1 The Sidrauski model
|
|
- Clifford May
- 5 years ago
- Views:
Transcription
1 The Sdrausk model There are many ways to brng money nto the macroeconomc debate. Among the fundamental ssues n economcs the treatment of money s probably the LESS satsfactory and there s very lttle agreement about what s the rght way to look at monetary ssues. The Sdrausk model assumes we derve drect utlty from holdng money. Ths utlty s due to the lqudty servces we get and not due to the value of money as an asset. In models lke ths there s no drect utlty from holdng total assets, only from money. Assume the representatve agent who lves for ever maxmzes the followng utlty: max V 0 = Z Assumng no populaton growth one wrtes: Because: 0 u (c t,m t ) e θt dt () where : u c,u m > 0, u cc,u mm < 0 (2) s.t. : C t + K + M/P = wn + rk + G (3) K/N = k (4) M/PN = m + πm µ M MPN PNM m = = = M/PN πm PN P 2 N 2 Usng ( 4) one can rewrte the budget constrant n per capta terms: Defne TOTAL assets as a = m + k c t + k + m + πm = w + rk + g a = rk + w + g c πm a = [ra + w + g] [c +(π + r) m] a = [ncome] [ consumpton ]
2 and assume NPG: Hamltonan: n lm t a t exp R o t r 0 vdv =0we can wrte down the current value H = u (c t,m t )+λ [ra + w + g c (π + r) m] where a s the state varable and c, m are control varables. u c (c t,m t ) = λ (5) u m (c t,m t ) = λ (π + r) λ = θλ rλ NPG :... To close the model we assume (compettve) equlbrum n the captal market and CRS n producton + compettve labor market to get: r t = f 0 (k t ), w t = f (k t ) f 0 (k t ) k t. An IMPORTANT addtonal assumpton s: g = G/N =( M/P)N =( M/M)(M/PN) µm. Ths assumpton states that government transfers equal ALL the revenue from prntng money. In the steady state we want to assume that not only a =0but also m = λ =0. The last equalty mples that n the steady state the value of assets does not change. m = 0 = µ = π (6) λ = 0 = θ = f 0 (k ss ) The frst equalty states that the rate of prntng n the steady state equals the rate of nflaton and the second condton mples that n the steady state money s SUPER NEUTRAL [the rate of money growth has no effect on real economc actvty - the economy s at the modfed golden rule ] (Ths condtons are general and could be modfed to account for economc growth etc.). 2
3 Usng (5, 6) one gets the optmum quantty of money n the steady state. Consumpton equals producton (we assumed no deprecaton), producton s at the modfed golden rule level and the demand for money s gven by: u m =(µ + θ) u c Snce money has no effect on real varables n the steady state the best money rule (FRIED- MAN S RULE) s to make the margnal utlty from money = zero (sataton level). Ths happens f the government REDUCE money (have dsnflaton!!) at the rate equal to the tme preference. We want to compensate people for the lqudty servce they need. Snce compensaton n the steady state s free (prntng/absorbng money s free) we should compensate them fully. FREIDMAN0S RULE = µ = θ 3
4 . Non unqueness n monetary models Can the market determne the prce level? In many general cases t cannot do so even f the model s well specfed a la Sdrausk. Ths s an mportant ssue snce f there s more than one representatve agent they have no mechansm to pck a prce level everybody agree upon. The concept of equlbrum s ll n such cases. Let us use a varant of the Sdrausk model. ths tme we wll assume that money s needed for lqudty purposes n frms so the producton functon s a functon of real balances. A very smlar model could use separable nstantaneous utlty between money and consumpton. Assume ndvduals maxmze: max V 0 = s.t. : Z 0 u (c t ) e θt dt (7) M = P [h(m t ) c t ]+G (8) where:h(m t ) s the producton functon and the budget constrant s wrtten n nomnal terms. c t ]+g In real terms the dynamc budget constrant s (here g = G/P ): Snce M/P = µm and M/P = m + π t m then π t = µ m/m. Usng the above we can rewrte the real dynamc constrant as: M/P =[h(m t ) m t = h (m t ) c t π t m t + g t. (9) The Current value Hamltonan s: H = u (c t )+λ t [h (m t ) c t π t m + g t ], and the FOC are: u c (t) = λ t = λ t = u cc (t) c t (0) λ t = λ t θ λ t h 0 (m t )+λ t π t = λ t = λ t [h 0 (m t ) π t θ] 4
5 Usng (7 0) one can wrte the dynamc optmal behavor as: c = u h c h 0 (m t )+ m/m µ θ u cc. () The full employment means output equal consumpton (there s no nvestment here) and equlbrum n the money market mples demand=supply or c t = h (m t ) and m t = m s t. Takng dervatve w.r.t. tme of equlbrum n goods market yelds: c = h 0 (m t ) m. (2) balances: Usng ( to 2) wecanrewrtethedynamcoptmalpathntermsofrealmoney ³ m/m h 0 (m t ) m t h (m t ) h 0 (m t ) m = u h c h 0 (m t )+ m/m µ θ u cc + u c (t) c u cc (t) OR = u c (t) c u cc (t) [h0 (m t ) µ θ] Defne the elastcty of output (producton) w.r.t money as α (m) : α (m t ) h0 (m t ) m t h (m t ) Defne the elastcty of the MARGINAL utlty w.r.t consumpton as β (m) : (t can be wrtten as a functon of m snce c = h (m)) We can rewrte the dynamc equaton as: m/m = β (m) u c (t) c u cc (t) β(m) α (m) [h 0 (m t ) µ θ] β(m) To examne ths equaton n a smple way let us assume smple functonal forms: h (m) =m δ, u(c t )= c γ γ (3) 5
6 so α (m) =δ and β (m) =γ. In ths case In the steady state: m (t) = γ δ γ h δ (m t ) δ µ θ m t defne : = δ = γ m (t) = hδ (m t ) δ (µ + θ) m t γ µ µ + θ m = δ δ. Thus: m steady state = [(δ ) (µ + θ)] = [sgn ( )] m h m, Analyzng ths equaton n the m space depends crucally on the sgn of. If > 0 we get non unqueness. There s no way to determne the value of the prce level n the steady state. Any prce level people agree upon leads them to the steady state BUT how (why) can they all choose the same prce level? If < 0 we have unqueness BUT n the general case the curve may bend back and we can have bubbles n the prce level. Every prce level that s hgher than the unque steady state prce level s an acceptable nflatonary bubble. 6
A NOTE ON CES FUNCTIONS Drago Bergholt, BI Norwegian Business School 2011
A NOTE ON CES FUNCTIONS Drago Bergholt, BI Norwegan Busness School 2011 Functons featurng constant elastcty of substtuton CES are wdely used n appled economcs and fnance. In ths note, I do two thngs. Frst,
More informationEconomics 2450A: Public Economics Section 10: Education Policies and Simpler Theory of Capital Taxation
Economcs 2450A: Publc Economcs Secton 10: Educaton Polces and Smpler Theory of Captal Taxaton Matteo Parads November 14, 2016 In ths secton we study educaton polces n a smplfed verson of framework analyzed
More informationEconomics 8105 Macroeconomic Theory Recitation 1
Economcs 8105 Macroeconomc Theory Rectaton 1 Outlne: Conor Ryan September 6th, 2016 Adapted From Anh Thu (Monca) Tran Xuan s Notes Last Updated September 20th, 2016 Dynamc Economc Envronment Arrow-Debreu
More informationEconomics 101. Lecture 4 - Equilibrium and Efficiency
Economcs 0 Lecture 4 - Equlbrum and Effcency Intro As dscussed n the prevous lecture, we wll now move from an envronment where we looed at consumers mang decsons n solaton to analyzng economes full of
More informationPROBLEM SET 7 GENERAL EQUILIBRIUM
PROBLEM SET 7 GENERAL EQUILIBRIUM Queston a Defnton: An Arrow-Debreu Compettve Equlbrum s a vector of prces {p t } and allocatons {c t, c 2 t } whch satsfes ( Gven {p t }, c t maxmzes βt ln c t subject
More informationMixed Taxation and Production Efficiency
Floran Scheuer 2/23/2016 Mxed Taxaton and Producton Effcency 1 Overvew 1. Unform commodty taxaton under non-lnear ncome taxaton Atknson-Stgltz (JPubE 1976) Theorem Applcaton to captal taxaton 2. Unform
More informationk t+1 + c t A t k t, t=0
Macro II (UC3M, MA/PhD Econ) Professor: Matthas Kredler Fnal Exam 6 May 208 You have 50 mnutes to complete the exam There are 80 ponts n total The exam has 4 pages If somethng n the queston s unclear,
More informationf(x,y) = (4(x 2 4)x,2y) = 0 H(x,y) =
Problem Set 3: Unconstraned mzaton n R N. () Fnd all crtcal ponts of f(x,y) (x 4) +y and show whch are ma and whch are mnma. () Fnd all crtcal ponts of f(x,y) (y x ) x and show whch are ma and whch are
More informationCopyright (C) 2008 David K. Levine This document is an open textbook; you can redistribute it and/or modify it under the terms of the Creative
Copyrght (C) 008 Davd K. Levne Ths document s an open textbook; you can redstrbute t and/or modfy t under the terms of the Creatve Commons Attrbuton Lcense. Compettve Equlbrum wth Pure Exchange n traders
More informationLet p z be the price of z and p 1 and p 2 be the prices of the goods making up y. In general there is no problem in grouping goods.
Economcs 90 Prce Theory ON THE QUESTION OF SEPARABILITY What we would lke to be able to do s estmate demand curves by segmentng consumers purchases nto groups. In one applcaton, we aggregate purchases
More informationOnline Appendix. t=1 (p t w)q t. Then the first order condition shows that
Artcle forthcomng to ; manuscrpt no (Please, provde the manuscrpt number!) 1 Onlne Appendx Appendx E: Proofs Proof of Proposton 1 Frst we derve the equlbrum when the manufacturer does not vertcally ntegrate
More informationSupporting Materials for: Two Monetary Models with Alternating Markets
Supportng Materals for: Two Monetary Models wth Alternatng Markets Gabrele Camera Chapman Unversty Unversty of Basel YL Chen Federal Reserve Bank of St. Lous 1 Optmal choces n the CIA model On date t,
More informationEquilibrium with Complete Markets. Instructor: Dmytro Hryshko
Equlbrum wth Complete Markets Instructor: Dmytro Hryshko 1 / 33 Readngs Ljungqvst and Sargent. Recursve Macroeconomc Theory. MIT Press. Chapter 8. 2 / 33 Equlbrum n pure exchange, nfnte horzon economes,
More informationWelfare Properties of General Equilibrium. What can be said about optimality properties of resource allocation implied by general equilibrium?
APPLIED WELFARE ECONOMICS AND POLICY ANALYSIS Welfare Propertes of General Equlbrum What can be sad about optmalty propertes of resource allocaton mpled by general equlbrum? Any crteron used to compare
More information3.2. Cournot Model Cournot Model
Matlde Machado Assumptons: All frms produce an homogenous product The market prce s therefore the result of the total supply (same prce for all frms) Frms decde smultaneously how much to produce Quantty
More information,, MRTS is the marginal rate of technical substitution
Mscellaneous Notes on roducton Economcs ompled by eter F Orazem September 9, 00 I Implcatons of conve soquants Two nput case, along an soquant 0 along an soquant Slope of the soquant,, MRTS s the margnal
More informationUniversity of California, Davis Date: June 22, 2009 Department of Agricultural and Resource Economics. PRELIMINARY EXAMINATION FOR THE Ph.D.
Unversty of Calforna, Davs Date: June 22, 29 Department of Agrcultural and Resource Economcs Department of Economcs Tme: 5 hours Mcroeconomcs Readng Tme: 2 mnutes PRELIMIARY EXAMIATIO FOR THE Ph.D. DEGREE
More informationIdiosyncratic Investment (or Entrepreneurial) Risk in a Neoclassical Growth Model. George-Marios Angeletos. MIT and NBER
Idosyncratc Investment (or Entrepreneural) Rsk n a Neoclasscal Growth Model George-Maros Angeletos MIT and NBER Motvaton emprcal mportance of entrepreneural or captal-ncome rsk ˆ prvate busnesses account
More informationSupporting Information for: Two Monetary Models with Alternating Markets
Supportng Informaton for: Two Monetary Models wth Alternatng Markets Gabrele Camera Chapman Unversty & Unversty of Basel YL Chen St. Lous Fed November 2015 1 Optmal choces n the CIA model On date t, gven
More informationLecture Notes, January 11, 2010
Economcs 200B UCSD Wnter 2010 Lecture otes, January 11, 2010 Partal equlbrum comparatve statcs Partal equlbrum: Market for one good only wth supply and demand as a functon of prce. Prce s defned as the
More informationHila Etzion. Min-Seok Pang
RESERCH RTICLE COPLEENTRY ONLINE SERVICES IN COPETITIVE RKETS: INTINING PROFITILITY IN THE PRESENCE OF NETWORK EFFECTS Hla Etzon Department of Technology and Operatons, Stephen. Ross School of usness,
More informationAdditional Codes using Finite Difference Method. 1 HJB Equation for Consumption-Saving Problem Without Uncertainty
Addtonal Codes usng Fnte Dfference Method Benamn Moll 1 HJB Equaton for Consumpton-Savng Problem Wthout Uncertanty Before consderng the case wth stochastc ncome n http://www.prnceton.edu/~moll/ HACTproect/HACT_Numercal_Appendx.pdf,
More informationGeneral Purpose Technologies (GPTs) and their Relevance to ICTs; Trade 4/3/2009 & Growth Implications by Iordanis Petsas
General Purpose Technologes (GPTs and ther Relevance to ICTs; Trade and Growth Implcatons Presented at CITI, Columba Busness School March 2009 By Unversty of Scranton and Baruch College (CUNY Introducton
More informationEcon674 Economics of Natural Resources and the Environment
Econ674 Economcs of Natural Resources and the Envronment Sesson 7 Exhaustble Resource Dynamc An Introducton to Exhaustble Resource Prcng 1. The dstncton between nonrenewable and renewable resources can
More information1. relation between exp. function and IUF
Dualty Dualty n consumer theory II. relaton between exp. functon and IUF - straghtforward: have m( p, u mn'd value of expendture requred to attan a gven level of utlty, gven a prce vector; u ( p, M max'd
More informationCS294 Topics in Algorithmic Game Theory October 11, Lecture 7
CS294 Topcs n Algorthmc Game Theory October 11, 2011 Lecture 7 Lecturer: Chrstos Papadmtrou Scrbe: Wald Krchene, Vjay Kamble 1 Exchange economy We consder an exchange market wth m agents and n goods. Agent
More informationPerfect Competition and the Nash Bargaining Solution
Perfect Competton and the Nash Barganng Soluton Renhard John Department of Economcs Unversty of Bonn Adenauerallee 24-42 53113 Bonn, Germany emal: rohn@un-bonn.de May 2005 Abstract For a lnear exchange
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationPrice competition with capacity constraints. Consumers are rationed at the low-price firm. But who are the rationed ones?
Prce competton wth capacty constrants Consumers are ratoned at the low-prce frm. But who are the ratoned ones? As before: two frms; homogeneous goods. Effcent ratonng If p < p and q < D(p ), then the resdual
More informationEndogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract
Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors Yuanzhu Lu Chna Economcs and Management Academy, Central Unversty o Fnance and Economcs Abstract We nvestgate endogenous
More informationOnline Appendix for A Simpler Theory of Optimal Capital Taxation by Emmanuel Saez and Stefanie Stantcheva
Onlne Appendx for A Smpler Theory of Optmal Captal Taxaton by Emmanuel Saez and Stefane Stantcheva A. Antcpated Reforms Addtonal Results Optmal tax wth antcpated reform and heterogeneous dscount rates
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationMarket structure and Innovation
Market structure and Innovaton Ths presentaton s based on the paper Market structure and Innovaton authored by Glenn C. Loury, publshed n The Quarterly Journal of Economcs, Vol. 93, No.3 ( Aug 1979) I.
More informationOnline Appendix for A Simpler Theory of Capital Taxation
Onlne Appendx for A Smpler Theory of Captal Taxaton Emmanuel Saez, UC Berkeley Stefane Stantcheva, Harvard July 2, 216 1 Proofs of Propostons n the Text 1.1 Proofs for Secton 2 Proof of Proposton 2. We
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationGames and Market Imperfections
Games and Market Imperfectons Q: The mxed complementarty (MCP) framework s effectve for modelng perfect markets, but can t handle mperfect markets? A: At least part of the tme A partcular type of game/market
More informationTheory Appendix for Market Penetration Costs and the New Consumers Margin in International Trade
Theory Appendx for Market Penetraton Costs and the New Consumers Margn n Internatonal Trade Costas Arkolaks y Yale Unversty, Federal Reserve Bank of Mnneapols, and NBER October 00 Abstract Ths s an onlne
More information9 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 - Chapter 9R -Davd Klenfeld - Fall 2005 9 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys a set
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationWinter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan
Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationUniqueness of Nash Equilibrium in Private Provision of Public Goods: Extension. Nobuo Akai *
Unqueness of Nash Equlbrum n Prvate Provson of Publc Goods: Extenson Nobuo Aka * nsttute of Economc Research Kobe Unversty of Commerce Abstract Ths note proves unqueness of Nash equlbrum n prvate provson
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationCredit Card Pricing and Impact of Adverse Selection
Credt Card Prcng and Impact of Adverse Selecton Bo Huang and Lyn C. Thomas Unversty of Southampton Contents Background Aucton model of credt card solctaton - Errors n probablty of beng Good - Errors n
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationProblem Set 3. 1 Offshoring as a Rybzcynski Effect. Economics 245 Fall 2011 International Trade
Due: Thu, December 1, 2011 Instructor: Marc-Andreas Muendler E-mal: muendler@ucsd.edu Economcs 245 Fall 2011 Internatonal Trade Problem Set 3 November 15, 2011 1 Offshorng as a Rybzcynsk Effect There are
More informationApplied Stochastic Processes
STAT455/855 Fall 23 Appled Stochastc Processes Fnal Exam, Bref Solutons 1. (15 marks) (a) (7 marks) The dstrbuton of Y s gven by ( ) ( ) y 2 1 5 P (Y y) for y 2, 3,... The above follows because each of
More informationInterpreting Slope Coefficients in Multiple Linear Regression Models: An Example
CONOMICS 5* -- Introducton to NOT CON 5* -- Introducton to NOT : Multple Lnear Regresson Models Interpretng Slope Coeffcents n Multple Lnear Regresson Models: An xample Consder the followng smple lnear
More informationRyan (2009)- regulating a concentrated industry (cement) Firms play Cournot in the stage. Make lumpy investment decisions
1 Motvaton Next we consder dynamc games where the choce varables are contnuous and/or dscrete. Example 1: Ryan (2009)- regulatng a concentrated ndustry (cement) Frms play Cournot n the stage Make lumpy
More information1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys
More informationy i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem
SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number
More information(1 ) (1 ) 0 (1 ) (1 ) 0
Appendx A Appendx A contans proofs for resubmsson "Contractng Informaton Securty n the Presence of Double oral Hazard" Proof of Lemma 1: Assume that, to the contrary, BS efforts are achevable under a blateral
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationCS286r Assign One. Answer Key
CS286r Assgn One Answer Key 1 Game theory 1.1 1.1.1 Let off-equlbrum strateges also be that people contnue to play n Nash equlbrum. Devatng from any Nash equlbrum s a weakly domnated strategy. That s,
More informationTest code: ME I/ME II, 2007
Test code: ME I/ME II, 007 Syllabus for ME I, 007 Matrx Algebra: Matrces and Vectors, Matrx Operatons. Permutaton and Combnaton. Calculus: Functons, Lmts, Contnuty, Dfferentaton of functons of one or more
More information1 Matrix representations of canonical matrices
1 Matrx representatons of canoncal matrces 2-d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3-d rotaton around the x-axs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3-d rotaton around the y-axs:
More informationA Representative Consumer Theory of Distribution: A Simple Characterization of the Ramsey Model * Cecilia García-Peñalosa CNRS and GREQAM
A Representatve Consumer Theory of Dstrbuton: A Smple Characterzaton of the Ramsey Model * Cecla García-Peñalosa CNRS and GREQAM Stephen J. Turnovsy Unversty of Washngton, Seattle June 26 Abstract: It
More informationSuggested solutions for the exam in SF2863 Systems Engineering. June 12,
Suggested solutons for the exam n SF2863 Systems Engneerng. June 12, 2012 14.00 19.00 Examner: Per Enqvst, phone: 790 62 98 1. We can thnk of the farm as a Jackson network. The strawberry feld s modelled
More informationBilateral Trade Flows and Nontraded Goods
The Emprcal Economcs Letters, 7(5): (May 008) ISSN 1681 8997 Blateral Trade Flows and Nontraded Goods Yh-mng Ln Department of Appled Economcs, Natonal Chay Unversty. 580 Snmn Road, Chay, 600, Tawan Emal:
More informationWhich Separator? Spring 1
Whch Separator? 6.034 - Sprng 1 Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng 3 Margn of a pont " # y (w $ + b) proportonal
More informationOptimal Growth Through Product Innovation
Optmal Growth Through Product Innovaton Rasmus Lentz Unversty of Wscons-Madson and CAM Dale T. Mortensen Northwestern Unversty, IZA, and NBER Aprl 26, 26 Abstract In Lentz and Mortensen (25), we formulate
More informationAmerican Law & Economics Association Annual Meetings
Amercan aw & Economcs Assocaton Annual Meetngs Year 2008 Paper 32 By-Product obbyng: Was Stgler Rght? Paul Pecorno Unversty of Alabama Ths workng paper ste s hosted by The Berkeley Electronc Press (bepress)
More informationECE559VV Project Report
ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate
More informationIn the figure below, the point d indicates the location of the consumer that is under competition. Transportation costs are given by td.
UC Berkeley Economcs 11 Sprng 006 Prof. Joseph Farrell / GSI: Jenny Shanefelter Problem Set # - Suggested Solutons. 1.. In ths problem, we are extendng the usual Hotellng lne so that now t runs from [-a,
More informationUnit 5: Government policy in competitive markets I E ciency
Unt 5: Government polcy n compettve markets I E cency Prof. Antono Rangel January 2, 2016 1 Pareto optmal allocatons 1.1 Prelmnares Bg pcture Consumers: 1,...,C,eachw/U,W Frms: 1,...,F,eachw/C ( ) Consumers
More information8 Derivation of Network Rate Equations from Single- Cell Conductance Equations
Physcs 178/278 - Davd Klenfeld - Wnter 2015 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons We consder a network of many neurons, each of whch obeys a set of conductancebased,
More informationHidden Markov Models & The Multivariate Gaussian (10/26/04)
CS281A/Stat241A: Statstcal Learnng Theory Hdden Markov Models & The Multvarate Gaussan (10/26/04) Lecturer: Mchael I. Jordan Scrbes: Jonathan W. Hu 1 Hdden Markov Models As a bref revew, hdden Markov models
More informationDiscontinuous Extraction of a Nonrenewable Resource
Dscontnuous Extracton of a Nonrenewable Resource Erc Iksoon Im 1 Professor of Economcs Department of Economcs, Unversty of Hawa at Hlo, Hlo, Hawa Uayant hakravorty Professor of Economcs Department of Economcs,
More informationPHYS 705: Classical Mechanics. Canonical Transformation II
1 PHYS 705: Classcal Mechancs Canoncal Transformaton II Example: Harmonc Oscllator f ( x) x m 0 x U( x) x mx x LT U m Defne or L p p mx x x m mx x H px L px p m p x m m H p 1 x m p m 1 m H x p m x m m
More informationA Generalized Solution of the Monopolistic Competition Model with Heterogeneous Firms and a Linear Demand (Melitz-Ottaviano)
A Generalzed Soluton of the Monopolstc Competton Model th Heterogeneous Frms and a near Demand (Meltz-Ottavano) Costas Arkolaks y Yale Unversty Frst verson: Aprl 008 Ths verson: Octoer 008 Astract Ths
More informationU.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017
U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that
More informationAppendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis
A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems
More informationChapter 2 - The Simple Linear Regression Model S =0. e i is a random error. S β2 β. This is a minimization problem. Solution is a calculus exercise.
Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where y + = β + β e for =,..., y and are observable varables e s a random error How can an estmaton rule be constructed for the
More informationPhysics 443, Solutions to PS 7
Physcs 443, Solutons to PS 7. Grffths 4.50 The snglet confguraton state s χ ) χ + χ χ χ + ) where that second equaton defnes the abbrevated notaton χ + and χ. S a ) S ) b χ â S )ˆb S ) χ In sphercal coordnates
More informationImplicit Integration Henyey Method
Implct Integraton Henyey Method In realstc stellar evoluton codes nstead of a drect ntegraton usng for example the Runge-Kutta method one employs an teratve mplct technque. Ths s because the structure
More informationLecture 21: Numerical methods for pricing American type derivatives
Lecture 21: Numercal methods for prcng Amercan type dervatves Xaoguang Wang STAT 598W Aprl 10th, 2014 (STAT 598W) Lecture 21 1 / 26 Outlne 1 Fnte Dfference Method Explct Method Penalty Method (STAT 598W)
More informationNotes on Kehoe Perri, Econometrica 2002
Notes on Kehoe Perr, Econometrca 2002 Jonathan Heathcote November 2nd 2005 There s nothng n these notes that s not n Kehoe Perr NBER Workng Paper 7820 or Kehoe and Perr Econometrca 2002. However, I have
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationThe Existence and Optimality of Equilibrium
The Exstence and Optmalty of Equlbrum Larry Blume March 29, 2006 1 Introducton These notes quckly survey two approaches to the exstence. The frst approach works wth excess demand, whle the second works
More informationHow Strong Are Weak Patents? Joseph Farrell and Carl Shapiro. Supplementary Material Licensing Probabilistic Patents to Cournot Oligopolists *
How Strong Are Weak Patents? Joseph Farrell and Carl Shapro Supplementary Materal Lcensng Probablstc Patents to Cournot Olgopolsts * September 007 We study here the specal case n whch downstream competton
More informationDEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA. 1. Matrices in Mathematica
demo8.nb 1 DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA Obectves: - defne matrces n Mathematca - format the output of matrces - appl lnear algebra to solve a real problem - Use Mathematca to perform
More informationCalculus of Variations Basics
Chapter 1 Calculus of Varatons Bascs 1.1 Varaton of a General Functonal In ths chapter, we derve the general formula for the varaton of a functonal of the form J [y 1,y 2,,y n ] F x,y 1,y 2,,y n,y 1,y
More informationMidterm Examination. Regression and Forecasting Models
IOMS Department Regresson and Forecastng Models Professor Wllam Greene Phone: 22.998.0876 Offce: KMC 7-90 Home page: people.stern.nyu.edu/wgreene Emal: wgreene@stern.nyu.edu Course web page: people.stern.nyu.edu/wgreene/regresson/outlne.htm
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationComplete subgraphs in multipartite graphs
Complete subgraphs n multpartte graphs FLORIAN PFENDER Unverstät Rostock, Insttut für Mathematk D-18057 Rostock, Germany Floran.Pfender@un-rostock.de Abstract Turán s Theorem states that every graph G
More information( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1
Problem Set 4 Suggested Solutons Problem (A) The market demand functon s the soluton to the followng utlty-maxmzaton roblem (UMP): The Lagrangean: ( x, x, x ) = + max U x, x, x x x x st.. x + x + x y x,
More informationLena Boneva and Oliver Linton. January 2017
Appendx to Staff Workng Paper No. 640 A dscrete choce model for large heterogeneous panels wth nteractve fxed effects wth an applcaton to the determnants of corporate bond ssuance Lena Boneva and Olver
More informationMathematical Economics MEMF e ME. Filomena Garcia. Topic 2 Calculus
Mathematcal Economcs MEMF e ME Flomena Garca Topc 2 Calculus Mathematcal Economcs - www.seg.utl.pt/~garca/economa_matematca . Unvarate Calculus Calculus Functons : X Y y ( gves or each element X one element
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #16 Scribe: Yannan Wang April 3, 2014
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #16 Scrbe: Yannan Wang Aprl 3, 014 1 Introducton The goal of our onlne learnng scenaro from last class s C comparng wth best expert and
More informationThe Feynman path integral
The Feynman path ntegral Aprl 3, 205 Hesenberg and Schrödnger pctures The Schrödnger wave functon places the tme dependence of a physcal system n the state, ψ, t, where the state s a vector n Hlbert space
More informationSolutions HW #2. minimize. Ax = b. Give the dual problem, and make the implicit equality constraints explicit. Solution.
Solutons HW #2 Dual of general LP. Fnd the dual functon of the LP mnmze subject to c T x Gx h Ax = b. Gve the dual problem, and make the mplct equalty constrants explct. Soluton. 1. The Lagrangan s L(x,
More informationCinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure
nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n
More informationComparative Advantage and Optimal Trade Taxes
Comparatve Advantage and Optmal Trade Taxes Arnaud Costnot (MIT), Dave Donaldson (MIT), Jonathan Vogel (Columba) and Iván Wernng (MIT) June 2014 Motvaton Two central questons... 1. Why do natons trade?
More informationThe Second Anti-Mathima on Game Theory
The Second Ant-Mathma on Game Theory Ath. Kehagas December 1 2006 1 Introducton In ths note we wll examne the noton of game equlbrum for three types of games 1. 2-player 2-acton zero-sum games 2. 2-player
More informationNormally, in one phase reservoir simulation we would deal with one of the following fluid systems:
TPG4160 Reservor Smulaton 2017 page 1 of 9 ONE-DIMENSIONAL, ONE-PHASE RESERVOIR SIMULATION Flud systems The term sngle phase apples to any system wth only one phase present n the reservor In some cases
More informationExternalities in wireless communication: A public goods solution approach to power allocation. by Shrutivandana Sharma
Externaltes n wreless communcaton: A publc goods soluton approach to power allocaton by Shrutvandana Sharma SI 786 Tuesday, Feb 2, 2006 Outlne Externaltes: Introducton Plannng wth externaltes Power allocaton:
More informationConjectures in Cournot Duopoly under Cost Uncertainty
Conjectures n Cournot Duopoly under Cost Uncertanty Suyeol Ryu and Iltae Km * Ths paper presents a Cournot duopoly model based on a condton when frms are facng cost uncertanty under rsk neutralty and rsk
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More information