Hello, my name is Olga Michasova and I present the work The generalized model of economic growth with human capital accumulation.

Size: px
Start display at page:

Download "Hello, my name is Olga Michasova and I present the work The generalized model of economic growth with human capital accumulation."

Transcription

1 Hello, my name is Olga Michasova and I present the work The generalized model of economic growth with human capital accumulation. 1

2 Without any doubts human capital is a key factor of economic growth because labour productivity has a strong impact on output. And the workers effectiveness is determined by their knowledge and skills. For the first time human capital was included in the neoclassical model of economic growth in the seminal work by R. Lucas in In the model human capital is a counterpart of the scientific and technological progress. The distinction in manner of Lucas specification from others, for example, the Uzawa s model) is the consideration of both internal (describing the direct increase in production efficiency, associated with an upgrade of workers professional skills) and external effects (which characterizes the human capital average value in the economic system in whole) of human capital. Human capital accumulation in Lucas model takes place within the peculiar educational sector of economics. This approach explains the difference between growth rates in different countries. Lucas model is the basis for further development and generalization of this field of economic growth theory. 2

3 This work presents the generalized mathematical model of endogenous growth with the human capital accumulation. There are two sectors in the model economy: production and educational sectors. The human capital h(t) of representative agent is formed in the second one. Let us suppose that the output sector externalities are determined not only by average level of human capital h a (t) (as in the original Lucas model), but also depend on the average share of non-leisure time which an agent spends in production u a (t). Furthermore, we assume that the externalities have an impact on the educational sector unlike the classical Lucas model. So this effect depends on both the average level of human capital h a (t) and the fraction of time devoted to human capital formation (education and trainings). Thus, it is assumed that the agent is interested in spending the same part of time for production activity as the average one at the market. Under these assumptions, the equation of dynamics of physical capital can be written in the following form (1) where A(t) is a function describing the exogenous technological progress ( - the rate of technological progress is constant); K(t) - physical capital; N(t) - labor force; u(t)h(t)n(t) - the effective labor force (or internal effect of human capital); c(t) - consumption per capita; - the share of physical capital; - positive parameter; K - the depreciation rate of physical capital. The equation of dynamic of the human capital accumulation is given by (2) where is a positive technological parameter; p, s, q and r - nonnegative parameters (elasticities); h - depreciation rate of human capital. (It should be mentioned that equation (2) reflects the fact that at the micro-level the agent examines the functions u a (t) and h a (t) as given exogenously, so that production function of human capital in the right-hand side of equation (2) demonstrates the presence of the diminishing scale effect at the micro-level and the lack of the scale effect at the macro-level.) The initial conditions should be added to the system. It is assumed that the agent chooses his consumption level c(t) and the share of his active time spent in production u(t) in order to maximize a utility function of the form (3) where is the subjective rate of time preference, and 1/ is the constant intertemporal elasticity of substitution. The optimal control problem related to the economic growth model with the human capital accumulation (1) - (3) is the search of control variables c(t) and u(t) to maximize the objective functional (3) on admissible trajectories {K(t),h(t)} of the dynamic system (1), (2) subject to conditions (4) 3

4 There are at least two economic interpretations of conditions (4): 1. The social planner s problem. There is a hypothetical social planner who chooses an optimal path (trajectory) of the economic system from the standpoint of society as a whole, initially possesses the complete information about its development, and is able to influence on its all-composite parts. Therefore we can assume that conditions (4) are fulfilled initially. 2. The competitive equilibrium. We consider the situation where firms and households do not have the complete information about the economic system development, but expect that the accumulation of human capital and the share of non-leisure time which an agent spends in production u(t) will follow known in every moment of time functions u a (t) and h a (t), which are exogenously given (from firm s point of view) and aren t affected by an agent. In these conditions, economic agents solve the optimization problem. The economic situation will be in equilibrium if the expected and the actual behaviors coincide, i.e. if equalities (4) are carried out. For each of these cases the appropriate optimization problems should be considered. 4

5 Furthermore we can write the generalized problem for them. After some transformations and transition to neoclassical variables per capita (k(t)=k(t)/n(t)) we get the following equations: (5)-(8) and transversality conditions: (9) Substitution 1 =q, 2 =0, 3 =p gets the social planner s problem and 1 =1, 2 =, 3 =1 - the problem of the competitive equilibrium. 5

6 It can be proved that system (5)-(8) has first integral of such form (10) And it also has the second first integral for particular case when is equal to. The existence of the first integral allows us to reduce the system (5)-(8) by one dimension. 6

7 Let us construct the system s balanced growth path (BGP) from (5)-(8): the particular solution {k(t),h(t),c(t),u(t)} for which the growth rates of all variables are constant. Moreover u(t) is constant on BGP. We define these rates of growth as with appropriate index. They are solutions of the following simple algebraic system: (11) When the determinant of the system doesn t equal to zero, the system (11) has a unique solution and the balanced growth path is given by (12) If we consider our result in comparison with Lucas one, the difference between equilibrium growth rates of human capital is characterized by the equation: (13) Obviously the output sector externalities are quite small, and thus this difference is more than zero. In other words human capital in generalized model is smaller than in Lucas one. While too big human capital is one of the most important issues for criticism of the Lucas model. 7

8 The next step of our investigation is the reducing of the system by one dimension for simplification of analytical study. We can define the new variables, which are stationary on the BGP: (14) Some manipulations leads to: (15)-(18) Here we can see that the system (15)-(18) has the closed subsystem (15)-(17) further which will be studied separately. 8

9 If we want to find the unique nonnegative steady state of the reduced model we should find the solution of the presented system. And you can see it at the slide as a function of the set of parameters : (19) The parameters {x e,q e } should are positive and u e should belong to in the range from 0 to 1. These conditions impose some additional restrictions to the set of parameters (lower-case - строчная) and allow us to select a subset BGP (capital-прописная) in a space of admissible parameters. This subset is not empty in general case. 9

10 Let s talk about the local stability properties of the BGP and regions of the parameter space with different types of equilibrium, defined by eigenvalues of Jacobian of the reduced system (15)-(17). The Jacobian evaluated at BGP is given by: (20) The type of the equilibrium point and, correspondingly, its stability, is defined by the amount of eigenvalues at the right half plane of the complex plane. Because of sufficient complexity of analytical results further study was realized numerically with MatLab software. 10

11 Our model can be used for the investigation of economic dynamics of developed counties, since human capital of such economies has decreasing return to scale. That is why it is expediently to research the dynamic of the system for the set of parameters which are equal or near to real values for developed countries (e.g., Germany or USA). It is worth to note that the problem of determination of real values of parameters for any economic growth model is one of the most urgent questions. In this study we use (taking into account some remarks) these assessments of parameters which is built on the basis of assessments from these works. The other parameters vector characterizes the output sector externalities and the scale effect in educational sector. Let s see how dynamic peculiarities of the system (15)-(17) depend on vector choice for the competitive economic system. 11

12 Let us consider subsets (k), where k is amount of eigenvalues in the right half of complex plane. This figure illustrates the general view of the fragment of the set BGP and its subsets (k). It should be mentioned that all possible variants of steady states types are realized in this problem. 12

13 We can see that the model demonstrates the indeterminacy effect the situation when a trajectory converging to BGP is not unique. This situation takes place when there are one ( (1) ) or all three ( (3) ) eigenvalues lays at right half of complex plane or all three eigenvalues lays at left half ( (0) ). 13

14 For (2) set two eigenvalues lays at right half plane. Here the two-dimensional manifold will be locally unstable and one-dimensional manifold locally stable. That is why we could define initial conditions definitely, and so the local determinacy is observed. 14

15 In our model the arrangement of sets (2) and (0) has a very important feature they have a common boundary. Let s consider only one result which shows that the dynamics of the investigated system can be quite complex. This example takes into account the transition from (0) to (2) across curve H along the segment of a vertical line p=0.9 when =0.4 (decreasing scale effect on years of schooling, near to Lucas value). Let s look at the changes of the phase space structure near stationary point depending on q value, which characterize the scale effect of human capital level in educational sector. 15

16 Calculations show that there are subcritical Andronov-Hopf bifurcation and direct and inverted fold bifurcations of limit cycles in the system. Thus there are three limit cycles (two of which are unstable) near equilibrium point or two limit cycles (stable and unstable), and the one unstable limit cycle when q>q 0. When q<q 2 equilibrium point is unstable. (Stable objects are depicted by a firm line, unstable by a dot-dash line). 16

17 Next two slides present as an example some trajectories near a steady state. They give a clear submission of the phase space structure of our system in the case of coexistence of three limit cycles. 17

18 Within the framework of the economic growth theory the balanced growth paths are peculiar turnpikes of economic development representing an equilibrium evolution of economic systems. In most cases they are unstable. Therefore, the fact that a stable periodic motion can exist in the neighborhood of the unstable balanced path ( a turnpike of development ) is very important and positive for the theory of economic growth. Essentially, it means that although the equilibrium evolution of the economic system is unrealized along the turnpike of development (because of its instability), some other oscillatory trajectories are quite feasible, sustainable and have the same trend as the turnpike of development. Thus, the evolution of the economic system can be realized almost along the turnpike of development within the bounds of a stable educational economic cycle. 18

19 The graphics for initial variables for trajectories relevant stable limit cycle are presented on the slide. 19

20 Thank you for your attention 20

21 21

22 22

23 23

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON4310 Intertemporal macroeconomics Date of exam: Thursday, November 27, 2008 Grades are given: December 19, 2008 Time for exam: 09:00 a.m. 12:00 noon

More information

Universidad de Montevideo Macroeconomia II. The Ramsey-Cass-Koopmans Model

Universidad de Montevideo Macroeconomia II. The Ramsey-Cass-Koopmans Model Universidad de Montevideo Macroeconomia II Danilo R. Trupkin Class Notes (very preliminar) The Ramsey-Cass-Koopmans Model 1 Introduction One shortcoming of the Solow model is that the saving rate is exogenous

More information

Great Depressions from a Neoclassical Perspective. Advanced Macroeconomic Theory

Great Depressions from a Neoclassical Perspective. Advanced Macroeconomic Theory Great Depressions from a Neoclassical Perspective Advanced Macroeconomic Theory 1 Review of Last Class Model with indivisible labor, either working for xed hours or not. allow social planner to choose

More information

ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE

ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.

More information

14.452 Economic Growth: Lectures 6 and 7, Neoclassical Growth

14.452 Economic Growth: Lectures 6 and 7, Neoclassical Growth 14.452 Economic Growth: Lectures 6 and 7, Neoclassical Growth Daron Acemoglu MIT November 15 and 17, 211. Daron Acemoglu (MIT) Economic Growth Lectures 6 and 7 November 15 and 17, 211. 1 / 71 Introduction

More information

Stability Of Structures: Basic Concepts

Stability Of Structures: Basic Concepts 23 Stability Of Structures: Basic Concepts ASEN 3112 Lecture 23 Slide 1 Objective This Lecture (1) presents basic concepts & terminology on structural stability (2) describes conceptual procedures for

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 29, 2011. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 29, 2011. 1 / 41 First-Generation Models

More information

Endogenous Growth Models

Endogenous Growth Models Endogenous Growth Models Lorenza Rossi Goethe University 2011-2012 Endogenous Growth Theory Neoclassical Exogenous Growth Models technological progress is the engine of growth technological improvements

More information

The Phase Plane. Phase portraits; type and stability classifications of equilibrium solutions of systems of differential equations

The Phase Plane. Phase portraits; type and stability classifications of equilibrium solutions of systems of differential equations The Phase Plane Phase portraits; type and stability classifications of equilibrium solutions of systems of differential equations Phase Portraits of Linear Systems Consider a systems of linear differential

More information

E322_Summer_08_Intermediate Macroeconomics. Final Exam: Sample Questions

E322_Summer_08_Intermediate Macroeconomics. Final Exam: Sample Questions E322_Summer_08_Intermediate Macroeconomics Final Exam: Sample Questions Chapter_05 1. A competitive equilibrium is Pareto optimal if there is no way to rearrange or to reallocate goods so that (a) anyone

More information

CHAPTER 7 Economic Growth I

CHAPTER 7 Economic Growth I CHAPTER 7 Economic Growth I Questions for Review 1. In the Solow growth model, a high saving rate leads to a large steady-state capital stock and a high level of steady-state output. A low saving rate

More information

Dynamics. Figure 1: Dynamics used to generate an exemplar of the letter A. To generate

Dynamics. Figure 1: Dynamics used to generate an exemplar of the letter A. To generate Dynamics Any physical system, such as neurons or muscles, will not respond instantaneously in time but will have a time-varying response termed the dynamics. The dynamics of neurons are an inevitable constraint

More information

Environmental problems and economic development in an endogenous fertility model

Environmental problems and economic development in an endogenous fertility model University of Heidelberg Department of Economics Discussion Paper Series No. 428 Environmental problems and economic development in an endogenous fertility model Frank Jöst, Martin Quaas and Johannes Schiller

More information

Lecture 14 More on Real Business Cycles. Noah Williams

Lecture 14 More on Real Business Cycles. Noah Williams Lecture 14 More on Real Business Cycles Noah Williams University of Wisconsin - Madison Economics 312 Optimality Conditions Euler equation under uncertainty: u C (C t, 1 N t) = βe t [u C (C t+1, 1 N t+1)

More information

The Real Business Cycle model

The Real Business Cycle model The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian

More information

The Budget Deficit, Public Debt and Endogenous Growth

The Budget Deficit, Public Debt and Endogenous Growth The Budget Deficit, Public Debt and Endogenous Growth Michael Bräuninger October 2002 Abstract This paper analyzes the effects of public debt on endogenous growth in an overlapping generations model. The

More information

Macroeconomics Lecture 1: The Solow Growth Model

Macroeconomics Lecture 1: The Solow Growth Model Macroeconomics Lecture 1: The Solow Growth Model Richard G. Pierse 1 Introduction One of the most important long-run issues in macroeconomics is understanding growth. Why do economies grow and what determines

More information

Chapter 15 Introduction to Linear Programming

Chapter 15 Introduction to Linear Programming Chapter 15 Introduction to Linear Programming An Introduction to Optimization Spring, 2014 Wei-Ta Chu 1 Brief History of Linear Programming The goal of linear programming is to determine the values of

More information

15 Limit sets. Lyapunov functions

15 Limit sets. Lyapunov functions 15 Limit sets. Lyapunov functions At this point, considering the solutions to ẋ = f(x), x U R 2, (1) we were most interested in the behavior of solutions when t (sometimes, this is called asymptotic behavior

More information

MASTER IN ENGINEERING AND TECHNOLOGY MANAGEMENT

MASTER IN ENGINEERING AND TECHNOLOGY MANAGEMENT MASTER IN ENGINEERING AND TECHNOLOGY MANAGEMENT ECONOMICS OF GROWTH AND INNOVATION Lecture 1, January 23, 2004 Theories of Economic Growth 1. Introduction 2. Exogenous Growth The Solow Model Mandatory

More information

Endogenous Growth Theory

Endogenous Growth Theory Chapter 3 Endogenous Growth Theory 3.1 One-Sector Endogenous Growth Models 3.2 Two-sector Endogenous Growth Model 3.3 Technological Change: Horizontal Innovations References: Aghion, P./ Howitt, P. (1992),

More information

Economic Growth: Theory and Empirics (2012) Problem set I

Economic Growth: Theory and Empirics (2012) Problem set I Economic Growth: Theory and Empirics (2012) Problem set I Due date: April 27, 2012 Problem 1 Consider a Solow model with given saving/investment rate s. Assume: Y t = K α t (A tl t ) 1 α 2) a constant

More information

Network Traffic Modelling

Network Traffic Modelling University of York Dissertation submitted for the MSc in Mathematics with Modern Applications, Department of Mathematics, University of York, UK. August 009 Network Traffic Modelling Author: David Slade

More information

Short-Run Production and Costs

Short-Run Production and Costs Short-Run Production and Costs The purpose of this section is to discuss the underlying work of firms in the short-run the production of goods and services. Why is understanding production important to

More information

2007/8. The problem of non-renewable energy resources in the production of physical capital. Agustin Pérez-Barahona

2007/8. The problem of non-renewable energy resources in the production of physical capital. Agustin Pérez-Barahona 2007/8 The problem of non-renewable energy resources in the production of physical capital Agustin Pérez-Barahona CORE DISCUSSION PAPER 2007/8 The problem of non-renewable energy resources in the production

More information

Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey

Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey MURAT ÜNGÖR Central Bank of the Republic of Turkey http://www.muratungor.com/ April 2012 We live in the age of

More information

Chapter 7: Economic Growth part 1

Chapter 7: Economic Growth part 1 Chapter 7: Economic Growth part 1 Learn the closed economy Solow model See how a country s standard of living depends on its saving and population growth rates Learn how to use the Golden Rule to find

More information

Introduction to Macroeconomics TOPIC 2: The Goods Market

Introduction to Macroeconomics TOPIC 2: The Goods Market TOPIC 2: The Goods Market Annaïg Morin CBS - Department of Economics August 2013 Goods market Road map: 1. Demand for goods 1.1. Components 1.1.1. Consumption 1.1.2. Investment 1.1.3. Government spending

More information

University of Saskatchewan Department of Economics Economics 414.3 Homework #1

University of Saskatchewan Department of Economics Economics 414.3 Homework #1 Homework #1 1. In 1900 GDP per capita in Japan (measured in 2000 dollars) was $1,433. In 2000 it was $26,375. (a) Calculate the growth rate of income per capita in Japan over this century. (b) Now suppose

More information

= C + I + G + NX ECON 302. Lecture 4: Aggregate Expenditures/Keynesian Model: Equilibrium in the Goods Market/Loanable Funds Market

= C + I + G + NX ECON 302. Lecture 4: Aggregate Expenditures/Keynesian Model: Equilibrium in the Goods Market/Loanable Funds Market Intermediate Macroeconomics Lecture 4: Introduction to the Goods Market Review of the Aggregate Expenditures model and the Keynesian Cross ECON 302 Professor Yamin Ahmad Components of Aggregate Demand

More information

Chapter 3 A Classical Economic Model

Chapter 3 A Classical Economic Model Chapter 3 A Classical Economic Model what determines the economy s total output/income how the prices of the factors of production are determined how total income is distributed what determines the demand

More information

Real Business Cycle Theory. Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35

Real Business Cycle Theory. Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Real Business Cycle Theory Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Introduction to DSGE models Dynamic Stochastic General Equilibrium (DSGE) models have become the main tool for

More information

Preparation course MSc Business&Econonomics: Economic Growth

Preparation course MSc Business&Econonomics: Economic Growth Preparation course MSc Business&Econonomics: Economic Growth Tom-Reiel Heggedal Economics Department 2014 TRH (Institute) Solow model 2014 1 / 27 Theory and models Objective of this lecture: learn Solow

More information

Example 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum. asin. k, a, and b. We study stability of the origin x

Example 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum. asin. k, a, and b. We study stability of the origin x Lecture 4. LaSalle s Invariance Principle We begin with a motivating eample. Eample 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum Dynamics of a pendulum with friction can be written

More information

The Optimal Growth Problem

The Optimal Growth Problem LECTURE NOTES ON ECONOMIC GROWTH The Optimal Growth Problem Todd Keister Centro de Investigación Económica, ITAM keister@itam.mx January 2005 These notes provide an introduction to the study of optimal

More information

Neoclassical growth theory

Neoclassical growth theory Chapter 1 Neoclassical growth theory 1.1 The Solow growth model The general questions of growth: What are the determinants of long-run economic growth? How can we explain the vast differences in both output

More information

Lecture 10: Aggregate Demand and Aggregate Supply I

Lecture 10: Aggregate Demand and Aggregate Supply I EC201 Intermediate Macroeconomics EC201 Intermediate Macroeconomics Lecture 10: Aggregate Demand and Aggregate Supply I Lecture Outline: - how to derive the aggregate demand from the IS-LM model; - a preliminary

More information

Introduction. Agents have preferences over the two goods which are determined by a utility function. Speci cally, type 1 agents utility is given by

Introduction. Agents have preferences over the two goods which are determined by a utility function. Speci cally, type 1 agents utility is given by Introduction General equilibrium analysis looks at how multiple markets come into equilibrium simultaneously. With many markets, equilibrium analysis must take explicit account of the fact that changes

More information

Lecture 1: Linear Programming Models. Readings: Chapter 1; Chapter 2, Sections 1&2

Lecture 1: Linear Programming Models. Readings: Chapter 1; Chapter 2, Sections 1&2 Lecture 1: Linear Programming Models Readings: Chapter 1; Chapter 2, Sections 1&2 1 Optimization Problems Managers, planners, scientists, etc., are repeatedly faced with complex and dynamic systems which

More information

Economic Growth. Chapter 11

Economic Growth. Chapter 11 Chapter 11 Economic Growth This chapter examines the determinants of economic growth. A startling fact about economic growth is the large variation in the growth experience of different countries in recent

More information

Economic Growth: Lecture 2: The Solow Growth Model

Economic Growth: Lecture 2: The Solow Growth Model 14.452 Economic Growth: Lecture 2: The Solow Growth Model Daron Acemoglu MIT October 29, 2009. Daron Acemoglu (MIT) Economic Growth Lecture 2 October 29, 2009. 1 / 68 Transitional Dynamics in the Discrete

More information

Intermediate Macroeconomics

Intermediate Macroeconomics Intermediate Macroeconomics Lecture 1 - Introduction to Economic Growth Zsófia L. Bárány Sciences Po 2011 September 7 About the course I. 2-hour lecture every week, Wednesdays from 12:30-14:30 3 big topics

More information

The Solow Model. Savings and Leakages from Per Capita Capital. (n+d)k. sk^alpha. k*: steady state 0 1 2.22 3 4. Per Capita Capital, k

The Solow Model. Savings and Leakages from Per Capita Capital. (n+d)k. sk^alpha. k*: steady state 0 1 2.22 3 4. Per Capita Capital, k Savings and Leakages from Per Capita Capital 0.1.2.3.4.5 The Solow Model (n+d)k sk^alpha k*: steady state 0 1 2.22 3 4 Per Capita Capital, k Pop. growth and depreciation Savings In the diagram... sy =

More information

( ) = ( ) = ( + ) which means that both capital and output grow permanently at a constant rate

( ) = ( ) = ( + ) which means that both capital and output grow permanently at a constant rate 1 Endogenous Growth We present two models that are very popular in the, so-called, new growth theory literature. They represent economies where, notwithstanding the absence of exogenous technical progress,

More information

4. In the Solow model with technological progress, the steady state growth rate of total output is: A) 0. B) g. C) n. D) n + g.

4. In the Solow model with technological progress, the steady state growth rate of total output is: A) 0. B) g. C) n. D) n + g. 1. The rate of labor augmenting technological progress (g) is the growth rate of: A) labor. B) the efficiency of labor. C) capital. D) output. 2. In the Solow growth model with population growth and technological

More information

Perfect Competition. We will use the second concept in here and your text, chapter 11.

Perfect Competition. We will use the second concept in here and your text, chapter 11. Perfect Competition There are two concepts of competition normally used in Economics: 1. The manner or process in which firms compete with one another for market share. 2. A description of a particular

More information

Notes 10: An Equation Based Model of the Macroeconomy

Notes 10: An Equation Based Model of the Macroeconomy Notes 10: An Equation Based Model of the Macroeconomy In this note, I am going to provide a simple mathematical framework for 8 of the 9 major curves in our class (excluding only the labor supply curve).

More information

Chapter 4 Technological Progress and Economic Growth

Chapter 4 Technological Progress and Economic Growth Chapter 4 Technological Progress and Economic Growth 4.1 Introduction Technical progress is defined as new, and better ways of doing things, and new techniques for using scarce resources more productively.

More information

VI. Real Business Cycles Models

VI. Real Business Cycles Models VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized

More information

Unifying Time-to-Build Theory

Unifying Time-to-Build Theory Unifying Time-to-Build Theory M. Bambi, and F. Gori speaker: M. Bambi (University of York, U.K.) OFCE-SKEMA, Nice, 2010 Time to Build Time to Build (TtB) means that capital takes time to becomes productive.

More information

Teaching modern general equilibrium macroeconomics to undergraduates: using the same t. advanced research. Gillman (Cardi Business School)

Teaching modern general equilibrium macroeconomics to undergraduates: using the same t. advanced research. Gillman (Cardi Business School) Teaching modern general equilibrium macroeconomics to undergraduates: using the same theory required for advanced research Max Gillman Cardi Business School pments in Economics Education (DEE) Conference

More information

INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition)

INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. Its

More information

14.452 Economic Growth: Lecture 11, Technology Diffusion, Trade and World Growth

14.452 Economic Growth: Lecture 11, Technology Diffusion, Trade and World Growth 14.452 Economic Growth: Lecture 11, Technology Diffusion, Trade and World Growth Daron Acemoglu MIT December 2, 2014. Daron Acemoglu (MIT) Economic Growth Lecture 11 December 2, 2014. 1 / 43 Introduction

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 10, 2013 Kjetil Storesletten () Lecture 3 September 10, 2013 1 / 44 Growth

More information

1 National Income and Product Accounts

1 National Income and Product Accounts Espen Henriksen econ249 UCSB 1 National Income and Product Accounts 11 Gross Domestic Product (GDP) Can be measured in three different but equivalent ways: 1 Production Approach 2 Expenditure Approach

More information

Module1. x 1000. y 800.

Module1. x 1000. y 800. Module1 1 Welcome to the first module of the course. It is indeed an exciting event to share with you the subject that has lot to offer both from theoretical side and practical aspects. To begin with,

More information

Growth and public debt: what are the relevant tradeoffs?

Growth and public debt: what are the relevant tradeoffs? Growth and public debt: what are the relevant tradeoffs? Kazuo NISHIMURA, Carine NOURRY, Thomas SEEGMULLER and Alain VENDITTI,. March 19, 2015 RIEB, Kobe University and KIER, Kyoto University Aix-Marseille

More information

EXOGENOUS GROWTH MODELS

EXOGENOUS GROWTH MODELS EXOGENOUS GROWTH MODELS Lorenza Rossi Goethe University 2011-2012 Course Outline FIRST PART - GROWTH THEORIES Exogenous Growth The Solow Model The Ramsey model and the Golden Rule Introduction to Endogenous

More information

The Golden Rule. Where investment I is equal to the savings rate s times total production Y: So consumption per worker C/L is equal to:

The Golden Rule. Where investment I is equal to the savings rate s times total production Y: So consumption per worker C/L is equal to: The Golden Rule Choosing a National Savings Rate What can we say about economic policy and long-run growth? To keep matters simple, let us assume that the government can by proper fiscal and monetary policies

More information

Volume 36, Issue 3. A variant of Uzawa's steady-state theorem in a Malthusian model

Volume 36, Issue 3. A variant of Uzawa's steady-state theorem in a Malthusian model Volume 36, Issue 3 A variant of Uzawa's steady-state theorem in a Malthusian model Defu Li School of Economics and management, Tongji University Jiuli Huang School of Economics, Nankai University Abstract

More information

Endogenous Growth Theory

Endogenous Growth Theory Endogenous Growth Theory Motivation The Solow and Ramsey models o er valuable insights but have important limitations: Di erences in capital accummulation cannot satisfactorily account for the prevailing

More information

Intrinsic Low-Dimensional Manifold Method for Rational Simplification of Chemical Kinetics

Intrinsic Low-Dimensional Manifold Method for Rational Simplification of Chemical Kinetics Intrinsic Low-Dimensional Manifold Method for Rational Simplification of Chemical Kinetics University of Notre Dame Department of Aerospace and Mechanical Engineering prepared by: Nicholas J. Glassmaker

More information

SUPPLEMENT TO CHAPTER

SUPPLEMENT TO CHAPTER SUPPLEMENT TO CHAPTER 6 Linear Programming SUPPLEMENT OUTLINE Introduction and Linear Programming Model, 2 Graphical Solution Method, 5 Computer Solutions, 14 Sensitivity Analysis, 17 Key Terms, 22 Solved

More information

Moisă ALTĂR Ciprian NECULA Gabriel BOBEICĂ

Moisă ALTĂR Ciprian NECULA Gabriel BOBEICĂ 7Modeling the Economic Growth in Romania MODELING TE ECONOMIC GROWT IN ROMANIA. TE ROLE OF UMAN CAPITAL Moisă ALTĂR Ciprian NECULA Gabriel BOBEICĂ Abstract The present study emphasizes the importance of

More information

DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES

DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES ISSN 1471-0498 DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES RELATIVE CONCERNS ON VISIBLE CONSUMPTION: A SOURCE OF ECONOMIC DISTORTIONS Climent Quintana-Domeque and Francesco Turino Number 676 October

More information

Simultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the

Simultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the Simultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the explanatory variables is jointly determined with the dependent

More information

6.2 The Economics of Ideas. 6.1 Introduction. Growth and Ideas. Ideas. The Romer model divides the world into objects and ideas: Chapter 6

6.2 The Economics of Ideas. 6.1 Introduction. Growth and Ideas. Ideas. The Romer model divides the world into objects and ideas: Chapter 6 The Romer model divides the world into objects and ideas: Chapter 6 and Ideas By Charles I. Jones Objects capital and labor from the Solow model Ideas items used in making objects Media Slides Created

More information

Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning

Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning John Duffy Department of Economics University of Pittsburgh 230 S. Bouquet Street Pittsburgh, PA 15260 USA E mail:

More information

Keywords: Overlapping Generations Model, Tax Reform, Turkey

Keywords: Overlapping Generations Model, Tax Reform, Turkey SIMULATING THE TURKISH TAX SYSTEM ADEM İLERİ Middle East Technical University Department of Economics aileri@metu.edu.tr PINAR DERİN-GÜRE Middle East Technical University Department of Economics pderin@metu.edu.tr

More information

OPRE 6201 : 2. Simplex Method

OPRE 6201 : 2. Simplex Method OPRE 6201 : 2. Simplex Method 1 The Graphical Method: An Example Consider the following linear program: Max 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2

More information

Technology and Economic Growth

Technology and Economic Growth Growth Accounting Formula Technology and Economic Growth A. %ΔY = %ΔA + (2/3) %ΔN + (1/3) %ΔK B. Ex. Suppose labor, capital, and technology each grow at 1% a year. %ΔY = 1 + (2/3) 1 + (1/3) 1 = 2 C. Growth

More information

On the Interaction and Competition among Internet Service Providers

On the Interaction and Competition among Internet Service Providers On the Interaction and Competition among Internet Service Providers Sam C.M. Lee John C.S. Lui + Abstract The current Internet architecture comprises of different privately owned Internet service providers

More information

Nº 252 Diciembre 2003

Nº 252 Diciembre 2003 Nº 252 Diciembre 2003 Documento de Trabajo ISSN (edición impresa) 0716-7334 ISSN (edición electrónica) 0717-7593 Social Security Financial Crises Rodrigo Cerda www.economia.puc.cl Versión impresa ISSN:

More information

c. Given your answer in part (b), what do you anticipate will happen in this market in the long-run?

c. Given your answer in part (b), what do you anticipate will happen in this market in the long-run? Perfect Competition Questions Question 1 Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm

More information

Constrained optimization.

Constrained optimization. ams/econ 11b supplementary notes ucsc Constrained optimization. c 2010, Yonatan Katznelson 1. Constraints In many of the optimization problems that arise in economics, there are restrictions on the values

More information

Economic Growth I: Capital Accumulation and Population Growth

Economic Growth I: Capital Accumulation and Population Growth CHAPTER 8 : Capital Accumulation and Population Growth Modified for ECON 2204 by Bob Murphy 2016 Worth Publishers, all rights reserved IN THIS CHAPTER, YOU WILL LEARN: the closed economy Solow model how

More information

The Real Business Cycle Model

The Real Business Cycle Model The Real Business Cycle Model Ester Faia Goethe University Frankfurt Nov 2015 Ester Faia (Goethe University Frankfurt) RBC Nov 2015 1 / 27 Introduction The RBC model explains the co-movements in the uctuations

More information

14.452 Economic Growth: Lectures 2 and 3: The Solow Growth Model

14.452 Economic Growth: Lectures 2 and 3: The Solow Growth Model 14.452 Economic Growth: Lectures 2 and 3: The Solow Growth Model Daron Acemoglu MIT November 1 and 3, 2011. Daron Acemoglu (MIT) Economic Growth Lectures 2 and 3 November 1 and 3, 2011. 1 / 96 Solow Growth

More information

Money and Public Finance

Money and Public Finance Money and Public Finance By Mr. Letlet August 1 In this anxious market environment, people lose their rationality with some even spreading false information to create trading opportunities. The tales about

More information

MASTER FINANCIAL AND MONETARY ECONOMICS MASTER FINAL WORK DISSERTATION ON THE WELFARE EFFECTS OF FINANCIAL DEVELOPMENT DIOGO MARTINHO DA SILVA

MASTER FINANCIAL AND MONETARY ECONOMICS MASTER FINAL WORK DISSERTATION ON THE WELFARE EFFECTS OF FINANCIAL DEVELOPMENT DIOGO MARTINHO DA SILVA MASTER FINANCIAL AND MONETARY ECONOMICS MASTER FINAL WORK DISSERTATION ON THE WELFARE EFFECTS OF FINANCIAL DEVELOPMENT DIOGO MARTINHO DA SILVA JANUARY-2013 1 MASTER MONETARY AND FINANCIAL ECONOMICS MASTER

More information

The RBC methodology also comes down to two principles:

The RBC methodology also comes down to two principles: Chapter 5 Real business cycles 5.1 Real business cycles The most well known paper in the Real Business Cycles (RBC) literature is Kydland and Prescott (1982). That paper introduces both a specific theory

More information

Structural Axial, Shear and Bending Moments

Structural Axial, Shear and Bending Moments Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants

More information

New Keynesian model. Marcin Kolasa. Warsaw School of Economics Department of Quantitative Economics. Marcin Kolasa (WSE) NK model 1 / 36

New Keynesian model. Marcin Kolasa. Warsaw School of Economics Department of Quantitative Economics. Marcin Kolasa (WSE) NK model 1 / 36 New Keynesian model Marcin Kolasa Warsaw School of Economics Department of Quantitative Economics Marcin Kolasa (WSE) NK model 1 / 36 Flexible vs. sticky prices Central assumption in the (neo)classical

More information

MASTER OF SCIENCE FINANCIAL ECONOMICS ABAC SCHOOL OF MANAGEMENT ASSUMPTION UNIVERSITY OF THAILAND

MASTER OF SCIENCE FINANCIAL ECONOMICS ABAC SCHOOL OF MANAGEMENT ASSUMPTION UNIVERSITY OF THAILAND MASTER OF SCIENCE FINANCIAL ECONOMICS ABAC SCHOOL OF MANAGEMENT ASSUMPTION UNIVERSITY OF THAILAND ECO 5001 Mathematics for Finance and Economics The uses of mathematical argument in extending the range,

More information

Rotation Rate of a Trajectory of an Algebraic Vector Field Around an Algebraic Curve

Rotation Rate of a Trajectory of an Algebraic Vector Field Around an Algebraic Curve QUALITATIVE THEORY OF DYAMICAL SYSTEMS 2, 61 66 (2001) ARTICLE O. 11 Rotation Rate of a Trajectory of an Algebraic Vector Field Around an Algebraic Curve Alexei Grigoriev Department of Mathematics, The

More information

Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability

Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability S. Widnall 16.07 Dynamics Fall 2009 Version 1.0 Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability Vibration, Instability An important class of problems in dynamics concerns the free

More information

Reaction diffusion systems and pattern formation

Reaction diffusion systems and pattern formation Chapter 5 Reaction diffusion systems and pattern formation 5.1 Reaction diffusion systems from biology In ecological problems, different species interact with each other, and in chemical reactions, different

More information

Name: Date: 3. Variables that a model tries to explain are called: A. endogenous. B. exogenous. C. market clearing. D. fixed.

Name: Date: 3. Variables that a model tries to explain are called: A. endogenous. B. exogenous. C. market clearing. D. fixed. Name: Date: 1 A measure of how fast prices are rising is called the: A growth rate of real GDP B inflation rate C unemployment rate D market-clearing rate 2 Compared with a recession, real GDP during a

More information

The Macroeconomy in the Long Run The Classical Model

The Macroeconomy in the Long Run The Classical Model PP556 Macroeconomic Questions The Macroeconomy in the ong Run The Classical Model what determines the economy s total output/income how the prices of the factors of production are determined how total

More information

Linear Programming. Solving LP Models Using MS Excel, 18

Linear Programming. Solving LP Models Using MS Excel, 18 SUPPLEMENT TO CHAPTER SIX Linear Programming SUPPLEMENT OUTLINE Introduction, 2 Linear Programming Models, 2 Model Formulation, 4 Graphical Linear Programming, 5 Outline of Graphical Procedure, 5 Plotting

More information

Does Debt Relief enhance Growth in Third World Countries?

Does Debt Relief enhance Growth in Third World Countries? Does Debt Relief enhance Growth in Third World Countries? Catherine Isabelle Cax Department of Economics, University of Copenhagen Supervisor: Carl-Johan Dalgaard Opponent: Abdulaziz Shifa 24th of November

More information

Mechanics 1: Conservation of Energy and Momentum

Mechanics 1: Conservation of Energy and Momentum Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation

More information

Basic models: Intertemporal optimization and resource extraction

Basic models: Intertemporal optimization and resource extraction Basic models: Intertemporal optimization and resource extraction Anton Bondarev Department of Economics, Basel University 14.10.2014 Plan of the lecture Idea of intergenerational optimization: Ramsey leads

More information

The Difference Between Market and Barter: Money and the Making of Markets

The Difference Between Market and Barter: Money and the Making of Markets The Difference Between Market and Barter: 2 Money and the Making of Markets Market is in many respects distinct from barter. This distinction needs to be emphasized, because the conventional theory treats

More information

Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2

Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...

More information

Economic Development and Gains from Trade

Economic Development and Gains from Trade Economics Education and Research Consortium Working Paper Series Economic Development and Gains from Trade Georgi Trofimov Working Paper No 98/06 This project (No 96-161) was supported by the Economics

More information

This paper is not to be removed from the Examination Halls

This paper is not to be removed from the Examination Halls This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON EC2065 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences, the Diplomas

More information

Long Run Growth Solow s Neoclassical Growth Model

Long Run Growth Solow s Neoclassical Growth Model Long Run Growth Solow s Neoclassical Growth Model 1 Simple Growth Facts Growth in real GDP per capita is non trivial, but only really since Industrial Revolution Dispersion in real GDP per capita across

More information

2. With an MPS of.4, the MPC will be: A) 1.0 minus.4. B).4 minus 1.0. C) the reciprocal of the MPS. D).4. Answer: A

2. With an MPS of.4, the MPC will be: A) 1.0 minus.4. B).4 minus 1.0. C) the reciprocal of the MPS. D).4. Answer: A 1. If Carol's disposable income increases from $1,200 to $1,700 and her level of saving increases from minus $100 to a plus $100, her marginal propensity to: A) save is three-fifths. B) consume is one-half.

More information

ECON 5010 Class Notes Endogenous Growth Theory

ECON 5010 Class Notes Endogenous Growth Theory ECON 5010 Class Notes Endogenous Growth Theory 1 Introduction One drawbac of the Solow model is that long-run growth in per capita income is entirely exogenous. In the absence of exogenous technological

More information