1 Riskaversion and intertemporal substitution under external habits.
|
|
- Amanda Atkins
- 6 years ago
- Views:
Transcription
1 Riskaversion and intertemporal substitution under external habits. Reall that e de ne the oe ient of relative riskaversion as R r u00 ( ) u 0 ( ) so for CRRA utility e have u () R r t ; hih determines the prie of risk. Reall that e an use the Euler equation to derive the onsumption CAPM, external habit) ov dut+ d+ ; ~r t+ E t ~r t+ r t+ du E t+ t d+ ov t+ r ; ~r t+ t+ E t t+ r t+ + ov t+ ; ~r t+ E t t+ : A high, leads to a high risk premium. At the same time, the high, leads to a lo intertemporal elastiity of substitution. Consider the ase of no unertainty and a onstant interest rate. The Euler equation is t ( + r) t+ t ( + r) ( + g) t ( + r) ( + g) + g (( + r) ) here g is the groth rate of onsumption. Clearly, a high value of R r ; implies a lo sensitivity of groth rates to interest rates or onversely, that interest rates hange a lot as the groth of onsumption hanges. With standard preferenes, the same parameters determines both riskaversion and (the inverse) of the intertemporal elastiity of
2 onsumption. Let s de ne the intertemporal elastiity of substitution (IES) as I dg ( + r) dr ( + g) d (( + r) ) A + r dr + g d (( + r) ) A + r dr (( + r) ) : Clearly, I R r : Let us see ho habits hange this. No, suppose there is a habit ith the standard property that it a ets the marginal utility positively and utility negatively. Consider the additive habit, u ( ; t ) ( ( t) if 6 and > 0 ln ( k t ) if : () Then, e have u 00 ( t ) u 0 ( t ) d 2 ( t ) d 2 t t (t d t ) t d This means that hen onsumption is lose to the habit, riskaversion is very high. The inverse of the seond fator, namely s t is often alled the surplus ratio. No, let s look at the intertemporal elastiity of onsumption under the additive external habit, so that Then, t t k : du t d ( t ) ( k ) 2
3 No, e "guess" the solution is a onstant groth rate g: Then, the Euler equation is ( k ) ( + r) (+ k ) k + g ( + r) (( + g) k ) k t ( + r) ( + g) + g ( + r) ( + g) + g (( + r) ) k t + g Note that this is the same as under no habit formation at all, i.e., the intertemporal elastiity of substitution is regardless of k: On the other hand, risk aversion an be arbitrarily high in this ase. We an alulate it expliitly, ( + g) t ( + g) k + g + g k ; implying that I R r + g + g k :. Externalities When the habit is external, there an externality. Consider no the referene utility model, t kc t ; (2) here C t is aggregate onsumption. Then, ( kc t ) ( + r) (+ kc t+ ) : Suppose an individual hooses loer and higher + : Then, she ontributes to reduing the marginal utility of onsumption for everyone else in t; and inreasing it at t + : Everyone else should then respond by also reduing period t onsumption and inreasing it in period t + : Could this generate multiple equilibria? In priniple, yes, but not ith these preferenes. Again, guess the solution is a onstant groth rate, ( kc t ) ( + r) (( + g) k (( + g)) C t ) ( + r) ( + g) + g (( + r) ) This is a unique solution, oiniding ith the no habit ase. 3
4 To analyze this a bit further in a simple ay. Suppose there is to periods only, that feliity is given by () and the referene level by (2). Individuals then solve max fu ( ; ) + u (( + r) ( ) ; 2 )g here is their initial endoment. The rst order ondition is ( v ) ( + r) (( + r) ( ) v 2 ) 0: To onsider a simple ase, set :We then get the folloing system of equations or implying ( v ) ( + r) (( + r) ( ) v 2 ) 0 k 2 k ( + r) ( ) ( k ) ( + r) (( + r) ( ) k ( + r) ( )) 0 + ; regardless of k: Clearly, the deentralized alloation under habits oinides ith the one under no habits. Is this an e ient alloation? Consider the planning problem max fu ( ; k ) + u (( + r) ( ) ; k ( + r) ( ))g ( ) ( ( k)) max + (( + r) ( ) ( k))! ( k) max + (( + r) ( )) : From this e onlude that the planner also ants the alloation implied by the deentralized equilibrium. i.e., ( + ). Why is that? To shed some more light. Consider the ase of "onspiuous onsumption". Suppose that referene utility arise on goods onsumption but not in leisure l: No, e just need one period to illustrate the point. Individuals solve max u (; ; l) s:t: ( l) Suppose ( v) u (; ; l) + l 4
5 Then, the private rst order ondition is ( v) Again, onsidering the log ase, this yields 0: + v + + k +! + ( k) hih inreases in k; and more so, the higher is : The planning solution is max ith rst order ondition ( k) ( k) + ; hih in the log ase, yields + : Comparing the deentralized outome ith the optimal, e see that onsumption in the deentralized ase is too high by a term ( + ( k)) ( + ) k: Introduing a tax on labor ould orret the externality. Clearly, our examples do extend to dynami ases. What ould it apply for asset aumulation? Could there be more reasonable asymmetries than leisure/onsumption? Returning nally to the issue of multipliity. Let s the solution to the private rst order ondition ith referene utility as (C) : Clearly, a private equilibrium is a xed point of : Therefore a neessary ondition for multipliity is that 0 (C) in some range. Let s alulate it in the additive ase. Here, (C) is de ned by the solution to ( kc) 0 5! (C) + kce ln + e ln
6 ith 0 (C) k + < : It is, hoever, in priniple possible to have multipliity. Consider the folloing extreme preferenes xa ( u (; C; l) x b ( C) + l if C C) + l if < C The marginal utility of leisure is onstant at unity hile the marginal of onsumption is x b if individual onsumption is belo the average C and x a if it is above. No, suppose x b > > x a : Then, the private optimum is learly C; and there is an in nite number of private equilibria, hile the only e ient one is 0: 6
Solutions to Problem Set 1
Eon602: Maro Theory Eonomis, HKU Instrutor: Dr. Yulei Luo September 208 Solutions to Problem Set. [0 points] Consider the following lifetime optimal onsumption-saving problem: v (a 0 ) max f;a t+ g t t
More informationTaste for variety and optimum product diversity in an open economy
Taste for variety and optimum produt diversity in an open eonomy Javier Coto-Martínez City University Paul Levine University of Surrey Otober 0, 005 María D.C. Garía-Alonso University of Kent Abstrat We
More information6 Dynamic Optimization in Continuous Time
6 Dynami Optimization in Continuous Time 6.1 Dynami programming in ontinuous time Consider the problem Z T max e rt u (k,, t) dt (1) (t) T s.t. k ú = f (k,, t) (2) k () = k, (3) with k (T )= k (ase 1),
More informationQ c, Q f denote the outputs of good C and F, respectively. The resource constraints are: T since the technology implies: Tc = Qc
Fall 2008 Eon 455 Ansers - Problem Set 3 Harvey Lapan 1. Consider a simpliied version o the Heksher-Ohlin model ith the olloing tehnology: To produe loth: three units o labor and one unit o land are required
More informationProduct Policy in Markets with Word-of-Mouth Communication. Technical Appendix
rodut oliy in Markets with Word-of-Mouth Communiation Tehnial Appendix August 05 Miro-Model for Inreasing Awareness In the paper, we make the assumption that awareness is inreasing in ustomer type. I.e.,
More informationBusiness Cycles: The Classical Approach
San Francisco State University ECON 302 Business Cycles: The Classical Approach Introduction Michael Bar Recall from the introduction that the output per capita in the U.S. is groing steady, but there
More informationEcon 201: Problem Set 3 Answers
Econ 20: Problem Set 3 Ansers Instructor: Alexandre Sollaci T.A.: Ryan Hughes Winter 208 Question a) The firm s fixed cost is F C = a and variable costs are T V Cq) = 2 bq2. b) As seen in class, the optimal
More informationErrata and changes for Lecture Note 1 (I would like to thank Tomasz Sulka for the following changes): ( ) ( ) lim = should be
Errata and hanges for Leture Note (I would like to thank Tomasz Sulka for the following hanges): Page 5 of LN: f f ' lim should be g g' f f ' lim lim g g ' Page 8 of LN: the following words (in RED) have
More informationVolume 29, Issue 3. On the definition of nonessentiality. Udo Ebert University of Oldenburg
Volume 9, Issue 3 On the definition of nonessentiality Udo Ebert University of Oldenburg Abstrat Nonessentiality of a good is often used in welfare eonomis, ost-benefit analysis and applied work. Various
More informationMicroeconomic Theory I Assignment #7 - Answer key
Miroeonomi Theory I Assignment #7 - Answer key. [Menu priing in monopoly] Consider the example on seond-degree prie disrimination (see slides 9-93). To failitate your alulations, assume H = 5, L =, and
More informationSignals & Systems - Chapter 6
Signals & Systems - Chapter 6 S. A real-valued signal x( is knon to be uniquely determined by its samples hen the sampling frequeny is s = 0,000π. For hat values of is (j) guaranteed to be zero? From the
More informationChapter 2 Lecture 5 Longitudinal stick fixed static stability and control 2 Topics
hapter 2 eture 5 ongitudinal stik fied stati stability and ontrol 2 Topis 2.2 mg and mα as sum of the ontributions of various omponent 2.3 ontributions of ing to mg and mα 2.3.1 orretion to mα for effets
More informationGeneral Equilibrium. What happens to cause a reaction to come to equilibrium?
General Equilibrium Chemial Equilibrium Most hemial reations that are enountered are reversible. In other words, they go fairly easily in either the forward or reverse diretions. The thing to remember
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationCommon Value Auctions with Costly Entry
Common Value Autions with Costly Entry Pauli Murto Juuso Välimäki June, 205 preliminary and inomplete Abstrat We onsider a model where potential bidders onsider paying an entry ost to partiipate in an
More informationNeoclassical Growth Model / Cake Eating Problem
Dynamic Optimization Institute for Advanced Studies Vienna, Austria by Gabriel S. Lee February 1-4, 2008 An Overview and Introduction to Dynamic Programming using the Neoclassical Growth Model and Cake
More informationEdexcel GCSE Maths Foundation Skills Book Ratio, proportion and rates of change 1
Guidane on the use of odes for this mark sheme ethod mark A C P ao oe ft Auray mark ark awarded independent of method Communiation mark Proof, proess or justifiation mark Corret answer only Or equivalent
More informationThree-dimensional Meso-scopic Analyses of Mortar and Concrete Model by Rigid Body Spring Model
Three-dimensional Meso-sopi Analyses of Mortar and Conrete Model by Rigid Body Spring Model K. Nagai, Y. Sato & T. Ueda Hokkaido University, Sapporo, Hokkaido, JAPAN ABSTRACT: Conrete is a heterogeneity
More informationNormative and descriptive approaches to multiattribute decision making
De. 009, Volume 8, No. (Serial No.78) China-USA Business Review, ISSN 57-54, USA Normative and desriptive approahes to multiattribute deision making Milan Terek (Department of Statistis, University of
More informationAppendix A Market-Power Model of Business Groups. Robert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, November 2001
Appendix A Market-Power Model of Business Groups Roert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, Novemer 200 Journal of Eonomi Behavior and Organization, 5, 2003, 459-485. To solve for the
More informationFour-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field
Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia
More informationVolunteering and the strategic value of ignorance
Volunteering and the strategi value of ignorane Florian Morath Max Plank Institute for Tax Law and Publi Finane November 10, 011 Abstrat Private provision of publi goods often takes plae as a war of attrition:
More informationkids (this case is for j = 1; j = 2 case is similar). For the interior solution case, we have 1 = c (x 2 t) + p 2
Problem 1 There are two subgames, or stages. At stage 1, eah ie ream parlor i (I all it firm i from now on) selets loation x i simultaneously. At stage 2, eah firm i hooses pries p i. To find SPE, we start
More informationController Design Based on Transient Response Criteria. Chapter 12 1
Controller Design Based on Transient Response Criteria Chapter 12 1 Desirable Controller Features 0. Stable 1. Quik responding 2. Adequate disturbane rejetion 3. Insensitive to model, measurement errors
More informationThe Laws of Acceleration
The Laws of Aeleration The Relationships between Time, Veloity, and Rate of Aeleration Copyright 2001 Joseph A. Rybzyk Abstrat Presented is a theory in fundamental theoretial physis that establishes the
More informationChapter 13, Chemical Equilibrium
Chapter 13, Chemial Equilibrium You may have gotten the impression that when 2 reatants mix, the ensuing rxn goes to ompletion. In other words, reatants are onverted ompletely to produts. We will now learn
More informationmax min z i i=1 x j k s.t. j=1 x j j:i T j
AM 221: Advaned Optimization Spring 2016 Prof. Yaron Singer Leture 22 April 18th 1 Overview In this leture, we will study the pipage rounding tehnique whih is a deterministi rounding proedure that an be
More informationIn the Ramsey model we maximized the utility U = u[c(t)]e nt e t dt. Now
PERMANENT INCOME AND OPTIMAL CONSUMPTION On the previous notes we saw how permanent income hypothesis can solve the Consumption Puzzle. Now we use this hypothesis, together with assumption of rational
More informationSTATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics
STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Fall, 202 Answer Key to Section 2 Questions Section. (Suggested Time: 45 Minutes) For 3 of
More informationSubject: Introduction to Component Matching and Off-Design Operation % % ( (1) R T % (
16.50 Leture 0 Subjet: Introdution to Component Mathing and Off-Design Operation At this point it is well to reflet on whih of the many parameters we have introdued (like M, τ, τ t, ϑ t, f, et.) are free
More informationComplete Shrimp Game Solution
Complete Shrimp Game Solution Florian Ederer Feruary 7, 207 The inverse demand urve is given y P (Q a ; Q ; Q ) = 00 0:5 (Q a + Q + Q ) The pro t funtion for rm i = fa; ; g is i (Q a ; Q ; Q ) = Q i [P
More informationAcoustic Waves in a Duct
Aousti Waves in a Dut 1 One-Dimensional Waves The one-dimensional wave approximation is valid when the wavelength λ is muh larger than the diameter of the dut D, λ D. The aousti pressure disturbane p is
More informationOligopolistic Markets with Sequential Search and Production Cost Uncertainty
Oligopolisti Markets with Sequential Searh and Prodution Cost Unertainty Maarten Janssen Paul Pihler Simon Weidenholzer February 14, 2011 Abstrat This artile analyzes a sequential searh model where firms
More informationOptimal control of solar energy systems
Optimal ontrol of solar energy systems Viorel Badesu Candida Oanea Institute Polytehni University of Buharest Contents. Optimal operation - systems with water storage tanks 2. Sizing solar olletors 3.
More informationLongitudinal Static Stability
ongitudinal Stati Stability Some definitions C m M V S pithing moment without dimensions (so without influene of ρ, V and S) it is a shape parameter whih varies with the angle of attak. Note the hord in
More informationHOW TO FACTOR. Next you reason that if it factors, then the factorization will look something like,
HOW TO FACTOR ax bx I now want to talk a bit about how to fator ax bx where all the oeffiients a, b, and are integers. The method that most people are taught these days in high shool (assuming you go to
More informationA Differential Equation for Specific Catchment Area
Proeedings of Geomorphometry 2009. Zurih, Sitzerland, 3 ugust - 2 September, 2009 Differential Equation for Speifi Cathment rea J. C. Gallant, M. F. Huthinson 2 CSIRO Land and Water, GPO Box 666, Canberra
More information2.2 BUDGET-CONSTRAINED CHOICE WITH TWO COMMODITIES
Essential Miroeonomis -- 22 BUDGET-CONSTRAINED CHOICE WITH TWO COMMODITIES Continuity of demand 2 Inome effets 6 Quasi-linear, Cobb-Douglas and CES referenes 9 Eenditure funtion 4 Substitution effets and
More informationRemark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the function V ( x ) to be positive definite.
Leture Remark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the funtion V ( x ) to be positive definite. ost often, our interest will be to show that x( t) as t. For that we will need
More informationTOBB-ETU - Econ 532 Practice Problems II (Solutions)
TOBB-ETU - Econ 532 Practice Problems II (Solutions) Q: Ramsey Model: Exponential Utility Assume that in nite-horizon households maximize a utility function of the exponential form 1R max U = e (n )t (1=)e
More information1 Bertrand duopoly with incomplete information
Game Theory Solution to Problem Set 5 1 Bertrand duopoly ith incomplete information The game i de ned by I = f1; g ; et of player A i = [0; 1) T i = fb L ; b H g, ith p(b L ) = u i (b i ; p i ; p j ) =
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationInternational Journal of Advanced Engineering Research and Studies E-ISSN
Researh Paper FINIE ELEMEN ANALYSIS OF A CRACKED CANILEVER BEAM Mihir Kumar Sutar Address for Correspondene Researh Sholar, Department of Mehanial & Industrial Engineering Indian Institute of ehnology
More informationReference. R. K. Herz,
Identifiation of CVD kinetis by the ethod of Koiyaa, et al. Coparison to 1D odel (2012) filenae: CVD_Koiyaa_1D_odel Koiyaa, et al. (1999) disussed ethods to identify the iportant steps in a CVD reation
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationChapter 2 Lecture 8 Longitudinal stick fixed static stability and control 5 Topics
Flight dynamis II Stability and ontrol hapter 2 Leture 8 Longitudinal stik fied stati stability and ontrol 5 Topis 2.6 ontributions of power plant to mg and mα 2.6.1 Diret ontributions of powerplant to
More informationChapter 14. The Concept of Equilibrium and the Equilibrium Constant. We have for the most part depicted reactions as going one way.
Chapter 14 The Conept of Equilibrium and the Equilibrium Constant In hapter 1 we dealt with Physial Equilibrium Physial Changes HO 2 (l) HO 2 (g) In hapter 14 we will learn about Chemial Equilibrium. We
More informationThe Corpuscular Structure of Matter, the Interaction of Material Particles, and Quantum Phenomena as a Consequence of Selfvariations.
The Corpusular Struture of Matter, the Interation of Material Partiles, and Quantum Phenomena as a Consequene of Selfvariations. Emmanuil Manousos APM Institute for the Advanement of Physis and Mathematis,
More informationOligopolistic Markets with Sequential Search and Asymmetric Information
Oligopolisti Markets with Sequential Searh and Asymmetri Information Maarten Janssen Paul Pihler Simon Weidenholzer 11th February 2010 Abstrat A large variety of markets, suh as retail markets for gasoline
More informationLecture Notes 8
14.451 Lecture Notes 8 Guido Lorenzoni Fall 29 1 Stochastic dynamic programming: an example We no turn to analyze problems ith uncertainty, in discrete time. We begin ith an example that illustrates the
More informationInternet Appendix for Proxy Advisory Firms: The Economics of Selling Information to Voters
Internet Appendix for Proxy Advisory Firms: The Eonomis of Selling Information to Voters Andrey Malenko and Nadya Malenko The first part of the Internet Appendix presents the supplementary analysis for
More informationComplexity of Regularization RBF Networks
Complexity of Regularization RBF Networks Mark A Kon Department of Mathematis and Statistis Boston University Boston, MA 02215 mkon@buedu Leszek Plaskota Institute of Applied Mathematis University of Warsaw
More informationIrreversibility and restoration in natural resource development
# Oxford University Press 1999 Oxford Eonomi Papers 51 (1999), 559±573 559 Irreversibility and restoration in natural resoure development By Jinhua Zhao* and David Zilberman{ * Department of Eonomis, Heady
More informationLight Model, Cognitive Throughput Model, and Subjective Alertness Model. Model Equation Summary
Light Model, Cognitive Throughput Model, and Subjetive Alertness Model Model Equation Summary Brigham and Women s ospital arvard Medial Shool Biomathematial Modeling Unit Division of Sleep Mediine Department
More informationUniversity of Wollongong Department of Economics Working Paper Series 2000
University of Wollongong Department of Eonomis Working Paper Series 000 Rational Non-additive Eating: Cyles, Overweightness, and Underweightness Amnon Levy WP 00-07 RATIONAL NON-ADDICTIVE EATING: CYCLES,
More informationChapter 15 Chemical Equilibrium
Chapter 5 Chemial Equilibrium 5. The Conept of Equilibrium Figure: 3. from Chemistry by MMurray & Fey Figure 3.(a) NO 4( g) NO( g) olorless brown we start with reatant, N O 4, so the solution is olorless
More informationAverage Rate Speed Scaling
Average Rate Speed Saling Nikhil Bansal David P. Bunde Ho-Leung Chan Kirk Pruhs May 2, 2008 Abstrat Speed saling is a power management tehnique that involves dynamially hanging the speed of a proessor.
More informationBeams on Elastic Foundation
Professor Terje Haukaas University of British Columbia, Vanouver www.inrisk.ub.a Beams on Elasti Foundation Beams on elasti foundation, suh as that in Figure 1, appear in building foundations, floating
More informationWork and Heat Definitions
Work and Heat Definitions FL- Surroundings: Everything outside system + q -q + System: he part of S the orld e are observing. Heat, q: transfer of energy resulting from a temperature difference Work, :
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationElements of Economic Analysis II Lecture VII: Equilibrium in a Competitive Market
Elements of Economic Analysis II Lecture VII: Equilibrium in a Competitive Market Kai Hao Yang 10/31/2017 1 Partial Equilibrium in a Competitive Market In the previous lecture, e derived the aggregate
More informationSOME FUNDAMENTAL ASPECTS OF COMPRESSIBLE FLOW
SOE FUNDAENAL ASECS OF CORESSIBLE FLOW ah number gas veloity mah number, speed of sound a a R < : subsoni : transoni > : supersoni >> : hypersoni art three : ah Number 7 Isentropi flow in a streamtube
More informationCoding for Random Projections and Approximate Near Neighbor Search
Coding for Random Projetions and Approximate Near Neighbor Searh Ping Li Department of Statistis & Biostatistis Department of Computer Siene Rutgers University Pisataay, NJ 8854, USA pingli@stat.rutgers.edu
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationMost results in this section are stated without proof.
Leture 8 Level 4 v2 he Expliit formula. Most results in this setion are stated without proof. Reall that we have shown that ζ (s has only one pole, a simple one at s =. It has trivial zeros at the negative
More informationON A PROCESS DERIVED FROM A FILTERED POISSON PROCESS
ON A PROCESS DERIVED FROM A FILTERED POISSON PROCESS MARIO LEFEBVRE and JEAN-LUC GUILBAULT A ontinuous-time and ontinuous-state stohasti proess, denoted by {Xt), t }, is defined from a proess known as
More informationProblem 1 (30 points)
Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public
More informationToulouse School of Economics, M2 Macroeconomics 1 Professor Franck Portier. Exam Solution
Toulouse Shool of Eonomis, 214-215 M2 Maroeonomis 1 Professor Frank Portier Exam Solution This is a 3 hours exam. Class slides and any handwritten material are allowed. You must write legibly. I True,
More informationProblem Set 2: Proposed solutions Econ Fall Cesar E. Tamayo Department of Economics, Rutgers University
Problem Set 2: Proposed solutions Econ 504 - Fall 202 Cesar E. Tamayo ctamayo@econ.rutgers.edu Department of Economics, Rutgers University Simple optimal growth (Problems &2) Suppose that we modify slightly
More informationProbability Distributions
STATGRAPHICS Re. 6805 Probability Distributions Summary... Data Input... Analysis Summary... 3 Analysis Options... 3 Cumulatie Distribution... 4 Inerse CDF... 5 Random Numbers... 6 DensityMass Funtion...
More informationOn Industry Structure and Firm Conduct in Long Run Equilibrium
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember On Industry Struture and Firm Condut in Long Run Equilibrium Prof. Jean-Paul Chavas Department of Agriultural and Applied Eonomis
More informationELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES.
ELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES. All systems with interation of some type have normal modes. One may desribe them as solutions in absene of soures; they are exitations of the system
More informationEvaluation of effect of blade internal modes on sensitivity of Advanced LIGO
Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple
More informationNonlinear Resource Allocation in Restoration of Compromised Systems
Nonlinear Resoure Alloation in Restoration of Compromised Systems Qunwei Zheng *, Xiaoyan Hong *, Sibabrata Ray * Computer Siene Department, Uniersity of Alabama, Tusaloosa, AL 35487 Google In. 64 Arizona
More informationECON607 Fall 2010 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2
ECON607 Fall 200 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2 The due date for this assignment is Tuesday, October 2. ( Total points = 50). (Two-sector growth model) Consider the
More informationChapter 26 Lecture Notes
Chapter 26 Leture Notes Physis 2424 - Strauss Formulas: t = t0 1 v L = L0 1 v m = m0 1 v E = m 0 2 + KE = m 2 KE = m 2 -m 0 2 mv 0 p= mv = 1 v E 2 = p 2 2 + m 2 0 4 v + u u = 2 1 + vu There were two revolutions
More informationarxiv: v1 [physics.gen-ph] 5 Jan 2018
The Real Quaternion Relativity Viktor Ariel arxiv:1801.03393v1 [physis.gen-ph] 5 Jan 2018 In this work, we use real quaternions and the basi onept of the final speed of light in an attempt to enhane the
More informationPublic School Choice: An Economic Analysis
Publi Shool Choie: An Eonomi Analysis Levon Barseghyan, Damon Clark and Stephen Coate May 25, 2018 Abstrat Publi shool hoie programs give households a hoie of publi shool and enourage shools to ompete
More informationCRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS
Russian Physis Journal, Vol. 48, No. 8, 5 CRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS A. N. Taskin, V. N. Udodov, and A. I. Potekaev UDC
More informationThe Dynamics of Bidding Markets with Financial Constraints
The Dynamis of Bidding Markets with Finanial Constraints Pablo F. Beker University of Warwik Ángel Hernando-Veiana Universidad Carlos III de Madrid July 1, 2014 Abstrat We develop a model of bidding markets
More informationAggregate Supply. Econ 208. April 3, Lecture 16. Econ 208 (Lecture 16) Aggregate Supply April 3, / 12
Aggregate Supply Econ 208 Lecture 16 April 3, 2007 Econ 208 (Lecture 16) Aggregate Supply April 3, 2007 1 / 12 Introduction rices might be xed for a brief period, but we need to look beyond this The di
More informationEconS 503 Homework #8. Answer Key
EonS 503 Homework #8 Answer Key Exerise #1 Damaged good strategy (Menu riing) 1. It is immediate that otimal rie is = 3 whih yields rofits of ππ = 3/ (the alternative being a rie of = 1, yielding ππ =
More informationIN-PLANE VIBRATIONS OF CURVED BEAMS WITH VARIABLE CROSS-SECTIONS CARRYING ADDITIONAL MASS
11 th International Conferene on Vibration Problems Z. Dimitrovová et al. (eds.) Lisbon, Portugal, 9-1 September 013 IN-PLANE VIBRATIONS OF CURVED BEAMS WITH VARIABLE CROSS-SECTIONS CARRYING ADDITIONAL
More informationComprehensive Exam. Macro Spring 2014 Retake. August 22, 2014
Comprehensive Exam Macro Spring 2014 Retake August 22, 2014 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question.
More informationOptimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach
Amerian Journal of heoretial and Applied tatistis 6; 5(-): -8 Published online January 7, 6 (http://www.sienepublishinggroup.om/j/ajtas) doi:.648/j.ajtas.s.65.4 IN: 36-8999 (Print); IN: 36-96 (Online)
More information23.1 Tuning controllers, in the large view Quoting from Section 16.7:
Lesson 23. Tuning a real ontroller - modeling, proess identifiation, fine tuning 23.0 Context We have learned to view proesses as dynami systems, taking are to identify their input, intermediate, and output
More informationEconS Advanced Microeconomics II Handout on Mechanism Design
EconS 503 - Advanced Microeconomics II Handout on Mechanism Design 1. Public Good Provision Imagine that you and your colleagues want to buy a co ee machine for your o ce. Suppose that some of you may
More informationSupplementary information for: All-optical signal processing using dynamic Brillouin gratings
Supplementary information for: All-optial signal proessing using dynami Brillouin gratings Maro Santagiustina, Sanghoon Chin 2, Niolay Primerov 2, Leonora Ursini, Lu Thévena 2 Department of Information
More informationLecture 11 Buckling of Plates and Sections
Leture Bukling of lates and Setions rolem -: A simpl-supported retangular plate is sujeted to a uniaxial ompressive load N, as shown in the sketh elow. a 6 N N a) Calulate and ompare ukling oeffiients
More informationCONTROL OF THERMAL CRACKING USING HEAT OF CEMENT HYDRATION IN MASSIVE CONCRETE STRUCTURES
CONROL OF HERMAL CRACKING USING HEA OF CEMEN HYDRAION IN MASSIVE CONCREE SRUCURES. Mizobuhi (1), G. Sakai (),. Ohno () and S. Matsumoto () (1) Department of Civil and Environmental Engineering, HOSEI University,
More informationHigher-Order Risk Attitudes toward Correlation
Higher-Order Risk Attitudes toward Correlation Jingyuan Li Department of Finane and Insurane, Lingnan University, Hong Kong E-mail: jingyuanli@ln.edu.hk August 10, 2013 Abstrat Higher-order risk attitudes
More informationFlorian Morath. Volunteering and the Strategic Value of Ignorance. Max Planck Institute for Intellectual Property, Competition and Tax Law
WISSENSCHAFTSZENTRUM BERLIN FÜR SOZIALFORSCHUNG SOCIAL SCIENCE RESEARCH CENTER BERLIN Florian Morath Volunteering and the Strategi Value of Ignorane Max Plank Institute for Intelletual Property, Competition
More informationBuckling loads of columns of regular polygon cross-section with constant volume and clamped ends
76 Bukling loads of olumns of regular polygon ross-setion with onstant volume and lamped ends Byoung Koo Lee Dept. of Civil Engineering, Wonkwang University, Iksan, Junuk, 7-79, Korea Email: kleest@wonkwang.a.kr
More informationStrauss PDEs 2e: Section Exercise 3 Page 1 of 13. u tt c 2 u xx = cos x. ( 2 t c 2 2 x)u = cos x. v = ( t c x )u
Strauss PDEs e: Setion 3.4 - Exerise 3 Page 1 of 13 Exerise 3 Solve u tt = u xx + os x, u(x, ) = sin x, u t (x, ) = 1 + x. Solution Solution by Operator Fatorization Bring u xx to the other side. Write
More informationMean Activity Coefficients of Peroxodisulfates in Saturated Solutions of the Conversion System 2NH 4. H 2 O at 20 C and 30 C
Mean Ativity Coeffiients of Peroxodisulfates in Saturated Solutions of the Conversion System NH 4 Na S O 8 H O at 0 C and 0 C Jan Balej Heřmanova 5, 170 00 Prague 7, Czeh Republi balejan@seznam.z Abstrat:
More informationCommon Mistakes & How to avoid them Class X - Math. Unit: Algebra. Types of Question Common Mistakes Points to be emphasised. points.
Common Mistakes & How to avoid them Class X - Math Unit: Algera Chapter: Pair of Linear Equations in Two Variales Types of Question Common Mistakes Points to e emphasised Solving the system of (i) Error
More informationConsider this problem. A person s utility function depends on consumption and leisure. Of his market time (the complement to leisure), h t
VI. INEQUALITY CONSTRAINED OPTIMIZATION Application of the Kuhn-Tucker conditions to inequality constrained optimization problems is another very, very important skill to your career as an economist. If
More informationADHESION MEASURES OF ELASTO-PLASTIC THIN FILM VIA BUCKLE-DRIVEN DELAMINATION
ADHESION MEASURES OF ELASTO-PLASTIC THIN FILM VIA BUCKLE-DRIVEN DELAMINATION Yu Shouwen and Li Qunyang Department of Engineering Mehanis, Tsinghua University, Beijing 184, China Yusw@mail.tsinghua.edu.n
More informationChapter 15: Chemical Equilibrium
Chapter 5: Chemial Equilibrium ahoot!. At eq, the rate of the forward reation is the rate of the reverse reation. equal to, slower than, faster than, the reverse of. Selet the statement that BEST desribes
More informationChemical Engineering Thermodynamics II ( ) 02 - The Molar Gibbs Free Energy & Fugacity of a Pure Component
Chemial Engineering Thermodynamis II (090533) 0 - The Molar Gibbs Free Energy & Fugaity of a ure Component Dr. Ali Khalaf Al-matar Chemial Engineering Department University of Jordan banihaniali@yahoo.om
More information