ENERGY REGULATORY ECONOMICS

Size: px
Start display at page:

Download "ENERGY REGULATORY ECONOMICS"

Transcription

1 ENERGY REGULATORY ECONOMICS 1

2 CONTRACT THEORY 2

3 Mechanism Design CONTRACT THEORY - Social choice funcion : mapping from a vecor of characerisiscs o a feasible social sae θ Θ f A - A mechanism is a couple M=(M 1,,M I ) and a funcion g( ) such ha m=(m 1,,m I ) g A - E gc ( ) is a mapping from θ o m 3

4 CONTRACT THEORY Mechanism Design -A mechanism implemens a social choice funcion, for a cerain equilibrium concep, if: Θ 1 x xθ I f( ) A E gc ( ) g( ) M 1 x xm I - Two conceps of equilibrium (c): Dominan and Nash. 4

5 CONTRACT THEORY Mechanism Design - Mechanism: * Direc if M i =Θ i, i=1,,i * Revealing if θ E gc (θ), θ Θ * Implemened by revelaion if i is direc and g(θ)=f(θ), θ Θ 5

6 CONTRACT THEORY Mechanism Design - The Revelaion Principle: Le (g,m) be a mechanism ha implemens he social choice funcion f( ) for he dominan equilibrium concep. Then here exiss a direc mechanism (Ψ,Θ) ha implemens by revelaion f( ) in dominan equlibria 6

7 CONTRACT THEORY Principal-agen model. Adverse selecion example: - Perfec informaion: max ( i -c(q i )) θ i q i - i 0 7

8 CONTRACT THEORY - Complee informaion: f. o. c. q i =q i * c (q i* ) = θ i ( q 2 * >q 1* ) i* = θ i q i * 8

9 CONTRACT THEORY - Assymeric informaion: max {Π [ 1 -c(q 1 )]+(1-π)[ 2 -c(q 2 )]} 1,q 1, 2,q 2 subjec o: θ 1 q 1-1 θ 1 q 2-2 (IC 1 ) θ 2 q 2-2 θ 2 q 1-1 (IC 2 ) θ 1 q (IR 1 ) θ 2 q (IR 2 ) 9

10 CONTRACT THEORY - Assymeric informaion: f.o.c: 1 = θ 1 q = θ 2 (q 2 -q 1 ) (IR 1 binding) (IC 2 binding) q 2 q 1 q 2 = q 2 * q 1 < q 1 * 10

11 CONTRACT THEORY Common properies: The highes ype ges an efficien allocaion Each ype is indifferen beween his conrac and ha of he immediaely lower conrac (wih he excepion of he lowes ype) All ypes ge an informaional ren ha increases wih he ype (wih he excepion of he lowes ype) 11

12 CONTRACT THEORY Common properies: All ypes obain a subefficen allocaion (wih he excepion of he highes ype) The lowes ype obains a zero surplus 12

13 THE CANONICAL MODEL OF REGULATION 13

14 THE CANONICAL MODEL OF REGULATION Assumpions: 1.- Regulaion is subjec o adverse selecion and moral hazard 2.- Coss, producs and prices are verifiable. However, he regulaor can differeniae he differen cos componens 3.- The firm can refuse o produce if he regulaory conrac doesn guaranee a minimum expeced uiliy 14

15 THE CANONICAL MODEL OF REGULATION Assumpions: 4.- The regulaor can make moneary ransfers o he firm 5.- The firm and he regulaor are risk neural wih respec o income 6.- The firm only cares abou is income and effor ^ (U=-ϕ(e), = + R(q)-c( )) 7.- The regulaor faces a shadow cos of public funds (λ>0) 15

16 THE CANONICAL MODEL OF REGULATION Assumpions: 8.- The regulaor s objecive is o maximize social welfare (benevolen-regulaor assumpion) 9.- The regulaor designs he regulaory conrac 16

17 THE CANONICAL MODEL OF REGULATION W S θ s q R q λ EU = (,, ) ( ) (1 + )ˆ + EU = ˆ + R( q) C( β, e, q) ψ( e, s) = ψ( e, s) W= S( θ, s, q) + λrq ( ) (1 + λ)( C( β, e, q) ψ( e, s)) + λeu 17

18 THE CANONICAL MODEL OF REGULATION Expeced social welfare: W=S(θ,s,q) - R(q) - (1+λ) + EU Menu of linear conracs: S(θ,s,q)=S ^ ~ c=β -e + ε U= - ϕ(β-c) 18

19 THE CANONICAL MODEL OF REGULATION Menu of linear conracs: - Under complee informaion: ϕ (e)=1 ó e=e * =ϕ(e * ) ó U(β)=0 ( β) 19

20 THE CANONICAL MODEL OF REGULATION Menu of linear conracs: - Revelaion Principle (revealing direc mechanism: {(β), c(β)}): - Under assymeric informaion Max β β subjec o: { S ( 1 + )( β e + ϕ ( e)) λu ( β )} λ df( β ) U(β) = -ϕ (e(β)), β β Arg max ( % β ) c( % β )) { } % β U(β) 0, β 20

21 THE CANONICAL MODEL OF REGULATION Menu of Linear Conracs: - Under assymeric informaion f.o.c. ϕ ( e * ( β )) = 1 1 λ + λ F ( β ) f ( β ) ϕ (e * ( β )) U * ( β ) = β β ϕ ( e * ~ ( β ) d β 21

22 THE CANONICAL MODEL OF REGULATION Menu of linear conracs: - Transfer funcion: (β) = U * (β) + ϕ(e * (β)) = (β(c)) = T(c) (c,c a ) = a(c a ) - b(c a )(c - c a ) 22

23 THE CANONICAL MODEL OF REGULATION The dichoomy beween Pricing and Cos Reimbursemen Rules: W = S( q) + λ pk( q) qk (1 + λ)( C+ ψ( e)) λu subjec o k U = ψ ( E( β, C, q)) U 0-23

24 THE CANONICAL MODEL OF REGULATION The dichoomy beween Pricing and Cos Reimbursemen Rules: f.o.c. ' pk Ck λ 1 λf( β) ψ ( e) d Lk = = Ce + ( Eβ ) k = 1,..., n p 1 ˆ k + λη k (1 λ) f( β) + dqk λ F( β ) d ψ '( e) = Ce ψ '( e) Eβ 1 + λ f( β) de 24

25 THE CANONICAL MODEL OF REGULATION The dichoomy beween Pricing and Cos Reimbursemen Rules: C = c(β,e,q) can be re-wrien as C = c(ζ(β,e),q) - Pricing rule: Ramsey-Boieux - Cos rule: * Price-cap regulaion for he mos efficien firm * Cos-of-service regulaion for he leas efficien firm 25

26 PRICE REGULATION 26

27 PRICE REGULATION - Inroducion - Price level regulaion - Price srucure regulaion - Regulaion of elecriciy ransmission 27

28 PRICE REGULATION INTRODUCTION Hisory of he opimal prices: - Firs bes: marginal cos (70 s) - Second bes: Ramsey pricing (80 s) - Third bes: Revelaion Principle/ Laffon-Tirole (93) - Fourh bes: Theoreical models under pracical consrains 28

29 PRICE REGULATION INTRODUCTION Desirable properies of applied mechanisms: - Pareo superioriy - Efficiency improvemens Few niches of legal and naural monopolies. (e.g.:ransmission and disribuion of gas and elecriciy) 29

30 PRICE REGULATION INTRODUCTION Regulaion of monopolies is imporan since hey are verically relaed wih compeiive secors. Two basic conceps: -Pricelevel - Price srucure 30

31 REGULATION OF PRICE LEVEL Alernaives: - Cos-of-service regulaion - Price caps: adjusmen facors (RPI, X, ec.) - Yardsick regulaion - Profi sharing - Hybrid regulaion 31

32 REGULATION OF PRICE STRUCTURE Toal-cos disribuion Price bands Resriced flexibiliy - Tariff baske - Average revenue 32

33 REGULATION OF ELECTRICITY TRANSMISSION Types of weighs: Laspeyres chain Paasche Fixed Laspeyres Ideal weighs (Laffon-Tirole) Flexible (average revenue) 33

34 REGULATION OF PRICE STRUCTURE Dispues regarding consumer groups and he regulaed-firm compeiors. A non-consrained monopoly esablishes an efficien price srucure bu a an inefficien level Conracual prices mus coexis wih regulaed prices ogeher wih qualiy regulaion so as o avoid cross subsidies 34

35 REGULATION OF TRANSMISSION Objecives: - Incenives o reduce he disance beween he generaing plans and demanding ceners - Reliabiliy of he frequency and he volage of he sysem - Coordinaion of he generaing saions and provision of soluions in cases of emergency 35

36 Main Problems: REGULATION OF TRANSMISSION - Capaciy use (shor-run). - Opimal invesmen (long-run). Proposal o regulae price level: - Price cap - RPI-X; 0% X 5%. - Regulaory lag (5 years) - Cos of service during each five-year ariff revisions 36

37 REGULATION OF TRANSMISSION Proposal o regulae price srucure: - I considers congesion problems (shor-run) as well as capaciy problems (long-run). - Two-par ariff: Usage charge: i solves congesion problems. Capaciy charge: recovering of capial coss. Rebalancing beween charges: invesmen incenives Transmissions quaniies are used as 37

38 38 REGULATION OF TRANSMISSION Proposal o regulae price srucure: - Model (Vogelsang, 1999): subjec o: ), ( k q c N F q p max + = + + j w j j w i i i w j j j w i i i X F q p F q p ) 1 )( ( 1 1 δ δ k q ( ) N q p p F F w + 1 1

39 39 REGULATION OF TRANSMISSION Proposal o regulae price srucure: - f.o.c.: - Under chained Laspeyres weighs here is convergence o Ramsey prices w q q q c p p q = + µ ε µ = = 1 0 w q q q c p

40 REGULATION OF TRANSMISSION Proposal o regulae price srucure : - Principles: Efficien operaion of he energy marke Efficien invesmen in he sysem Sign-posing of locaional advanages in generaion and disribuion Asse coss recovery Simpliciy and ransparency Poliical feasibiliy 40

41 OTHER TOPICS 41

42 OTHER TOPICS - Verical Inegraion - Liberalizaion - Horizonal Srucure - Regional Srucure - Access-Price Regulaion - Qualiy and Environmenal Regulaion -Ownership 42

43 OTHER TOPICS Verically Inegraed Monopoly Naural Monopoly M Conesable Secor Consumers Marke 1 M Price Regulaion Marke 2 43

44 OTHER TOPICS Naural Monopoly Verical Separaion M Access-Price Regulaion Conesable Secor Consumers Marke 1 Ohers Price Regulaion Marke 2 44

45 OTHER TOPICS Verical Inegraion wih Liberalizaion Naural Monopoly Conesable Secor M M Price Regulaion Access Price Regulaion Ohers Consumers Marke 1 Marke 2 45

46 OTHER TOPICS Topics in Compeiion and Liberalizaion - Cream Skimming - Excess Enry - Compeiion for he Marke - Enry Barriers - Predaory Pricing - Enry Assisance 46

47 OTHER TOPICS Access Pricing: - Under verical separaion: access price is equal o he marginal cos of access (as long as here is a ransference) - Under verical inegraion: * Final price regulaion: access price is equal o he difference of he regulaed final price less he marginal cos in he conesable marke (ECPR: M s incremenal cos for allowing access in erms of los benefis) 47

48 OTHER TOPICS Access Pricing: - Under verical inegraion: * Non/regulaed final price: equal o he cos under verical separaion 48

Product differentiation

Product differentiation differeniaion Horizonal differeniaion Deparmen of Economics, Universiy of Oslo ECON480 Spring 010 Las modified: 010.0.16 The exen of he marke Differen producs or differeniaed varians of he same produc

More information

Macroeconomic Theory Ph.D. Qualifying Examination Fall 2005 ANSWER EACH PART IN A SEPARATE BLUE BOOK. PART ONE: ANSWER IN BOOK 1 WEIGHT 1/3

Macroeconomic Theory Ph.D. Qualifying Examination Fall 2005 ANSWER EACH PART IN A SEPARATE BLUE BOOK. PART ONE: ANSWER IN BOOK 1 WEIGHT 1/3 Macroeconomic Theory Ph.D. Qualifying Examinaion Fall 2005 Comprehensive Examinaion UCLA Dep. of Economics You have 4 hours o complee he exam. There are hree pars o he exam. Answer all pars. Each par has

More information

Hydropower Economics: An Overview

Hydropower Economics: An Overview ydropower Economics: An Overview Finn R Førsund Professor Emerius Universiy of Oslo * Slides prepared for ECON4925 - Resource Economics Ocober 5 2017 ydropower economics 1 Curriculum ydropower Economics:

More information

T. J. HOLMES AND T. J. KEHOE INTERNATIONAL TRADE AND PAYMENTS THEORY FALL 2011 EXAMINATION

T. J. HOLMES AND T. J. KEHOE INTERNATIONAL TRADE AND PAYMENTS THEORY FALL 2011 EXAMINATION ECON 841 T. J. HOLMES AND T. J. KEHOE INTERNATIONAL TRADE AND PAYMENTS THEORY FALL 211 EXAMINATION This exam has wo pars. Each par has wo quesions. Please answer one of he wo quesions in each par for a

More information

Economics 8105 Macroeconomic Theory Recitation 6

Economics 8105 Macroeconomic Theory Recitation 6 Economics 8105 Macroeconomic Theory Reciaion 6 Conor Ryan Ocober 11h, 2016 Ouline: Opimal Taxaion wih Governmen Invesmen 1 Governmen Expendiure in Producion In hese noes we will examine a model in which

More information

Economic Growth & Development: Part 4 Vertical Innovation Models. By Kiminori Matsuyama. Updated on , 11:01:54 AM

Economic Growth & Development: Part 4 Vertical Innovation Models. By Kiminori Matsuyama. Updated on , 11:01:54 AM Economic Growh & Developmen: Par 4 Verical Innovaion Models By Kiminori Masuyama Updaed on 20-04-4 :0:54 AM Page of 7 Inroducion In he previous models R&D develops producs ha are new ie imperfec subsiues

More information

Competitive and Cooperative Inventory Policies in a Two-Stage Supply-Chain

Competitive and Cooperative Inventory Policies in a Two-Stage Supply-Chain Compeiive and Cooperaive Invenory Policies in a Two-Sage Supply-Chain (G. P. Cachon and P. H. Zipkin) Presened by Shruivandana Sharma IOE 64, Supply Chain Managemen, Winer 2009 Universiy of Michigan, Ann

More information

Power System Transformation towards Renewables: An Evaluation of Regulatory Approaches for Network Expansion

Power System Transformation towards Renewables: An Evaluation of Regulatory Approaches for Network Expansion Power Sysem Transformaion owards Renewables: An Evaluaion of Regulaory Approaches for Nework Expansion J. Egerer, J. Rosellón, W-P. Schill DIW Berlin and CIDE BELEC 2013 Ocober 10h, 2013 Ouline The Model

More information

Lecture 8. Lecturer: Finn R. Førsund. Transmission 1

Lecture 8. Lecturer: Finn R. Førsund. Transmission 1 ECON 4930 Spring 011 Elecriciy Economics ecure 8 ecurer: Finn R. Førsund Transmission 1 A sysem ransmission nework Two nodes wih one line he simples case Convering variables o energy unis (kwh) The energy

More information

HOTELLING LOCATION MODEL

HOTELLING LOCATION MODEL HOTELLING LOCATION MODEL THE LINEAR CITY MODEL The Example of Choosing only Locaion wihou Price Compeiion Le a be he locaion of rm and b is he locaion of rm. Assume he linear ransporaion cos equal o d,

More information

LABOR MATCHING MODELS: BASIC DSGE IMPLEMENTATION APRIL 12, 2012

LABOR MATCHING MODELS: BASIC DSGE IMPLEMENTATION APRIL 12, 2012 LABOR MATCHING MODELS: BASIC DSGE IMPLEMENTATION APRIL 12, 2012 FIRM VACANCY-POSTING PROBLEM Dynamic firm profi-maimizaion problem ma 0 ( ) f Ξ v, n + 1 = 0 ( f y wn h g v ) Discoun facor beween ime 0

More information

Cooperative Ph.D. Program in School of Economic Sciences and Finance QUALIFYING EXAMINATION IN MACROECONOMICS. August 8, :45 a.m. to 1:00 p.m.

Cooperative Ph.D. Program in School of Economic Sciences and Finance QUALIFYING EXAMINATION IN MACROECONOMICS. August 8, :45 a.m. to 1:00 p.m. Cooperaive Ph.D. Program in School of Economic Sciences and Finance QUALIFYING EXAMINATION IN MACROECONOMICS Augus 8, 213 8:45 a.m. o 1: p.m. THERE ARE FIVE QUESTIONS ANSWER ANY FOUR OUT OF FIVE PROBLEMS.

More information

Policy regimes Theory

Policy regimes Theory Advanced Moneary Theory and Policy EPOS 2012/13 Policy regimes Theory Giovanni Di Barolomeo giovanni.dibarolomeo@uniroma1.i The moneary policy regime The simple model: x = - s (i - p e ) + x e + e D p

More information

Vehicle Arrival Models : Headway

Vehicle Arrival Models : Headway Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where

More information

Lecture Notes 3: Quantitative Analysis in DSGE Models: New Keynesian Model

Lecture Notes 3: Quantitative Analysis in DSGE Models: New Keynesian Model Lecure Noes 3: Quaniaive Analysis in DSGE Models: New Keynesian Model Zhiwei Xu, Email: xuzhiwei@sju.edu.cn The moneary policy plays lile role in he basic moneary model wihou price sickiness. We now urn

More information

MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 4, 2011 BUILDING THE EQUILIBRIUM. p = 1. Dixit-Stiglitz Model

MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 4, 2011 BUILDING THE EQUILIBRIUM. p = 1. Dixit-Stiglitz Model MONOPOLISTIC COMPETITION IN A DSGE MODEL: PART II OCTOBER 4, 211 Dixi-Sigliz Model BUILDING THE EQUILIBRIUM DS MODEL I or II Puing hings ogeher impose symmery across all i 1 pzf k( k, n) = r & 1 pzf n(

More information

Economics 6130 Cornell University Fall 2016 Macroeconomics, I - Part 2

Economics 6130 Cornell University Fall 2016 Macroeconomics, I - Part 2 Economics 6130 Cornell Universiy Fall 016 Macroeconomics, I - Par Problem Se # Soluions 1 Overlapping Generaions Consider he following OLG economy: -period lives. 1 commodiy per period, l = 1. Saionary

More information

Midterm Exam. Macroeconomic Theory (ECON 8105) Larry Jones. Fall September 27th, Question 1: (55 points)

Midterm Exam. Macroeconomic Theory (ECON 8105) Larry Jones. Fall September 27th, Question 1: (55 points) Quesion 1: (55 poins) Macroeconomic Theory (ECON 8105) Larry Jones Fall 2016 Miderm Exam Sepember 27h, 2016 Consider an economy in which he represenaive consumer lives forever. There is a good in each

More information

FINM 6900 Finance Theory

FINM 6900 Finance Theory FINM 6900 Finance Theory Universiy of Queensland Lecure Noe 4 The Lucas Model 1. Inroducion In his lecure we consider a simple endowmen economy in which an unspecified number of raional invesors rade asses

More information

Final Exam Advanced Macroeconomics I

Final Exam Advanced Macroeconomics I Advanced Macroeconomics I WS 00/ Final Exam Advanced Macroeconomics I February 8, 0 Quesion (5%) An economy produces oupu according o α α Y = K (AL) of which a fracion s is invesed. echnology A is exogenous

More information

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 6 SECTION 6.1: LIFE CYCLE CONSUMPTION AND WEALTH T 1. . Let ct. ) is a strictly concave function of c

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 6 SECTION 6.1: LIFE CYCLE CONSUMPTION AND WEALTH T 1. . Let ct. ) is a strictly concave function of c John Riley December 00 S O EVEN NUMBERED EXERCISES IN CHAPER 6 SECION 6: LIFE CYCLE CONSUMPION AND WEALH Eercise 6-: Opimal saving wih more han one commodiy A consumer has a period uiliy funcion δ u (

More information

Discussion Papers. Toward a Combined Merchant- Regulatory Mechanism for Electricity Transmission Expansion. William Hogan Juan Rosellón Ingo Vogelsang

Discussion Papers. Toward a Combined Merchant- Regulatory Mechanism for Electricity Transmission Expansion. William Hogan Juan Rosellón Ingo Vogelsang Deusches Insiu für Wirschafsforschung www.diw.de Discussion Papers 25 William Hogan Juan Rosellón Ingo Vogelsang Toward a Combined Merchan- Regulaory Mechanism for Elecriciy Transmission Expansion Berlin,

More information

Online Appendix to Solution Methods for Models with Rare Disasters

Online Appendix to Solution Methods for Models with Rare Disasters Online Appendix o Soluion Mehods for Models wih Rare Disasers Jesús Fernández-Villaverde and Oren Levinal In his Online Appendix, we presen he Euler condiions of he model, we develop he pricing Calvo block,

More information

Decomposing Value Added Growth Over Sectors into Explanatory Factors

Decomposing Value Added Growth Over Sectors into Explanatory Factors Business School Decomposing Value Added Growh Over Secors ino Explanaory Facors W. Erwin Diewer (UBC and UNSW Ausralia) and Kevin J. Fox (UNSW Ausralia) EMG Workshop UNSW 2 December 2016 Summary Decompose

More information

EE 315 Notes. Gürdal Arslan CLASS 1. (Sections ) What is a signal?

EE 315 Notes. Gürdal Arslan CLASS 1. (Sections ) What is a signal? EE 35 Noes Gürdal Arslan CLASS (Secions.-.2) Wha is a signal? In his class, a signal is some funcion of ime and i represens how some physical quaniy changes over some window of ime. Examples: velociy of

More information

Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims

Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,

More information

Reserves measures have an economic component eg. what could be extracted at current prices?

Reserves measures have an economic component eg. what could be extracted at current prices? 3.2 Non-renewable esources A. Are socks of non-renewable resources fixed? eserves measures have an economic componen eg. wha could be exraced a curren prices? - Locaion and quaniies of reserves of resources

More information

Final Exam. Tuesday, December hours

Final Exam. Tuesday, December hours San Francisco Sae Universiy Michael Bar ECON 560 Fall 03 Final Exam Tuesday, December 7 hours Name: Insrucions. This is closed book, closed noes exam.. No calculaors of any kind are allowed. 3. Show all

More information

Delivered versus Mill Nonlinear Pricing in Free Entry Markets

Delivered versus Mill Nonlinear Pricing in Free Entry Markets Delivered versus Mill Nonlinear Pricing in Free Enry Markes Sílvia Ferreira Jorge DEGEI - Universidade de Aveiro Faculdade de Economia, Universidade Nova de Lisboa sjorge@egi.ua.p Cesalina Pacheco Pires

More information

A Specification Test for Linear Dynamic Stochastic General Equilibrium Models

A Specification Test for Linear Dynamic Stochastic General Equilibrium Models Journal of Saisical and Economeric Mehods, vol.1, no.2, 2012, 65-70 ISSN: 2241-0384 (prin), 2241-0376 (online) Scienpress Ld, 2012 A Specificaion Tes for Linear Dynamic Sochasic General Equilibrium Models

More information

Incentives for Transmission Investment in Natural Gas and

Incentives for Transmission Investment in Natural Gas and Incenives for Transmission Invesmen in Naural Gas and Elecriciy i Neworks Theory and Roadmap Juan Rosellón CIDE and EE2-TU Dresden Naional Forum on Energy, Environmen and Climae Change Policy, Mexico Ciy,

More information

Explaining Total Factor Productivity. Ulrich Kohli University of Geneva December 2015

Explaining Total Factor Productivity. Ulrich Kohli University of Geneva December 2015 Explaining Toal Facor Produciviy Ulrich Kohli Universiy of Geneva December 2015 Needed: A Theory of Toal Facor Produciviy Edward C. Presco (1998) 2 1. Inroducion Toal Facor Produciviy (TFP) has become

More information

The Brock-Mirman Stochastic Growth Model

The Brock-Mirman Stochastic Growth Model c December 3, 208, Chrisopher D. Carroll BrockMirman The Brock-Mirman Sochasic Growh Model Brock and Mirman (972) provided he firs opimizing growh model wih unpredicable (sochasic) shocks. The social planner

More information

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms

More information

E β t log (C t ) + M t M t 1. = Y t + B t 1 P t. B t 0 (3) v t = P tc t M t Question 1. Find the FOC s for an optimum in the agent s problem.

E β t log (C t ) + M t M t 1. = Y t + B t 1 P t. B t 0 (3) v t = P tc t M t Question 1. Find the FOC s for an optimum in the agent s problem. Noes, M. Krause.. Problem Se 9: Exercise on FTPL Same model as in paper and lecure, only ha one-period govenmen bonds are replaced by consols, which are bonds ha pay one dollar forever. I has curren marke

More information

1 Answers to Final Exam, ECN 200E, Spring

1 Answers to Final Exam, ECN 200E, Spring 1 Answers o Final Exam, ECN 200E, Spring 2004 1. A good answer would include he following elemens: The equiy premium puzzle demonsraed ha wih sandard (i.e ime separable and consan relaive risk aversion)

More information

Solutions Problem Set 3 Macro II (14.452)

Solutions Problem Set 3 Macro II (14.452) Soluions Problem Se 3 Macro II (14.452) Francisco A. Gallego 04/27/2005 1 Q heory of invesmen in coninuous ime and no uncerainy Consider he in nie horizon model of a rm facing adjusmen coss o invesmen.

More information

CENTRALIZED VERSUS DECENTRALIZED PRODUCTION PLANNING IN SUPPLY CHAINS

CENTRALIZED VERSUS DECENTRALIZED PRODUCTION PLANNING IN SUPPLY CHAINS CENRALIZED VERSUS DECENRALIZED PRODUCION PLANNING IN SUPPLY CHAINS Georges SAHARIDIS* a, Yves DALLERY* a, Fikri KARAESMEN* b * a Ecole Cenrale Paris Deparmen of Indusial Engineering (LGI), +3343388, saharidis,dallery@lgi.ecp.fr

More information

Dynamic firm profit-maximization problem. max ( ( )) Total output sold in perfectlycompetitive

Dynamic firm profit-maximization problem. max ( ( )) Total output sold in perfectlycompetitive LABOR SEARCH MODELS: BASIC DSGE IMPLEMENTATION NOVEMBER 2, 200 FIRM VACANCY-POSTING PROBLEM Dynamic firm profi-maimizaion problem f f Ξ 0 y wn g v v, n + = 0 ma ( ( Discoun facor beween ime 0 and because

More information

Lecture Notes 5: Investment

Lecture Notes 5: Investment Lecure Noes 5: Invesmen Zhiwei Xu (xuzhiwei@sju.edu.cn) Invesmen decisions made by rms are one of he mos imporan behaviors in he economy. As he invesmen deermines how he capials accumulae along he ime,

More information

Different assumptions in the literature: Wages/prices set one period in advance and last for one period

Different assumptions in the literature: Wages/prices set one period in advance and last for one period Øisein Røisland, 5.3.7 Lecure 8: Moneary policy in New Keynesian models: Inroducing nominal rigidiies Differen assumpions in he lieraure: Wages/prices se one period in advance and las for one period Saggering

More information

ACE 562 Fall Lecture 4: Simple Linear Regression Model: Specification and Estimation. by Professor Scott H. Irwin

ACE 562 Fall Lecture 4: Simple Linear Regression Model: Specification and Estimation. by Professor Scott H. Irwin ACE 56 Fall 005 Lecure 4: Simple Linear Regression Model: Specificaion and Esimaion by Professor Sco H. Irwin Required Reading: Griffihs, Hill and Judge. "Simple Regression: Economic and Saisical Model

More information

Unit Commitment under Market Equilibrium Constraints

Unit Commitment under Market Equilibrium Constraints Uni Commimen under Marke Equilibrium Consrains Luce Brocorne 1 Fabio D Andreagiovanni 2 Jérôme De Boeck 3,1 Bernard Forz 3,1 1 INOCS, INRIA Lille Nord-Europe, France 2 Universié de Technologie de Compiègne,

More information

Lecture 20: Riccati Equations and Least Squares Feedback Control

Lecture 20: Riccati Equations and Least Squares Feedback Control 34-5 LINEAR SYSTEMS Lecure : Riccai Equaions and Leas Squares Feedback Conrol 5.6.4 Sae Feedback via Riccai Equaions A recursive approach in generaing he marix-valued funcion W ( ) equaion for i for he

More information

Problem Set #3: AK models

Problem Set #3: AK models Universiy of Warwick EC9A2 Advanced Macroeconomic Analysis Problem Se #3: AK models Jorge F. Chavez December 3, 2012 Problem 1 Consider a compeiive economy, in which he level of echnology, which is exernal

More information

2017 3rd International Conference on E-commerce and Contemporary Economic Development (ECED 2017) ISBN:

2017 3rd International Conference on E-commerce and Contemporary Economic Development (ECED 2017) ISBN: 7 3rd Inernaional Conference on E-commerce and Conemporary Economic Developmen (ECED 7) ISBN: 978--6595-446- Fuures Arbirage of Differen Varieies and based on he Coinegraion Which is under he Framework

More information

3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon

3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon 3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of

More information

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model Modal idenificaion of srucures from roving inpu daa by means of maximum likelihood esimaion of he sae space model J. Cara, J. Juan, E. Alarcón Absrac The usual way o perform a forced vibraion es is o fix

More information

Global Optimization for Scheduling Refinery Crude Oil Operations

Global Optimization for Scheduling Refinery Crude Oil Operations Global Opimizaion for Scheduling Refinery Crude Oil Operaions Ramkumar Karuppiah 1, Kevin C. Furman 2 and Ignacio E. Grossmann 1 (1) Deparmen of Chemical Engineering Carnegie Mellon Universiy (2) Corporae

More information

COMPETITIVE GROWTH MODEL

COMPETITIVE GROWTH MODEL COMPETITIVE GROWTH MODEL I Assumpions We are going o now solve he compeiive version of he opimal growh moel. Alhough he allocaions are he same as in he social planning problem, i will be useful o compare

More information

This document was generated at 1:04 PM, 09/10/13 Copyright 2013 Richard T. Woodward. 4. End points and transversality conditions AGEC

This document was generated at 1:04 PM, 09/10/13 Copyright 2013 Richard T. Woodward. 4. End points and transversality conditions AGEC his documen was generaed a 1:4 PM, 9/1/13 Copyrigh 213 Richard. Woodward 4. End poins and ransversaliy condiions AGEC 637-213 F z d Recall from Lecure 3 ha a ypical opimal conrol problem is o maimize (,,

More information

1. Consider a pure-exchange economy with stochastic endowments. The state of the economy

1. Consider a pure-exchange economy with stochastic endowments. The state of the economy Answer 4 of he following 5 quesions. 1. Consider a pure-exchange economy wih sochasic endowmens. The sae of he economy in period, 0,1,..., is he hisory of evens s ( s0, s1,..., s ). The iniial sae is given.

More information

Seminar 5 Sustainability

Seminar 5 Sustainability Seminar 5 Susainabiliy Soluions Quesion : Hyperbolic Discouning -. Suppose a faher inheris a family forune of 0 million NOK an he wans o use some of i for himself (o be precise, he share ) bu also o beques

More information

Short-Term Trading for a Wind Power Producer

Short-Term Trading for a Wind Power Producer Shor-Term Trading for a Wind Power Producer Anonio J. Conejo Juan M. Morales Juan Pérez Univ. Casilla La Mancha Spain 2010 1 2 Wha 1. Aim 2. Moivaion 3. Problem descripion 4. Mahemaical formulaion 5. Sochasic

More information

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing

Application of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology

More information

Applying Genetic Algorithms for Inventory Lot-Sizing Problem with Supplier Selection under Storage Capacity Constraints

Applying Genetic Algorithms for Inventory Lot-Sizing Problem with Supplier Selection under Storage Capacity Constraints IJCSI Inernaional Journal of Compuer Science Issues, Vol 9, Issue 1, No 1, January 2012 wwwijcsiorg 18 Applying Geneic Algorihms for Invenory Lo-Sizing Problem wih Supplier Selecion under Sorage Capaciy

More information

Scheduling of Crude Oil Movements at Refinery Front-end

Scheduling of Crude Oil Movements at Refinery Front-end Scheduling of Crude Oil Movemens a Refinery Fron-end Ramkumar Karuppiah and Ignacio Grossmann Carnegie Mellon Universiy ExxonMobil Case Sudy: Dr. Kevin Furman Enerprise-wide Opimizaion Projec March 15,

More information

Essential Microeconomics : OPTIMAL CONTROL 1. Consider the following class of optimization problems

Essential Microeconomics : OPTIMAL CONTROL 1. Consider the following class of optimization problems Essenial Microeconomics -- 6.5: OPIMAL CONROL Consider he following class of opimizaion problems Max{ U( k, x) + U+ ( k+ ) k+ k F( k, x)}. { x, k+ } = In he language of conrol heory, he vecor k is he vecor

More information

Energy Curtailment Regulation Impact on. Distributed Generation Integration

Energy Curtailment Regulation Impact on. Distributed Generation Integration Energy Curailmen Regulaion Impac on 1 Disribued Generaion Inegraion Yalin Huang and Lennar Söder Absrac This paper invesigaes he relaionship beween energy curailmen regulaion and invesmens in disribuion

More information

Simulating models with heterogeneous agents

Simulating models with heterogeneous agents Simulaing models wih heerogeneous agens Wouer J. Den Haan London School of Economics c by Wouer J. Den Haan Individual agen Subjec o employmen shocks (ε i, {0, 1}) Incomplee markes only way o save is hrough

More information

Sophisticated Monetary Policies. Andrew Atkeson. V.V. Chari. Patrick Kehoe

Sophisticated Monetary Policies. Andrew Atkeson. V.V. Chari. Patrick Kehoe Sophisicaed Moneary Policies Andrew Akeson UCLA V.V. Chari Universiy of Minnesoa Parick Kehoe Federal Reserve Bank of Minneapolis and Universiy of Minnesoa Barro, Lucas-Sokey Approach o Policy Solve Ramsey

More information

Documentos de Trabalho em Economia Working Papers in Economics

Documentos de Trabalho em Economia Working Papers in Economics Universidade de Aveiro Deparameno de Economia, Gesão e Engenharia Indusrial Documenos de Trabalho em Economia Working Papers in Economics Área Cienífica de Economia E/ nº / 004 Delivered versus Mill Nonlinear

More information

THE UNIVERSITY OF TEXAS AT AUSTIN McCombs School of Business

THE UNIVERSITY OF TEXAS AT AUSTIN McCombs School of Business THE UNIVERITY OF TEXA AT AUTIN McCombs chool of Business TA 7.5 Tom hively CLAICAL EAONAL DECOMPOITION - MULTIPLICATIVE MODEL Examples of easonaliy 8000 Quarerly sales for Wal-Mar for quarers a l e s 6000

More information

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,

More information

Monetary and Macroprudential Policies in a Currency Union

Monetary and Macroprudential Policies in a Currency Union Moneary and Macroprudenial Policies in a Currency Union PhD Candidae: Tsinikos Konsaninos Tor Vergaa Universiy, 10/12/2013 Supervisors: Prof. Pierpaolo Benigno LUISS, EIEF), Prof. Fabrizio Maesini Tor

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

Long term versus short term regulation: A model of investment behaviors. in the Telecommunications Sector

Long term versus short term regulation: A model of investment behaviors. in the Telecommunications Sector Long erm versus shor erm regulaion: A model of invesmen behaviors in he Telecommunicaions Secor David Flacher & Hugues Jennequin Paris 13 Universiy CEPN CNRS UMR 7115 France david@flacher.fr jennequin@seg.univ-paris13.fr

More information

Affine term structure models

Affine term structure models Affine erm srucure models A. Inro o Gaussian affine erm srucure models B. Esimaion by minimum chi square (Hamilon and Wu) C. Esimaion by OLS (Adrian, Moench, and Crump) D. Dynamic Nelson-Siegel model (Chrisensen,

More information

(1) (2) Differentiation of (1) and then substitution of (3) leads to. Therefore, we will simply consider the second-order linear system given by (4)

(1) (2) Differentiation of (1) and then substitution of (3) leads to. Therefore, we will simply consider the second-order linear system given by (4) Phase Plane Analysis of Linear Sysems Adaped from Applied Nonlinear Conrol by Sloine and Li The general form of a linear second-order sysem is a c b d From and b bc d a Differeniaion of and hen subsiuion

More information

Distance Between Two Ellipses in 3D

Distance Between Two Ellipses in 3D Disance Beween Two Ellipses in 3D David Eberly Magic Sofware 6006 Meadow Run Cour Chapel Hill, NC 27516 eberly@magic-sofware.com 1 Inroducion An ellipse in 3D is represened by a cener C, uni lengh axes

More information

Open loop vs Closed Loop. Example: Open Loop. Example: Feedforward Control. Advanced Control I

Open loop vs Closed Loop. Example: Open Loop. Example: Feedforward Control. Advanced Control I Open loop vs Closed Loop Advanced I Moor Command Movemen Overview Open Loop vs Closed Loop Some examples Useful Open Loop lers Dynamical sysems CPG (biologically inspired ), Force Fields Feedback conrol

More information

1 Consumption and Risky Assets

1 Consumption and Risky Assets Soluions o Problem Se 8 Econ 0A - nd Half - Fall 011 Prof David Romer, GSI: Vicoria Vanasco 1 Consumpion and Risky Asses Consumer's lifeime uiliy: U = u(c 1 )+E[u(c )] Income: Y 1 = Ȳ cerain and Y F (

More information

Sub Module 2.6. Measurement of transient temperature

Sub Module 2.6. Measurement of transient temperature Mechanical Measuremens Prof. S.P.Venkaeshan Sub Module 2.6 Measuremen of ransien emperaure Many processes of engineering relevance involve variaions wih respec o ime. The sysem properies like emperaure,

More information

Appendix 14.1 The optimal control problem and its solution using

Appendix 14.1 The optimal control problem and its solution using 1 Appendix 14.1 he opimal conrol problem and is soluion using he maximum principle NOE: Many occurrences of f, x, u, and in his file (in equaions or as whole words in ex) are purposefully in bold in order

More information

Dynamic Contracting under Adverse Selection and Renegotiation

Dynamic Contracting under Adverse Selection and Renegotiation Dynamic Conracing under Adverse Selecion and Renegoiaion Lucas Maesri FGV/EPGE January 30, 07 Absrac In a repeaed principal-agen model wih adverse selecion and renegoiaion, a monopolis o ers long-erm conracs

More information

This document was generated at 7:34 PM, 07/27/09 Copyright 2009 Richard T. Woodward

This document was generated at 7:34 PM, 07/27/09 Copyright 2009 Richard T. Woodward his documen was generaed a 7:34 PM, 07/27/09 Copyrigh 2009 Richard. Woodward 15. Bang-bang and mos rapid approach problems AGEC 637 - Summer 2009 here are some problems for which he opimal pah does no

More information

Lars Nesheim. 17 January Last lecture solved the consumer choice problem.

Lars Nesheim. 17 January Last lecture solved the consumer choice problem. Lecure 4 Locaional Equilibrium Coninued Lars Nesheim 17 January 28 1 Inroducory remarks Las lecure solved he consumer choice problem. Compued condiional demand funcions: C (I x; p; r (x)) and x; p; r (x))

More information

Robust estimation based on the first- and third-moment restrictions of the power transformation model

Robust estimation based on the first- and third-moment restrictions of the power transformation model h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,

More information

OBJECTIVES OF TIME SERIES ANALYSIS

OBJECTIVES OF TIME SERIES ANALYSIS OBJECTIVES OF TIME SERIES ANALYSIS Undersanding he dynamic or imedependen srucure of he observaions of a single series (univariae analysis) Forecasing of fuure observaions Asceraining he leading, lagging

More information

Macroeconomics Qualifying Examination

Macroeconomics Qualifying Examination Macroeconomics Qualifying Examinaion January 205 Deparmen of Economics UNC Chapel Hill Insrucions: This examinaion consiss of four quesions. Answer all quesions. If you believe a quesion is ambiguously

More information

t is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t...

t is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t... Mah 228- Fri Mar 24 5.6 Marix exponenials and linear sysems: The analogy beween firs order sysems of linear differenial equaions (Chaper 5) and scalar linear differenial equaions (Chaper ) is much sronger

More information

BU Macro BU Macro Fall 2008, Lecture 4

BU Macro BU Macro Fall 2008, Lecture 4 Dynamic Programming BU Macro 2008 Lecure 4 1 Ouline 1. Cerainy opimizaion problem used o illusrae: a. Resricions on exogenous variables b. Value funcion c. Policy funcion d. The Bellman equaion and an

More information

Implementing high-powered contracts to motivate intertemporal effort supply

Implementing high-powered contracts to motivate intertemporal effort supply RAND Journal of Economics Vol. 0, No., Summer 009 pp. 96 6 Implemening high-powered conracs o moivae ineremporal effor supply Leon Yang Chu and David E.M. Sappingon We characerize he opimal conrac beween

More information

Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k

Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,

More information

The Goals of his Research To undersand financial crises wih a model of muliple seady sae equilibria To undersand he role of fiscal policy in resoring

The Goals of his Research To undersand financial crises wih a model of muliple seady sae equilibria To undersand he role of fiscal policy in resoring Fiscal Policy Can Reduce Unemploymen: Bu There is a Beer Alernaive Federal Reserve Bank of Alana January 9 h 2010 Roger E. A. Farmer Deparmen of Economics UCLA 1 The Goals of his Research To undersand

More information

An introduction to the theory of SDDP algorithm

An introduction to the theory of SDDP algorithm An inroducion o he heory of SDDP algorihm V. Leclère (ENPC) Augus 1, 2014 V. Leclère Inroducion o SDDP Augus 1, 2014 1 / 21 Inroducion Large scale sochasic problem are hard o solve. Two ways of aacking

More information

Lecture Notes 2. The Hilbert Space Approach to Time Series

Lecture Notes 2. The Hilbert Space Approach to Time Series Time Series Seven N. Durlauf Universiy of Wisconsin. Basic ideas Lecure Noes. The Hilber Space Approach o Time Series The Hilber space framework provides a very powerful language for discussing he relaionship

More information

I. Introduction to place/transition nets. Place/Transition Nets I. Example: a vending machine. Example: a vending machine

I. Introduction to place/transition nets. Place/Transition Nets I. Example: a vending machine. Example: a vending machine Inroducory Tuorial I. Inroducion o place/ransiion nes Place/Transiion Nes I Prepared by: Jörg Desel, Caholic Universiy in Eichsä and Karsen Schmid, Humbold-Universiä zu Berlin Speaker: Wolfgang Reisig,

More information

Probabilistic Robotics

Probabilistic Robotics Probabilisic Roboics Bayes Filer Implemenaions Gaussian filers Bayes Filer Reminder Predicion bel p u bel d Correcion bel η p z bel Gaussians : ~ π e p N p - Univariae / / : ~ μ μ μ e p Ν p d π Mulivariae

More information

Zürich. ETH Master Course: L Autonomous Mobile Robots Localization II

Zürich. ETH Master Course: L Autonomous Mobile Robots Localization II Roland Siegwar Margaria Chli Paul Furgale Marco Huer Marin Rufli Davide Scaramuzza ETH Maser Course: 151-0854-00L Auonomous Mobile Robos Localizaion II ACT and SEE For all do, (predicion updae / ACT),

More information

Stochastic Perishable Inventory Systems: Dual-Balancing and Look-Ahead Approaches

Stochastic Perishable Inventory Systems: Dual-Balancing and Look-Ahead Approaches Sochasic Perishable Invenory Sysems: Dual-Balancing and Look-Ahead Approaches by Yuhe Diao A hesis presened o he Universiy Of Waerloo in fulfilmen of he hesis requiremen for he degree of Maser of Applied

More information

Learning a Class from Examples. Training set X. Class C 1. Class C of a family car. Output: Input representation: x 1 : price, x 2 : engine power

Learning a Class from Examples. Training set X. Class C 1. Class C of a family car. Output: Input representation: x 1 : price, x 2 : engine power Alpaydin Chaper, Michell Chaper 7 Alpaydin slides are in urquoise. Ehem Alpaydin, copyrigh: The MIT Press, 010. alpaydin@boun.edu.r hp://www.cmpe.boun.edu.r/ ehem/imle All oher slides are based on Michell.

More information

CHAPTER 2: Mathematics for Microeconomics

CHAPTER 2: Mathematics for Microeconomics CHAPTER : Mahemaics for Microeconomics The problems in his chaper are primarily mahemaical. They are inended o give sudens some pracice wih he conceps inroduced in Chaper, bu he problems in hemselves offer

More information

Moral Hazard, Social Well-being and Tropical Deforestation

Moral Hazard, Social Well-being and Tropical Deforestation Journal of Environmen and Ecology ISSN 57-69 3, Vol. 4, No. Moral Hazard, Social Well-being and Tropical Deforesaion Eienne Bienvenu Akono Faculy of Economics and Applied Managemen Universiy of Douala,

More information

Examples of Dynamic Programming Problems

Examples of Dynamic Programming Problems M.I.T. 5.450-Fall 00 Sloan School of Managemen Professor Leonid Kogan Examples of Dynamic Programming Problems Problem A given quaniy X of a single resource is o be allocaed opimally among N producion

More information

( ) (, ) F K L = F, Y K N N N N. 8. Economic growth 8.1. Production function: Capital as production factor

( ) (, ) F K L = F, Y K N N N N. 8. Economic growth 8.1. Production function: Capital as production factor 8. Economic growh 8.. Producion funcion: Capial as producion facor Y = α N Y (, ) = F K N Diminishing marginal produciviy of capial and labor: (, ) F K L F K 2 ( K, L) K 2 (, ) F K L F L 2 ( K, L) L 2

More information

A Dynamic Model of Economic Fluctuations

A Dynamic Model of Economic Fluctuations CHAPTER 15 A Dynamic Model of Economic Flucuaions Modified for ECON 2204 by Bob Murphy 2016 Worh Publishers, all righs reserved IN THIS CHAPTER, OU WILL LEARN: how o incorporae dynamics ino he AD-AS model

More information

O Q L N. Discrete-Time Stochastic Dynamic Programming. I. Notation and basic assumptions. ε t : a px1 random vector of disturbances at time t.

O Q L N. Discrete-Time Stochastic Dynamic Programming. I. Notation and basic assumptions. ε t : a px1 random vector of disturbances at time t. Econ. 5b Spring 999 C. Sims Discree-Time Sochasic Dynamic Programming 995, 996 by Chrisopher Sims. This maerial may be freely reproduced for educaional and research purposes, so long as i is no alered,

More information

1 Price Indexation and In ation Inertia

1 Price Indexation and In ation Inertia Lecures on Moneary Policy, In aion and he Business Cycle Moneary Policy Design: Exensions [0/05 Preliminary and Incomplee/Do No Circulae] Jordi Galí Price Indexaion and In aion Ineria. In aion Dynamics

More information

INCENTIVE COMPATIBILITY AND MECHANISM DESIGN

INCENTIVE COMPATIBILITY AND MECHANISM DESIGN Essenial Microeconomics -- INCENTIVE COMPATIBILITY AND MECHANISM DESIGN Signaling games 2 Incenive Compaibiliy 7 Spence s example: Educaional signaling 9 Single Crossing Propery Mechanism Design 7 Local

More information