Advanced Macroeconomics

Size: px
Start display at page:

Download "Advanced Macroeconomics"

Transcription

1 Advanced Macroeconomics Endogenous Growth Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 1 / 18

2 Introduction The Solow and Ramsey models are exogenous growth models: Long-run growth (of output per capita) not possible without technological progress Technological progress governed by an exogenous process (not explained by the model) Two generations of endogenous growth models: 1st: Long-run growth without technological progress 2nd: Endogenous technological change Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 2 / 18

3 AK model - basic setup Production function: Y t = F (K t ) = AK t where: A > 0 is a constant (i.e. there is no technological progress, g = 0) Production function in intensive form (per capita): y t = f (k t ) = Ak t where: y t = Yt L t, k t = Kt L t Production function is then not neoclassical: F K = f (k) = A Otherwise identical to the Ramsey model Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 3 / 18

4 Equilibrium dynamics The equilibrium dynamics of the model at any time t can be characterized by 3 equations (compare to the Ramsey model): ( ct+1 ) θ = β(a + 1 δ) (1) k t+1 k t c t = A + 1 δ 1 c t 1 + n 1 + n k t (2) ( ) 1 + n t = 0 A + 1 δ (3) lim t k t+1 Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 4 / 18

5 Two technical assumptions Positive consumption growth requires: A > 1 β 1 + δ (A.1) Developing the condition for lifetime utility to be bounded: From (1): c t = [β (A + 1 δ)] t θ c 0 = (1 + γ c ) t c 0 (4) where γ c = [β (A + 1 δ)] 1 θ 1 is the growth rate of c so the lifetime utility becomes: U 0 = B 0 t=0 1 θ = L 0c 1 θ [ 0 β(1 + n)(1 + γc ) 1 θ] t 1 θ β t c1 θ t which means that U 0 is bounded if t=0 β(1 + n)(1 + γ c ) 1 θ < 1 (A.2) Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 5 / 18

6 Initial consumption level Capital accumulation using (4): k t+1 = A + 1 δ k t c n 1 + n (1 + γ c) t (5) Equation (5) is a first-order difference equation, which can be solved by iteration to yield: ( ) k t = a t k 0 c 0 1 ( 1+γc a ) t (6) 1 + n a (1 + γ c ) where a = A+1 δ 1+n Plugging (6) into the transversality condition (3) and using assumption (A.2) yields an explicit formula for c 0 given k 0 : c 0 = (1 + n)(a (1 + γ c ))k 0 (7) Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 6 / 18

7 Capital dynamics and the savings rate Substituting for c 0 from (7) into (6) gives: k t = (1 + γ c ) t k 0 (8) Conclusions: Equations (4), (8) and (7) give the full solution of the model for any given k 0 Consumption, capital (and hence output) per capita grow at the same rate all the time: c t+1 = k t+1 = y t+1 = [β (A + 1 δ)] 1 θ c t k t y t Hence, the savings rate is constant and equal to: s = (1 + n)β 1 θ (A + 1 δ) 1 θ A 1 + δ (9) Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 7 / 18

8 Sustained growth via capital accumulation Capital accumulation graphically: k t+1 = (1 + γ c )k t k t+1 45 o k 0 k t Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 8 / 18

9 The role of policy Long-run growth with taxes (see the Ramsey model for derivations) c t+1 = y [ t+1 = β 1 + τ ] 1 i(1 δ) + (1 τ k )(1 τ f )(A δ) θ c t y t (1 + τ i ) Changes in taxes have a permanent effect on the growth rate of output per capita (in the Ramsey model only the long-run level of output is permanently affected, the effect on the growth rate is only transitory) (10) Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 9 / 18

10 Adding human capital I Problems with the standard AK model Assuming that only physical capital matters for production seems unrealistic It implies that the share of capital in national income should be 1 (since wages, as the marginal product of labour, are 0) Let us instead assume that there are two inputs to the production function: physical capital K t and human capital H t : Y t = F (K t, H t ) where F exhibits all standard neoclassical properties Constant returns to scale allow us to write alternatively: Y t = K t f (H t /K t ) where f exhibits all properties of a neoclassical production function in itensive form Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 10 / 18

11 Adding human capital II An important difference to the Solow or Ramsey model: both physical and human capital are subject to accumulation: K t+1 = (1 δ K )K t + I K,t H t+1 = (1 δ H )H t + I H,t Output can be used on a one-for-one basis for consumption C t, investment in physical capital I K,t or investment in human capital I H,t : Y t = C t + I K,t + I H,t Firms maximize profits and factor markets are competitive: F K t = f (H t /K t ) H t /K t f (H t /K t ) = R K,t F H t = f (H t /K t ) = R H,t Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 11 / 18

12 Adding human capital III Optimality implies that the rates of return the households earn on both types of capital must be the same: or equivalently: R K,t δ K = R H,t δ H f (H t /K t ) (H t /K t + 1)f (H t /K t ) = δ K δ H which determines a unique, constant value of H/K at all times Conclusions: We get a model with essentially the same dynamics as the standard AK model (think about f (H/K) = A, where A is a constant) Important difference: it generates stable factor distribution of income, with a significant fraction accruing to labour Important observation: there are decreasing returns to accumulation of each factor (physical and human capital) but constant returns to accumulation of broadly defined capital - hence endogenous growth Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 12 / 18

13 1st generation endogenous growth models - summary Long-run growth possible even without technological progress The engine of growth: capital accumulation not facing decreasing returns (unlike in the Solow or Ramsey models) Consumption and output growth rates are constant; in particular, they do not depend on the initial capital level; hence: There is no transitional dynamics in the model It does not imply conditional nor unconditional convergence Savings rate is constant, but not exogenous as in the Solow model As in the Ramsey model, the competitive equilibrium (without distortionary taxation) is Pareto optimal Changes in preferences or policy parameters can have a permanent effect on the economy s growth rate Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 13 / 18

14 2nd generation endogenous growth models - preliminaries Basic idea: technological change is costly (requires R&D) and results from innovations driven by profit motives Nonrivalry of ideas underlying technology (Romer, 1986) Problems with the classical assumptions: Standard replication argument implies that the production function exhibits constant returns to scale in capital and labour, but increasig returns to scale in capital, labour and technology Euler s theorem and perfect competition imply that the factor payments exhaust the output, so that each firm s profit equals zero at every time: no funds to finance innovation It follows that: Imperfect competition on the goods market necessary Excludability (at least partial) of ideas needed, otherwise making improvements to technology would not be profitable Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 14 / 18

15 R&D-based growth model - a sketch A fully-fledged R&D-based growth model requires a detailed modelling of production and innovation sectors, here we only sketch the main concepts Final output production function: Y t = F (K t, A t L Y,t ) (11) where L Y,t is labour input used in the goods production sector Knowledge production function (deterministic for simplicity): A t+1 A t = BL A,t A φ t (12) where L A,t is labour input used in the R&D sector Assume for simplicity that the division of labour between the two sectors is constant: L A,t = a L L t L Y,t = (1 a L )L t where 0 < a L < 1 is an exogenous parameter Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 15 / 18

16 R&D-based growth model - dynamics I Technological change dynamics: γ A,t+1 = A t+1 A t A t = BL A,t A φ 1 t (13) Romer (1990): φ = 1 Equation (13) becomes: γ A,t+1 = BL A,t The rate of technological progress depends positively on population (larger communities should grow faster: scale effects ) Kremer (1993): this picture fits the human history (since 1 million B.C.); most researchers find this result unattractive With growing population, technological progress should accelerate - at odds with the data Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 16 / 18

17 R&D-based growth model - dynamics II Jones (1995): φ < 1 Equation (13) implies: γ A,t+1 = Ba LL t A φ 1 t γ A,t Ba L L t 1 A φ 1 = (1 + n)(1 + γ A,t ) φ 1 t 1 The unique positive value of γ A,t such that γ A,t is constant: γ A = (1 + n) 1 1 φ 1 Long-run growth possible only if population is growing No scale effects : the rate of growth does not depend on the size of population (nor its proportion engaged in R&D) There are scale effects in levels: the higher L t (for given a L ), the higher the level of technology (from (13)): A t+1 = A t + Ba L L t A φ t and so the higher output per capita Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 17 / 18

18 2nd generation endogenous growth models - summary Technological progress endogenous and depends on the amount of resources engaged in R&D Their micro-foundations (not worked out in this course) imply that the decentralized equilibrium does not coincide with social planner s choices and so is not Pareto optimal The amount of resources spent on research usually too small: researchers do not internalize positive effects of their inventions on productivity of future research Long-run properties critically depend on the knowledge production function: knife-edge assumptions needed for sustained growth with constant population Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 18 / 18

Advanced Macroeconomics

Advanced Macroeconomics Advanced Macroeconomics The Ramsey Model Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 30 Introduction Authors: Frank Ramsey (1928), David Cass (1965) and Tjalling

More information

Advanced Macroeconomics

Advanced Macroeconomics Advanced Macroeconomics The Ramsey Model Micha l Brzoza-Brzezina/Marcin Kolasa Warsaw School of Economics Micha l Brzoza-Brzezina/Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 47 Introduction Authors:

More information

Economic Growth: Lecture 9, Neoclassical Endogenous Growth

Economic Growth: Lecture 9, Neoclassical Endogenous Growth 14.452 Economic Growth: Lecture 9, Neoclassical Endogenous Growth Daron Acemoglu MIT November 28, 2017. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 28, 2017. 1 / 41 First-Generation Models

More information

The Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013)

The Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013) The Ramsey Model (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 213) 1 Introduction The Ramsey model (or neoclassical growth model) is one of the prototype models in dynamic macroeconomics.

More information

Endogenous Growth. Lecture 17 & 18. Topics in Macroeconomics. December 8 & 9, 2008

Endogenous Growth. Lecture 17 & 18. Topics in Macroeconomics. December 8 & 9, 2008 Review: Solow Model Review: Ramsey Model Endogenous Growth Lecture 17 & 18 Topics in Macroeconomics December 8 & 9, 2008 Lectures 17 & 18 1/29 Topics in Macroeconomics Outline Review: Solow Model Review:

More information

Permanent Income Hypothesis Intro to the Ramsey Model

Permanent Income Hypothesis Intro to the Ramsey Model Consumption and Savings Permanent Income Hypothesis Intro to the Ramsey Model Lecture 10 Topics in Macroeconomics November 6, 2007 Lecture 10 1/18 Topics in Macroeconomics Consumption and Savings Outline

More information

DEPARTMENT OF ECONOMICS Fall 2015 P. Gourinchas/D. Romer MIDTERM EXAM

DEPARTMENT OF ECONOMICS Fall 2015 P. Gourinchas/D. Romer MIDTERM EXAM UNIVERSITY OF CALIFORNIA Economics 202A DEPARTMENT OF ECONOMICS Fall 2015 P. Gourinchas/D. Romer MIDTERM EXAM The exam consists of two parts. There are 85 points total. Part I has 18 points and Part II

More information

Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PS 5, preliminary version

Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PS 5, preliminary version Macroeconomics I, UPF Professor ntonio Ciccone SOUTIONS PS 5, preliminary version 1 The Solow K model with transitional dynamics Consider the following Solow economy: production is determined by Y F (K,

More information

Endogenous Growth: AK Model

Endogenous Growth: AK Model Endogenous Growth: AK Model Prof. Lutz Hendricks Econ720 October 24, 2017 1 / 35 Endogenous Growth Why do countries grow? A question with large welfare consequences. We need models where growth is endogenous.

More information

New Notes on the Solow Growth Model

New Notes on the Solow Growth Model New Notes on the Solow Growth Model Roberto Chang September 2009 1 The Model The firstingredientofadynamicmodelisthedescriptionofthetimehorizon. In the original Solow model, time is continuous and the

More information

Chapter 3 Task 1-4. Growth and Innovation Fridtjof Zimmermann

Chapter 3 Task 1-4. Growth and Innovation Fridtjof Zimmermann Chapter 3 Task 1-4 Growth and Innovation Fridtjof Zimmermann Recept on how to derive the Euler-Equation (Keynes-Ramsey-Rule) 1. Construct the Hamiltonian Equation (Lagrange) H c, k, t, μ = U + μ(side Condition)

More information

A simple macro dynamic model with endogenous saving rate: the representative agent model

A simple macro dynamic model with endogenous saving rate: the representative agent model A simple macro dynamic model with endogenous saving rate: the representative agent model Virginia Sánchez-Marcos Macroeconomics, MIE-UNICAN Macroeconomics (MIE-UNICAN) A simple macro dynamic model with

More information

problem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming

problem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming 1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves

More information

Assumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t )

Assumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t ) 6. Economic growth Let us recall the main facts on growth examined in the first chapter and add some additional ones. (1) Real output (per-worker) roughly grows at a constant rate (i.e. labor productivity

More information

Dynamic (Stochastic) General Equilibrium and Growth

Dynamic (Stochastic) General Equilibrium and Growth Dynamic (Stochastic) General Equilibrium and Growth Martin Ellison Nuffi eld College Michaelmas Term 2018 Martin Ellison (Nuffi eld) D(S)GE and Growth Michaelmas Term 2018 1 / 43 Macroeconomics is Dynamic

More information

Econ 204A: Section 3

Econ 204A: Section 3 Econ 204A: Section 3 Ryan Sherrard University of California, Santa Barbara 18 October 2016 Sherrard (UCSB) Section 3 18 October 2016 1 / 19 Notes on Problem Set 2 Total Derivative Review sf (k ) = (δ +

More information

General motivation behind the augmented Solow model

General motivation behind the augmented Solow model General motivation behind the augmented Solow model Empirical analysis suggests that the elasticity of output Y with respect to capital implied by the Solow model (α 0.3) is too low to reconcile the model

More information

Neoclassical Models of Endogenous Growth

Neoclassical Models of Endogenous Growth Neoclassical Models of Endogenous Growth October 2007 () Endogenous Growth October 2007 1 / 20 Motivation What are the determinants of long run growth? Growth in the "e ectiveness of labour" should depend

More information

Lecture 15. Dynamic Stochastic General Equilibrium Model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017

Lecture 15. Dynamic Stochastic General Equilibrium Model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017 Lecture 15 Dynamic Stochastic General Equilibrium Model Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents

More information

1. Money in the utility function (start)

1. Money in the utility function (start) Monetary Economics: Macro Aspects, 1/3 2012 Henrik Jensen Department of Economics University of Copenhagen 1. Money in the utility function (start) a. The basic money-in-the-utility function model b. Optimal

More information

Lecture notes on modern growth theory

Lecture notes on modern growth theory Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic

More information

HOMEWORK #3 This homework assignment is due at NOON on Friday, November 17 in Marnix Amand s mailbox.

HOMEWORK #3 This homework assignment is due at NOON on Friday, November 17 in Marnix Amand s mailbox. Econ 50a second half) Yale University Fall 2006 Prof. Tony Smith HOMEWORK #3 This homework assignment is due at NOON on Friday, November 7 in Marnix Amand s mailbox.. This problem introduces wealth inequality

More information

Toulouse School of Economics, M2 Macroeconomics 1 Professor Franck Portier. Exam Solution

Toulouse School of Economics, M2 Macroeconomics 1 Professor Franck Portier. Exam Solution Toulouse School of Economics, 2013-2014 M2 Macroeconomics 1 Professor Franck Portier Exam Solution This is a 3 hours exam. Class slides and any handwritten material are allowed. You must write legibly.

More information

Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany

Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model Burkhard Heer University of Augsburg, Germany October 3, 2018 Contents I 1 Central Planner 2 3 B. Heer c Public Economics: Chapter

More information

One-Sector Models of Endogenous Growth. Instructor: Dmytro Hryshko

One-Sector Models of Endogenous Growth. Instructor: Dmytro Hryshko One-Sector Models of Endogenous Growth Instructor: Dmytro Hryshko 1 Mid-1980s: dissatisfaction with exogenously driven explanations of long-run productivity growth. 2 It led to construction of models in

More information

004: Macroeconomic Theory

004: Macroeconomic Theory 004: Macroeconomic Theory Lecture 22 Mausumi Das Lecture Notes, DSE November 11, 2014 Das (Lecture Notes, DSE) Macro November 11, 2014 1 / 12 AK Production Technology: First Step Towards Endogenous Growth?

More information

u(c t, x t+1 ) = c α t + x α t+1

u(c t, x t+1 ) = c α t + x α t+1 Review Questions: Overlapping Generations Econ720. Fall 2017. Prof. Lutz Hendricks 1 A Savings Function Consider the standard two-period household problem. The household receives a wage w t when young

More information

14.452: Introduction to Economic Growth Problem Set 4

14.452: Introduction to Economic Growth Problem Set 4 14.452: Introduction to Economic Growth Problem Set 4 Daron Acemoglu Due date: December 5, 12pm noon Please only hand in Question 3, which will be graded. The rest will be reviewed in the recitation but

More information

(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming

(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming 1. Government Purchases and Endogenous Growth Consider the following endogenous growth model with government purchases (G) in continuous time. Government purchases enhance production, and the production

More information

Suggested Solutions to Problem Set 2

Suggested Solutions to Problem Set 2 Macroeconomic Theory, Fall 03 SEF, HKU Instructor: Dr. Yulei Luo October 03 Suggested Solutions to Problem Set. 0 points] Consider the following Ramsey-Cass-Koopmans model with fiscal policy. First, we

More information

Macroeconomic Theory and Analysis V Suggested Solutions for the First Midterm. max

Macroeconomic Theory and Analysis V Suggested Solutions for the First Midterm. max Macroeconomic Theory and Analysis V31.0013 Suggested Solutions for the First Midterm Question 1. Welfare Theorems (a) There are two households that maximize max i,g 1 + g 2 ) {c i,l i} (1) st : c i w(1

More information

The economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0

The economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0 Review Questions: Two Sector Models Econ720. Fall 207. Prof. Lutz Hendricks A Planning Problem The economy is populated by a unit mass of infinitely lived households with preferences given by β t uc Mt,

More information

Macroeconomics Theory II

Macroeconomics Theory II Macroeconomics Theory II Francesco Franco FEUNL February 2016 Francesco Franco (FEUNL) Macroeconomics Theory II February 2016 1 / 18 Road Map Research question: we want to understand businesses cycles.

More information

Economic Growth: Lecture 8, Overlapping Generations

Economic Growth: Lecture 8, Overlapping Generations 14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations

More information

Lecture 2 The Centralized Economy

Lecture 2 The Centralized Economy Lecture 2 The Centralized Economy Economics 5118 Macroeconomic Theory Kam Yu Winter 2013 Outline 1 Introduction 2 The Basic DGE Closed Economy 3 Golden Rule Solution 4 Optimal Solution The Euler Equation

More information

Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path

Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ryoji Ohdoi Dept. of Industrial Engineering and Economics, Tokyo Tech This lecture note is mainly based on Ch. 8 of Acemoglu

More information

Equilibrium in a Production Economy

Equilibrium in a Production Economy Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in

More information

The Real Business Cycle Model

The Real Business Cycle Model The Real Business Cycle Model Macroeconomics II 2 The real business cycle model. Introduction This model explains the comovements in the fluctuations of aggregate economic variables around their trend.

More information

Lecture 2 The Centralized Economy: Basic features

Lecture 2 The Centralized Economy: Basic features Lecture 2 The Centralized Economy: Basic features Leopold von Thadden University of Mainz and ECB (on leave) Advanced Macroeconomics, Winter Term 2013 1 / 41 I Motivation This Lecture introduces the basic

More information

Neoclassical Business Cycle Model

Neoclassical Business Cycle Model Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy

More information

Chapter 7. Endogenous Growth II: R&D and Technological Change

Chapter 7. Endogenous Growth II: R&D and Technological Change Chapter 7 Endogenous Growth II: R&D and Technological Change 225 Economic Growth: Lecture Notes 7.1 Expanding Product Variety: The Romer Model There are three sectors: one for the final good sector, one

More information

"0". Doing the stuff on SVARs from the February 28 slides

0. Doing the stuff on SVARs from the February 28 slides Monetary Policy, 7/3 2018 Henrik Jensen Department of Economics University of Copenhagen "0". Doing the stuff on SVARs from the February 28 slides 1. Money in the utility function (start) a. The basic

More information

ECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu)

ECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu) ECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu) Instructor: Dmytro Hryshko 1 / 21 Consider the neoclassical economy without population growth and technological progress. The optimal growth

More information

Generic Analysis of Endogenous Growth Models

Generic Analysis of Endogenous Growth Models c November 20, 2017, Christopher D. Carroll Endogenous Generic Analysis of Endogenous Growth Models The neoclassical theory of economic growth, as formulated by Solow (1956), and Cass (1965)-Koopmans (1965),

More information

Dynamic Optimization: An Introduction

Dynamic Optimization: An Introduction Dynamic Optimization An Introduction M. C. Sunny Wong University of San Francisco University of Houston, June 20, 2014 Outline 1 Background What is Optimization? EITM: The Importance of Optimization 2

More information

Monetary Economics: Solutions Problem Set 1

Monetary Economics: Solutions Problem Set 1 Monetary Economics: Solutions Problem Set 1 December 14, 2006 Exercise 1 A Households Households maximise their intertemporal utility function by optimally choosing consumption, savings, and the mix of

More information

Real Business Cycle Model (RBC)

Real Business Cycle Model (RBC) Real Business Cycle Model (RBC) Seyed Ali Madanizadeh November 2013 RBC Model Lucas 1980: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that

More information

Knowledge licensing in a Model of R&D-driven Endogenous Growth

Knowledge licensing in a Model of R&D-driven Endogenous Growth Knowledge licensing in a Model of R&D-driven Endogenous Growth Vahagn Jerbashian Universitat de Barcelona June 2016 Early growth theory One of the seminal papers, Solow (1957) discusses how physical capital

More information

Problem 1 (30 points)

Problem 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 information

Intermediate Macroeconomics, EC2201. L2: Economic growth II

Intermediate Macroeconomics, EC2201. L2: Economic growth II Intermediate Macroeconomics, EC2201 L2: Economic growth II Anna Seim Department of Economics, Stockholm University Spring 2017 1 / 64 Contents and literature The Solow model. Human capital. The Romer model.

More information

Economic Growth: Lectures 10 and 11, Endogenous Technological Change

Economic Growth: Lectures 10 and 11, Endogenous Technological Change 14.452 Economic Growth: Lectures 10 and 11, Endogenous Technological Change Daron Acemoglu MIT December 1 and 6, 2011. Daron Acemoglu (MIT) Economic Growth Lectures 10 end 11 December 1 and 6, 2011. 1

More information

TOBB-ETU - Econ 532 Practice Problems II (Solutions)

TOBB-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 information

Structural change in a multi-sector model of the climate and the economy

Structural change in a multi-sector model of the climate and the economy Structural change in a multi-sector model of the climate and the economy Gustav Engström The Beijer Institute of Environmental Economics Stockholm, December 2012 G. Engström (Beijer) Stockholm, December

More information

Macroeconomics Theory II

Macroeconomics Theory II Macroeconomics Theory II Francesco Franco FEUNL February 2011 Francesco Franco Macroeconomics Theory II 1/34 The log-linear plain vanilla RBC and ν(σ n )= ĉ t = Y C ẑt +(1 α) Y C ˆn t + K βc ˆk t 1 + K

More information

ECON 402: Advanced Macroeconomics 1. Advanced Macroeconomics, ECON 402. New Growth Theories

ECON 402: Advanced Macroeconomics 1. Advanced Macroeconomics, ECON 402. New Growth Theories ECON 402: Advanced Macroeconomics 1 Advanced Macroeconomics, ECON 402 New Growth Theories The conclusions derived from the growth theories we have considered thus far assumes that economic growth is tied

More information

Economic Growth: Lectures 9 and 10, Endogenous Technological Change

Economic Growth: Lectures 9 and 10, Endogenous Technological Change 14.452 Economic Growth: Lectures 9 and 10, Endogenous Technological Change Daron Acemoglu MIT Nov. 29 and Dec. 4 Daron Acemoglu (MIT) Economic Growth Lectures 9 and 10 Nov. 29 and Dec. 4 1 / 73 Endogenous

More information

Competitive Equilibrium and the Welfare Theorems

Competitive Equilibrium and the Welfare Theorems Competitive Equilibrium and the Welfare Theorems Craig Burnside Duke University September 2010 Craig Burnside (Duke University) Competitive Equilibrium September 2010 1 / 32 Competitive Equilibrium and

More information

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4

Solow Growth Model. Michael Bar. February 28, Introduction Some facts about modern growth Questions... 4 Solow Growth Model Michael Bar February 28, 208 Contents Introduction 2. Some facts about modern growth........................ 3.2 Questions..................................... 4 2 The Solow Model 5

More information

A Summary of Economic Methodology

A Summary of Economic Methodology A Summary of Economic Methodology I. The Methodology of Theoretical Economics All economic analysis begins with theory, based in part on intuitive insights that naturally spring from certain stylized facts,

More information

Expanding Variety Models

Expanding Variety Models Expanding Variety Models Yin-Chi Wang The Chinese University of Hong Kong November, 2012 References: Acemoglu (2009) ch13 Introduction R&D and technology adoption are purposeful activities The simplest

More information

Economic Growth: Lecture 7, Overlapping Generations

Economic Growth: Lecture 7, Overlapping Generations 14.452 Economic Growth: Lecture 7, Overlapping Generations Daron Acemoglu MIT November 17, 2009. Daron Acemoglu (MIT) Economic Growth Lecture 7 November 17, 2009. 1 / 54 Growth with Overlapping Generations

More information

Handout: Competitive Equilibrium

Handout: Competitive Equilibrium 1 Competitive equilibrium Handout: Competitive Equilibrium Definition 1. A competitive equilibrium is a set of endogenous variables (Ĉ, N s, N d, T, π, ŵ), such that given the exogenous variables (G, z,

More information

Economics 210B Due: September 16, Problem Set 10. s.t. k t+1 = R(k t c t ) for all t 0, and k 0 given, lim. and

Economics 210B Due: September 16, Problem Set 10. s.t. k t+1 = R(k t c t ) for all t 0, and k 0 given, lim. and Economics 210B Due: September 16, 2010 Problem 1: Constant returns to saving Consider the following problem. c0,k1,c1,k2,... β t Problem Set 10 1 α c1 α t s.t. k t+1 = R(k t c t ) for all t 0, and k 0

More information

Economic Growth: Lectures 5-7, Neoclassical Growth

Economic Growth: Lectures 5-7, Neoclassical Growth 14.452 Economic Growth: Lectures 5-7, Neoclassical Growth Daron Acemoglu MIT November 7, 9 and 14, 2017. Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November 7, 9 and 14, 2017. 1 / 83 Introduction

More information

Macroeconomic Theory and Analysis Suggested Solution for Midterm 1

Macroeconomic Theory and Analysis Suggested Solution for Midterm 1 Macroeconomic Theory and Analysis Suggested Solution for Midterm February 25, 2007 Problem : Pareto Optimality The planner solves the following problem: u(c ) + u(c 2 ) + v(l ) + v(l 2 ) () {c,c 2,l,l

More information

Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti)

Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti) Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti) Kjetil Storesletten September 5, 2014 Kjetil Storesletten () Lecture 3 September 5, 2014 1 / 56 Growth

More information

Growth Theory: Review

Growth Theory: Review Growth Theory: Review Lecture 1, Endogenous Growth Economic Policy in Development 2, Part 2 March 2009 Lecture 1, Exogenous Growth 1/104 Economic Policy in Development 2, Part 2 Outline Growth Accounting

More information

ECON 581: Growth with Overlapping Generations. Instructor: Dmytro Hryshko

ECON 581: Growth with Overlapping Generations. Instructor: Dmytro Hryshko ECON 581: Growth with Overlapping Generations Instructor: Dmytro Hryshko Readings Acemoglu, Chapter 9. Motivation Neoclassical growth model relies on the representative household. OLG models allow for

More information

Schumpeterian Growth Models

Schumpeterian Growth Models Schumpeterian Growth Models Yin-Chi Wang The Chinese University of Hong Kong November, 2012 References: Acemoglu (2009) ch14 Introduction Most process innovations either increase the quality of an existing

More information

Part A: Answer question A1 (required), plus either question A2 or A3.

Part A: Answer question A1 (required), plus either question A2 or A3. Ph.D. Core Exam -- Macroeconomics 5 January 2015 -- 8:00 am to 3:00 pm Part A: Answer question A1 (required), plus either question A2 or A3. A1 (required): Ending Quantitative Easing Now that the U.S.

More information

Theoretical premises of the Keynesian approach

Theoretical premises of the Keynesian approach origin of Keynesian approach to Growth can be traced back to an article written after the General Theory (1936) Roy Harrod, An Essay in Dynamic Theory, Economic Journal, 1939 Theoretical premises of the

More information

1 The Basic RBC Model

1 The Basic RBC Model IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of

More information

Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models

Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models Advanced Economic Growth: Lecture 2, Review of Endogenous Growth: Expanding Variety Models Daron Acemoglu MIT September 10, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 2 September 10, 2007 1 / 56

More information

The Solow Model. Prof. Lutz Hendricks. January 26, Econ520

The Solow Model. Prof. Lutz Hendricks. January 26, Econ520 The Solow Model Prof. Lutz Hendricks Econ520 January 26, 2017 1 / 28 Issues The production model measures the proximate causes of income gaps. Now we start to look at deep causes. The Solow model answers

More information

1 The social planner problem

1 The social planner problem The social planner problem max C t;k t+ U t = E t X t C t () that can be written as: s.t.: Y t = A t K t (2) Y t = C t + I t (3) I t = K t+ (4) A t = A A t (5) et t i:i:d: 0; 2 max C t;k t+ U t = E t "

More information

ECON 5118 Macroeconomic Theory

ECON 5118 Macroeconomic Theory ECON 5118 Macroeconomic Theory Winter 013 Test 1 February 1, 013 Answer ALL Questions Time Allowed: 1 hour 0 min Attention: Please write your answers on the answer book provided Use the right-side pages

More information

4- Current Method of Explaining Business Cycles: DSGE Models. Basic Economic Models

4- Current Method of Explaining Business Cycles: DSGE Models. Basic Economic Models 4- Current Method of Explaining Business Cycles: DSGE Models Basic Economic Models In Economics, we use theoretical models to explain the economic processes in the real world. These models de ne a relation

More information

Small Open Economy RBC Model Uribe, Chapter 4

Small Open Economy RBC Model Uribe, Chapter 4 Small Open Economy RBC Model Uribe, Chapter 4 1 Basic Model 1.1 Uzawa Utility E 0 t=0 θ t U (c t, h t ) θ 0 = 1 θ t+1 = β (c t, h t ) θ t ; β c < 0; β h > 0. Time-varying discount factor With a constant

More information

Topic 8: Optimal Investment

Topic 8: Optimal Investment Topic 8: Optimal Investment Yulei Luo SEF of HKU November 22, 2013 Luo, Y. SEF of HKU) Macro Theory November 22, 2013 1 / 22 Demand for Investment The importance of investment. First, the combination of

More information

FEDERAL RESERVE BANK of ATLANTA

FEDERAL RESERVE BANK of ATLANTA FEDERAL RESERVE BANK of ATLANTA On the Solution of the Growth Model with Investment-Specific Technological Change Jesús Fernández-Villaverde and Juan Francisco Rubio-Ramírez Working Paper 2004-39 December

More information

Online Appendix I: Wealth Inequality in the Standard Neoclassical Growth Model

Online Appendix I: Wealth Inequality in the Standard Neoclassical Growth Model Online Appendix I: Wealth Inequality in the Standard Neoclassical Growth Model Dan Cao Georgetown University Wenlan Luo Georgetown University July 2016 The textbook Ramsey-Cass-Koopman neoclassical growth

More information

14.06 Lecture Notes Intermediate Macroeconomics. George-Marios Angeletos MIT Department of Economics

14.06 Lecture Notes Intermediate Macroeconomics. George-Marios Angeletos MIT Department of Economics 14.06 Lecture Notes Intermediate Macroeconomics George-Marios Angeletos MIT Department of Economics Spring 2004 Chapter 2 The Solow Growth Model (and a look ahead) 2.1 Centralized Dictatorial Allocations

More information

Macroeconomics I. University of Tokyo. Lecture 12. The Neo-Classical Growth Model: Prelude to LS Chapter 11.

Macroeconomics I. University of Tokyo. Lecture 12. The Neo-Classical Growth Model: Prelude to LS Chapter 11. Macroeconomics I University of Tokyo Lecture 12 The Neo-Classical Growth Model: Prelude to LS Chapter 11. Julen Esteban-Pretel National Graduate Institute for Policy Studies The Cass-Koopmans Model: Environment

More information

the growth rate in the labour force. fk () = F(,1): fk () and strictly concave, with positive marginal productivities. Given that the Inadaconditions

the growth rate in the labour force. fk () = F(,1): fk () and strictly concave, with positive marginal productivities. Given that the Inadaconditions 1 Jon Vislie ECON 4350 (Growth and Investment) Spring 2009 Seminar 2 (wee 9) Problem 1. In the standard neoclassical growth model (the Solow model ), we have, under certain circumstances, a steady state

More information

SGZ Macro Week 3, Lecture 2: Suboptimal Equilibria. SGZ 2008 Macro Week 3, Day 1 Lecture 2

SGZ Macro Week 3, Lecture 2: Suboptimal Equilibria. SGZ 2008 Macro Week 3, Day 1 Lecture 2 SGZ Macro Week 3, : Suboptimal Equilibria 1 Basic Points Effects of shocks can be magnified (damped) in suboptimal economies Multiple equilibria (stationary states, dynamic paths) in suboptimal economies

More information

Growth and Ideas. Romer (1990) and Jones (2005) Chad Jones Stanford GSB. Romer (1990) and Jones (2005) p. 1

Growth and Ideas. Romer (1990) and Jones (2005) Chad Jones Stanford GSB. Romer (1990) and Jones (2005) p. 1 Growth and Ideas Romer (1990) and Jones (2005) Chad Jones Stanford GSB Romer (1990) and Jones (2005) p. 1 Key References Romer, Paul M. 1990. Endogenous Technological Change Journal of Political Economy

More information

Labor Union and the Wealth-Income Ratio

Labor Union and the Wealth-Income Ratio Labor Union and the Wealth-Income Ratio Angus C. Chu Zonglai Kou Xueyue Liu November 2017 Abstract We explore how labor union affects the wealth-income ratio in an innovation-driven growth model and find

More information

Master 2 Macro I. Lecture 2 : Balance Growth Paths

Master 2 Macro I. Lecture 2 : Balance Growth Paths 2012-2013 Master 2 Macro I Lecture 2 : Balance Growth Paths Franck Portier (based on Gilles Saint-Paul lecture notes) franck.portier@tse-fr.eu Toulouse School of Economics Version 1.1 24/09/2012 Changes

More information

The Solow Growth Model

The Solow Growth Model The Solow Growth Model 1. Set-Up 2. Dynamics, Simulations and Steady-States 3. Comparative Dynamics 4. Golden Rule 5. Convergence 1 Set-Up Closed economy, single good produced each period, Yt. Discrete

More information

The welfare cost of energy insecurity

The welfare cost of energy insecurity The welfare cost of energy insecurity Baltasar Manzano (Universidade de Vigo) Luis Rey (bc3) IEW 2013 1 INTRODUCTION The 1973-1974 oil crisis revealed the vulnerability of developed economies to oil price

More information

Foundations of Modern Macroeconomics Second Edition

Foundations of Modern Macroeconomics Second Edition Foundations of Modern Macroeconomics Second Edition Chapter 5: The government budget deficit Ben J. Heijdra Department of Economics & Econometrics University of Groningen 1 September 2009 Foundations of

More information

From Difference to Differential Equations I

From Difference to Differential Equations I From Difference to Differential Equations I Start with a simple difference equation x (t + 1) x (t) = g(x (t)). (30) Now consider the following approximation for any t [0, 1], x (t + t) x (t) t g(x (t)),

More information

Life Cycle Saving, Bequests, and the Role of Population in R&D based Growth

Life Cycle Saving, Bequests, and the Role of Population in R&D based Growth Auburn University Department of Economics Working Paper Series Life Cycle Saving, Bequests, and the Role of Population in R&D based Growth Bharat Diwakar and Gilad Sorek Auburn University AUWP 206 05 This

More information

Optimal Simple And Implementable Monetary and Fiscal Rules

Optimal Simple And Implementable Monetary and Fiscal Rules Optimal Simple And Implementable Monetary and Fiscal Rules Stephanie Schmitt-Grohé Martín Uribe Duke University September 2007 1 Welfare-Based Policy Evaluation: Related Literature (ex: Rotemberg and Woodford,

More information

Economic Growth: Lecture 13, Stochastic Growth

Economic Growth: Lecture 13, Stochastic Growth 14.452 Economic Growth: Lecture 13, Stochastic Growth Daron Acemoglu MIT December 10, 2013. Daron Acemoglu (MIT) Economic Growth Lecture 13 December 10, 2013. 1 / 52 Stochastic Growth Models Stochastic

More information

Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models

Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models Daron Acemoglu MIT September 12, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 3 September 12, 2007 1 / 40 Introduction

More information

Lecture 4 The Centralized Economy: Extensions

Lecture 4 The Centralized Economy: Extensions Lecture 4 The Centralized Economy: Extensions Leopold von Thadden University of Mainz and ECB (on leave) Advanced Macroeconomics, Winter Term 2013 1 / 36 I Motivation This Lecture considers some applications

More information

The Solow Growth Model

The Solow Growth Model The Solow Growth Model Lectures 5, 6 & 7 Topics in Macroeconomics Topic 2 October 20, 21 & 27, 2008 Lectures 5, 6 & 7 1/37 Topics in Macroeconomics From Growth Accounting to the Solow Model Goal 1: Stylized

More information

Housing with overlapping generations

Housing with overlapping generations Housing with overlapping generations Chiara Forlati, Michael Hatcher, Alessandro Mennuni University of Southampton Preliminary and Incomplete May 16, 2015 Abstract We study the distributional and efficiency

More information

Growth Theory: Review

Growth Theory: Review Growth Theory: Review Lecture 1.1, Exogenous Growth Topics in Growth, Part 2 June 11, 2007 Lecture 1.1, Exogenous Growth 1/76 Topics in Growth, Part 2 Growth Accounting: Objective and Technical Framework

More information