49 Introduction
More informationMicroeconomics, IB and IBP
Microeconomics, IB and IBP ORDINARY EXAM, December 007 Open book, 4 hours Question 1 Suppose the supply of low-skilled labour is given by w = LS 10 where L S is the quantity of low-skilled labour (in million
More information2. Find the equilibrium price and quantity in this market.
1 Supply and Demand Consider the following supply and demand functions for Ramen noodles. The variables are de ned in the table below. Constant values are given for the last 2 variables. Variable Meaning
More informationEconS Income E ects
EconS 305 - Income E ects Eric Dunaway Washington State University eric.dunaway@wsu.edu September 23, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 13 September 23, 2015 1 / 41 Introduction Over the net
More informationFINANCE THEORY: Intertemporal. and Optimal Firm Investment Decisions. Eric Zivot Econ 422 Summer R.W.Parks/E. Zivot ECON 422:Fisher 1.
FINANCE THEORY: Intertemporal Consumption-Saving and Optimal Firm Investment Decisions Eric Zivot Econ 422 Summer 21 ECON 422:Fisher 1 Reading PCBR, Chapter 1 (general overview of financial decision making)
More informationAdvanced Microeconomics
Advanced Microeconomics Pareto optimality in microeconomics Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 33 Part D. Bargaining theory and Pareto optimality
More information14.03 Fall Problem Set 4. Due Friday, November 5th at 5pm. Their utility functions and initial endowments are the following:
14.03 Fall 2004 roblem Set 4 Due Friday, November 5th at 5pm 1. Gains from International Trade Claudia (C) and Jesse (J) live in the land of Carvel, where only ice cream scoops (I) and brownies (B) are
More informationSome Problems. 3. Consider the Cournot model with inverse demand p(y) = 9 y and marginal cost equal to 0.
Econ 301 Peter Norman Some Problems 1. Suppose that Bruce leaves Sheila behind for a while and goes to a bar where Claude is having a beer for breakfast. Each must now choose between ghting the other,
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 informationThe endowment of the island is given by. e b = 2, e c = 2c 2.
Economics 121b: Intermediate Microeconomics Problem Set 4 1. Edgeworth Box and Pareto Efficiency Consider the island economy with Friday and Robinson. They have agreed to share their resources and they
More informationEconomics 11: Solutions to Practice Final
Economics 11: s to Practice Final September 20, 2009 Note: In order to give you extra practice on production and equilibrium, this practice final is skewed towards topics covered after the midterm. The
More informationTrade on Markets. Both consumers' initial endowments are represented bythesamepointintheedgeworthbox,since
Trade on Markets A market economy entails ownership of resources. The initial endowment of consumer 1 is denoted by (x 1 ;y 1 ), and the initial endowment of consumer 2 is denoted by (x 2 ;y 2 ). Both
More informationThe ratio of consumption to income, called the average propensity to consume, falls as income rises
Part 6 - THE MICROECONOMICS BEHIND MACROECONOMICS Ch16 - Consumption In previous chapters we explained consumption with a function that relates consumption to disposable income: C = C(Y - T). This was
More informationMaster in Industrial Organization and Markets. Spring 2012 Microeconomics III Assignment 1: Uncertainty
Master in Industrial Organization and Markets. Spring Microeconomics III Assignment : Uncertainty Problem Determine which of the following assertions hold or not. Justify your answers with either an example
More informationMicro Theory I Assignment #5 - Answer key
Micro Theory I Assignment #5 - Answer key 1. Exercises from MWG (Chapter 6): (a) Exercise 6.B.1 from MWG: Show that if the preferences % over L satisfy the independence axiom, then for all 2 (0; 1) and
More informationUniversidad Carlos III de Madrid May Microeconomics Grade
Universidad Carlos III de Madrid May 015 Microeconomics Name: Group: 1 3 4 5 Grade You have hours and 45 minutes to answer all the questions. The maximum grade for each question is in parentheses. You
More informationTOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems III
TOBB-ETU, Economics Department Macroeconomics II ECON 532) Practice Problems III Q: Consumption Theory CARA utility) Consider an individual living for two periods, with preferences Uc 1 ; c 2 ) = uc 1
More informationEconS Advanced Microeconomics II Handout on Social Choice
EconS 503 - Advanced Microeconomics II Handout on Social Choice 1. MWG - Decisive Subgroups Recall proposition 21.C.1: (Arrow s Impossibility Theorem) Suppose that the number of alternatives is at least
More informationEconomics 135. Course Review. Professor Kevin D. Salyer. June UC Davis. Professor Kevin D. Salyer (UC Davis) Money and Banking 06/07 1 / 11
Economics 135 Course Review Professor Kevin D. Salyer UC Davis June 2007 Professor Kevin D. Salyer (UC Davis) Money and Banking 06/07 1 / 11 Course Review Two goals Professor Kevin D. Salyer (UC Davis)
More informationProblem Set (1 p) (1) 1 (100)
University of British Columbia Department of Economics, Macroeconomics (Econ 0) Prof. Amartya Lahiri Problem Set Risk Aversion Suppose your preferences are given by u(c) = c ; > 0 Suppose you face the
More informationUniversidad Carlos III de Madrid June Microeconomics Grade
Universidad Carlos III de Madrid June 05 Microeconomics Name: Group: 5 Grade You have hours and 5 minutes to answer all the questions. The maximum grade for each question is in parentheses. You should
More informationAS/ECON AF Answers to Assignment 1 October Q1. Find the equation of the production possibility curve in the following 2 good, 2 input
AS/ECON 4070 3.0AF Answers to Assignment 1 October 008 economy. Q1. Find the equation of the production possibility curve in the following good, input Food and clothing are both produced using labour and
More informationb) The first secret of happiness is consuming on the Budget line, that is the condition That is
Problem 1 a). At bundle (80, 20),. This means at consumption bundle (80, 20) Monica is willing to trade 1 banana for 4 kiwis. Geometrically it means the slope of the indifference cure is -1/4 at the bundle
More informationQuestion 1: Productivity, Output and Employment (20 Marks)
Answers for ECON222 exercise 2 Winter 2010 Question 1: Productivity, Output and Employment (20 Marks) Part a): (6 Marks) Start by taking the derivative of the production wrt labour, which is then set equal
More informationEcon 277A: Economic Development I. Final Exam (06 May 2012)
Econ 277A: Economic Development I Semester II, 2011-12 Tridip Ray ISI, Delhi Final Exam (06 May 2012) There are 2 questions; you have to answer both of them. You have 3 hours to write this exam. 1. [30
More informationECON Financial Economics
ECON 8 - Financial Economics Michael Bar August, 0 San Francisco State University, department of economics. ii Contents Decision Theory under Uncertainty. Introduction.....................................
More informationExercises - Moral hazard
Exercises - Moral hazard 1. (from Rasmusen) If a salesman exerts high e ort, he will sell a supercomputer this year with probability 0:9. If he exerts low e ort, he will succeed with probability 0:5. The
More informationANSWER: We can find consumption and saving by solving:
Economics 154a, Spring 2005 Intermediate Macroeconomics Problem Set 4: Answer Key 1. Consider an economy that consists of a single consumer who lives for two time periods. The consumers income in the current
More informationMean-Variance Analysis
Mean-Variance Analysis Mean-variance analysis 1/ 51 Introduction How does one optimally choose among multiple risky assets? Due to diversi cation, which depends on assets return covariances, the attractiveness
More informationEconS Consumer Theory: Additional Topics
EconS 305 - Consumer Theory: Additional Topics Eric Dunaway Washington State University eric.dunaway@wsu.edu September 27, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 1 / 46 Introduction
More informationCredit Card Competition and Naive Hyperbolic Consumers
Credit Card Competition and Naive Hyperbolic Consumers Elif Incekara y Department of Economics, Pennsylvania State University June 006 Abstract In this paper, we show that the consumer might be unresponsive
More informationIntroduction to Economics I: Consumer Theory
Introduction to Economics I: Consumer Theory Leslie Reinhorn Durham University Business School October 2014 What is Economics? Typical De nitions: "Economics is the social science that deals with the production,
More informationEcon Review Set 3 - Answers
Econ 4808 Review Set 3 - Answers Outline: 1. Limits, continuity & derivatives. 2. Economic applications of derivatives. Unconstrained optimization. Elasticities. 2.1 Revenue and pro t functions 2.2 Productions
More information1 Non-traded goods and the real exchange rate
University of British Columbia Department of Economics, International Finance (Econ 556) Prof. Amartya Lahiri Handout #3 1 1 on-traded goods and the real exchange rate So far we have looked at environments
More informationEcon 210, Final, Fall 2014.
Econ 210, Final, Fall 2014. Prof. Guse, W & L University Instructions. You have 3 hours to complete the exam. You will answer questions worth a total of 80 points. Please write all of your responses on
More information14.02 Principles of Macroeconomics Solutions to Problem Set # 2
4.02 Principles of Macroeconomics Solutions to Problem Set # 2 September 25, 2009 True/False/Uncertain [20 points] Please state whether each of the following claims are True, False or Uncertain, and provide
More informationPractice Questions Chapters 9 to 11
Practice Questions Chapters 9 to 11 Producer Theory ECON 203 Kevin Hasker These questions are to help you prepare for the exams only. Do not turn them in. Note that not all questions can be completely
More informationProduct Di erentiation: Exercises Part 1
Product Di erentiation: Exercises Part Sotiris Georganas Royal Holloway University of London January 00 Problem Consider Hotelling s linear city with endogenous prices and exogenous and locations. Suppose,
More informationSan Francisco State University ECON 302. Money
San Francisco State University ECON 302 What is Money? Money Michael Bar We de ne money as the medium of echange in the economy, i.e. a commodity or nancial asset that is generally acceptable in echange
More information1. If the consumer has income y then the budget constraint is. x + F (q) y. where is a variable taking the values 0 or 1, representing the cases not
Chapter 11 Information Exercise 11.1 A rm sells a single good to a group of customers. Each customer either buys zero or exactly one unit of the good; the good cannot be divided or resold. However, it
More informationFinancial Fragility and the Exchange Rate Regime Chang and Velasco JET 2000 and NBER 6469
Financial Fragility and the Exchange Rate Regime Chang and Velasco JET 2000 and NBER 6469 1 Introduction and Motivation International illiquidity Country s consolidated nancial system has potential short-term
More informationIntroduction to Economic Analysis Fall 2009 Problems on Chapter 3: Savings and growth
Introduction to Economic Analysis Fall 2009 Problems on Chapter 3: Savings and growth Alberto Bisin October 29, 2009 Question Consider a two period economy. Agents are all identical, that is, there is
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 informationExogenous variables are determined outside a macroeconomic model. Figure 5.1 A Model Takes Exogenous Variables and Determines Endogenous Variables
Chapter 5 A Closed-Economy One-Period Macroeconomic Model What is a model used for? Exogenous variables are determined outside a macroeconomic model. Figure 5.1 A Model Takes Exogenous Variables and Determines
More informationUCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory
UCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory (SPRING 2016) Instructions: You have 4 hours for the exam Answer any 5 out of the 6 questions. All questions are weighted equally.
More informationLecture 10: Two-Period Model
Lecture 10: Two-Period Model Consumer s consumption/savings decision responses of consumer to changes in income and interest rates. Government budget deficits and the Ricardian Equivalence Theorem. Budget
More informationEconomics 313: Intermediate Microeconomics II. Sample Final Examination. Version 1. Instructor: Dr. Donna Feir
Last Name: First Name: Student Number: Economics 313: Intermediate Microeconomics II Sample Final Examination Version 1 Instructor: Dr. Donna Feir Instructions: Make sure you write your name and student
More informationLecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model (Continued)
Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model (Continued) In previous lectures we saw that
More information9 D/S of/for Labor. 9.1 Demand for Labor. Microeconomics I - Lecture #9, April 14, 2009
Microeconomics I - Lecture #9, April 14, 2009 9 D/S of/for Labor 9.1 Demand for Labor Demand for labor depends on the price of labor, price of output and production function. In optimum a firm employs
More informationMacroeconomics IV Problem Set 3 Solutions
4.454 - Macroeconomics IV Problem Set 3 Solutions Juan Pablo Xandri 05/09/0 Question - Jacklin s Critique to Diamond- Dygvig Take the Diamond-Dygvig model in the recitation notes, and consider Jacklin
More informationLecture Notes 1
4.45 Lecture Notes Guido Lorenzoni Fall 2009 A portfolio problem To set the stage, consider a simple nite horizon problem. A risk averse agent can invest in two assets: riskless asset (bond) pays gross
More information1 Multiple Choice (30 points)
1 Multiple Choice (30 points) Answer the following questions. You DO NOT need to justify your answer. 1. (6 Points) Consider an economy with two goods and two periods. Data are Good 1 p 1 t = 1 p 1 t+1
More informationECON 222, Spring 2009 Assignment #3, Answer Key
ECON 222, Spring 2009 Assignment #3, Answer Ke Question (40 marks) a) TF growth rate is constant and equal to At A t a, and the population growth rate is Nt N t n: From the growth-accounting equation we
More information(Note: Please label your diagram clearly.) Answer: Denote by Q p and Q m the quantity of pizzas and movies respectively.
1. Suppose the consumer has a utility function U(Q x, Q y ) = Q x Q y, where Q x and Q y are the quantity of good x and quantity of good y respectively. Assume his income is I and the prices of the two
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 informationII. Competitive Trade Using Money
II. Competitive Trade Using Money Neil Wallace June 9, 2008 1 Introduction Here we introduce our rst serious model of money. We now assume that there is no record keeping. As discussed earler, the role
More informationSome Notes on Timing in Games
Some Notes on Timing in Games John Morgan University of California, Berkeley The Main Result If given the chance, it is better to move rst than to move at the same time as others; that is IGOUGO > WEGO
More informationExploding Bubbles In a Macroeconomic Model. Narayana Kocherlakota
Bubbles Exploding Bubbles In a Macroeconomic Model Narayana Kocherlakota presented by Kaiji Chen Macro Reading Group, Jan 16, 2009 1 Bubbles Question How do bubbles emerge in an economy when collateral
More informationFinal Solutions ECON 301 May 13, 2012
Final Solutions ECON May, Problem a) Because it is easier and more familiar, we will work with the monotonic transformation (and thus equivalent) utility function: U(x, x ) = log x + log x. MRS = MUx MU
More informationEconS 301 Written Assignment #3 - ANSWER KEY
EconS 30 Written Assignment #3 - ANSWER KEY Exercise #. Consider a consumer with Cobb-Douglas utility function uu(xx, ) xx /3 /3 Assume that the consumer faces a price of $ for good, and a total income
More informationConsumption. ECON 30020: Intermediate Macroeconomics. Prof. Eric Sims. Spring University of Notre Dame
Consumption ECON 30020: Intermediate Macroeconomics Prof. Eric Sims University of Notre Dame Spring 2018 1 / 27 Readings GLS Ch. 8 2 / 27 Microeconomics of Macro We now move from the long run (decades
More informationExercises on chapter 4
Exercises on chapter 4 Exercise : OLG model with a CES production function This exercise studies the dynamics of the standard OLG model with a utility function given by: and a CES production function:
More informationProblem Set 3. Consider a closed economy inhabited by an in ntely lived representative agent who maximizes lifetime utility given by. t ln c t.
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Problem Set 3 Guess and Verify Consider a closed economy inhabited by an in ntely lived representative
More informationDepartment of Economics The Ohio State University Final Exam Answers Econ 8712
Department of Economics The Ohio State University Final Exam Answers Econ 872 Prof. Peck Fall 207. (35 points) The following economy has three consumers, one firm, and four goods. Good is the labor/leisure
More informationModels of Wage-setting.. January 15, 2010
Models of Wage-setting.. Huw Dixon 200 Cardi January 5, 200 Models of Wage-setting. Importance of Unions in wage-bargaining: more important in EU than US. Several Models. In a unionised labour market,
More informationEconomics Honors Exam Review (Micro) Mar Based on Zhaoning Wang s final review packet for Ec 1010a, Fall 2013
Economics Honors Exam Review (Micro) Mar. 2017 Based on Zhaoning Wang s final review packet for Ec 1010a, Fall 201 1. The inverse demand function for apples is defined by the equation p = 214 5q, where
More informationEconomics 101. Lecture 8 - Intertemporal Choice and Uncertainty
Economics 101 Lecture 8 - Intertemporal Choice and Uncertainty 1 Intertemporal Setting Consider a consumer who lives for two periods, say old and young. When he is young, he has income m 1, while when
More informationConsumption-Savings Decisions and State Pricing
Consumption-Savings Decisions and State Pricing Consumption-Savings, State Pricing 1/ 40 Introduction We now consider a consumption-savings decision along with the previous portfolio choice decision. These
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 informationSolutions to Problem Set 1
Solutions to Problem Set Theory of Banking - Academic Year 06-7 Maria Bachelet maria.jua.bachelet@gmail.com February 4, 07 Exercise. An individual consumer has an income stream (Y 0, Y ) and can borrow
More informationGains from Trade and Comparative Advantage
Gains from Trade and Comparative Advantage 1 Introduction Central questions: What determines the pattern of trade? Who trades what with whom and at what prices? The pattern of trade is based on comparative
More informationA note on the term structure of risk aversion in utility-based pricing systems
A note on the term structure of risk aversion in utility-based pricing systems Marek Musiela and Thaleia ariphopoulou BNP Paribas and The University of Texas in Austin November 5, 00 Abstract We study
More informationANSWERS TO PRACTICE PROBLEMS oooooooooooooooo
University of California, Davis Department of Economics Giacomo Bonanno Economics 03: Economics of uncertainty and information TO PRACTICE PROBLEMS oooooooooooooooo PROBLEM # : The expected value of the
More information1 Consumer Choice. 2 Consumer Preferences. 2.1 Properties of Consumer Preferences. These notes essentially correspond to chapter 4 of the text.
These notes essentially correspond to chapter 4 of the text. 1 Consumer Choice In this chapter we will build a model of consumer choice and discuss the conditions that need to be met for a consumer to
More informationEconS Utility. Eric Dunaway. Washington State University September 15, 2015
EconS 305 - Utility Eric Dunaway Washington State University eric.dunaway@wsu.edu September 15, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 10 September 15, 2015 1 / 38 Introduction Last time, we saw how
More informationDepartment of Economics The Ohio State University Final Exam Questions and Answers Econ 8712
Prof. Peck Fall 016 Department of Economics The Ohio State University Final Exam Questions and Answers Econ 871 1. (35 points) The following economy has one consumer, two firms, and four goods. Goods 1
More informationMossin s Theorem for Upper-Limit Insurance Policies
Mossin s Theorem for Upper-Limit Insurance Policies Harris Schlesinger Department of Finance, University of Alabama, USA Center of Finance & Econometrics, University of Konstanz, Germany E-mail: hschlesi@cba.ua.edu
More informationECO 2013: Macroeconomics Valencia Community College
ECO 2013: Macroeconomics Valencia Community College Exam 3 Fall 2008 1. The most important determinant of consumer spending is: A. the level of household debt. B. consumer expectations. C. the stock of
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 informationThese notes essentially correspond to chapter 7 of the text.
These notes essentially correspond to chapter 7 of the text. 1 Costs When discussing rms our ultimate goal is to determine how much pro t the rm makes. In the chapter 6 notes we discussed production functions,
More information