LectureNotesManuelli

LectureNotesManuelli - Notes on Discrete Time Economic...

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Notes on Discrete Time Economic Models: The Growth Model Rody Manuelli Department of Economics. University of Wisconsin-Madison August 8, 2007
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ii
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Contents Introduction vii 1 Basic Results in Dynamic Optimization 1 1 .1 Con cav i tyandOp t im i za t ion. .................... 1 1 .2 Op t i t ionSub j e c tt oCon s t ra in t s................ 2 1 .3 ATw oP e r iodM od e l......................... 4 1 .4 AnEx t en s iono fth eKuhn -T u ck e rTh eo r em . ........... 8 2 The Basic Growth Model: Steady States 15 2 .1 Th eBa s i cG row thM e l ...................... 15 2 .2 Th eP lann e r sP rob l em. ....................... 16 2 .3 S t eadyS t a t eAna ly s i s ........................ 19 3T h eB a s i r o w t hM o d e l :D y n am i c s 2 7 3 .1 G loba lDynam i c s........................... 27 3.1.1 The E f e c t so fP e rman tSho s.............. 36 3.1.2 The E f e c t fT empo rySho 37 3 .2 Lo ca i c s............................ 48 3 .3 App l i t ion s.............................. 49 3 .3 s t an tSav ingRa t e s.................... 3 .2 P opu la t ionG thandT e chn i lChang e......... 4 Competitive Equilibrium 53 4 .1 Ba s i cR e su l t s ............................. 53 4.2 Taxes and De f c i t s .......................... 68 4 .3 Th eS t ru c tu r axa t :S t ta t eImp l i t s ...... 75 4 s i cS t t s i s................. 77 4 .2 Chang ingth eT axRa t eonC ap i t a lIn com e ........ 79 4 .3 AD ig r e s s :Th eU s e rCo s to fC i t a l .......... 81 4 .4 Chang t eonL abo rIn c om e ......... 82 4 .5 D r e s s :P a r t ia lEqu i l ib r iumAna s i s.......... 83 4 .6 Ind iv idua landCo rpo t ax a t ............ 87 4.3.7 A Balanced Budget (Revenue Neutral) Change in Tax Rates 93 4 .8 T t ionandHum anCap i t a l................ 97 iii
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iv CONTENTS 4 .4 H e t e rog en e i ty. ............................ 101 4 .4 .1 Th eD i s t r ibu t iono fInd iv idua lCon sump t ion . ...... 104 4 .2 Th eT im eP a tho fCon t ionIn equa l i ty . ....... 107
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Preface These notes were originally developed as part of the f rst year Macroeconomic Theory course at the University of Wisconsin. Several generations of students deserve credit for f nding numerous errors, and pointing alternative ways of discussing and presenting the material. They deserve recognition. The last iteration has bene f tted from detailed comments by Nick Mader. v
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vi PREFACE
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Introduction The purpose of these notes is to brie f y present some results from dynamic optimization as they apply to standard exogenous growth models. In addition, they also describe some basic techniques that can be used to study the dynamics of these models. The main application is the standard growth model. This basic model is used to study a variety of issues, ranging from population growth, the impact of new technologies on income distribution, and the e f ects of alternative tax and spending policies. The notes are designed so that the exercises are an integral part of them (even though no answers are supplied at this time). It is suggested that the reader should try to work through as many of these exercises as possible. vii
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viii INTRODUCTION
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Chapter 1 Basic Results in Dynamic Optimization This section presents —with no proofs— some elementary results in dynamic opti- mization. The objective is to provide a brief overview of the basic mathematical techniques necessary to analyze dynamic models. Even though these tools will su ce to follow the arguments in these notes, they are not a good substitute for the formal study of dynamic optimization.
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This note was uploaded on 01/18/2012 for the course ECON 101 taught by Professor Bansak during the Summer '07 term at San Diego State.

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LectureNotesManuelli - Notes on Discrete Time Economic...

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