The Cobb-Douglas Production Functions
|
|
- Polly Hamilton
- 5 years ago
- Views:
Transcription
1 The Cobb-Douglas Production Functions Lecture 40 Section 7.1 Robb T. Koether Hampden-Sydney College Mon, Apr 10, 2017 Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
2 Objectives Objectives Define the Cobb-Douglas production functions. Explore their properties of scaling and elasticity. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
3 The Cobb-Douglas Production Functions Definition (The Cobb-Douglas Production Functions) Let K the capital investment, L be the labor investment, Q be the output in units, A, α, and β be positive constants with α + β = 1. The Cobb-Douglas production functions are functions of the form Q(K, L) = AK α L β. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
4 Constant Returns to Scale Theorem If Q(K, L) = AK α L β, then the model predicts constant returns to scale. That is, if capital investment and labor investment are both scaled by a factor s, then output will also scale by the factor s. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
5 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
6 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Then Q(sK, sl) = A(sK ) α (sl) β Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
7 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Then Q(sK, sl) = A(sK ) α (sl) β = A(s α K α )(s β L β ) Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
8 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Then Q(sK, sl) = A(sK ) α (sl) β = A(s α K α )(s β L β ) = AK α L β s α+β Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
9 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Then Q(sK, sl) = A(sK ) α (sl) β = A(s α K α )(s β L β ) = AK α L β s α+β = s(ak α L β ) Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
10 Constant Returns to Scale Replace K with sk and L with sl for some scale factor s. Then Q(sK, sl) = A(sK ) α (sl) β = A(s α K α )(s β L β ) = AK α L β s α+β = s(ak α L β ) = sq(k, L). Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
11 Theorem If Q(K, L) = AK α L β, then α is the capital investment elasticity of production, and β is the labor investment elasticity of production. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
12 Consider labor investment L to be held fixed, so that Q(K ) = AK α L β. The formula for capital investment elasticity of production, in this case, is E(Q) = K Q(K ) Q (K ). (We dropped the minus sign because production goes up, not down, as investment goes up.) Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
13 We compute the derivative Q (K ) = A(αK α 1 )L β. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
14 We compute the derivative Q (K ) = A(αK α 1 )L β. Then E(Q) = K Q(K ) Q (K ) Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
15 We compute the derivative Q (K ) = A(αK α 1 )L β. Then E(Q) = K Q(K ) Q (K ) = K AK α L β A(αK α 1 )L β Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
16 We compute the derivative Q (K ) = A(αK α 1 )L β. Then E(Q) = K Q(K ) Q (K ) = K AK α L β A(αK α 1 )L β = K K α (αk α 1 ) Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
17 We compute the derivative Q (K ) = A(αK α 1 )L β. Then E(Q) = K Q(K ) Q (K ) = K AK α L β A(αK α 1 )L β = K K α (αk α 1 ) = αk α K α Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
18 We compute the derivative Q (K ) = A(αK α 1 )L β. Then E(Q) = K Q(K ) Q (K ) = K AK α L β A(αK α 1 )L β = K K α (αk α 1 ) = αk α K α = α. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
19 Elasticity It is convenient, but not necessary, that α + β = 1. Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
20 Elasticity It is convenient, but not necessary, that α + β = 1. What behavior would you predict if α + β < 1? Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
21 Elasticity It is convenient, but not necessary, that α + β = 1. What behavior would you predict if α + β < 1? What behavior would you predict if α + β > 1? Robb T. Koether (Hampden-Sydney College) The Cobb-Douglas Production Functions Mon, Apr 10, / 9
Maximums and Minimums
Maximums and Minimums Lecture 25 Section 3.1 Robb T. Koether Hampden-Sydney College Mon, Mar 6, 2017 Robb T. Koether (Hampden-Sydney College) Maximums and Minimums Mon, Mar 6, 2017 1 / 9 Objectives Objectives
More informationThe Interpretation of λ
The Interpretation of λ Lecture 49 Section 7.5 Robb T. Koether Hampden-Sydney College Wed, Apr 26, 2017 Robb T. Koether (Hampden-Sydney College) The Interpretation of λ Wed, Apr 26, 2017 1 / 6 Objectives
More informationComposition of Functions
Composition of Functions Lecture 34 Section 7.3 Robb T. Koether Hampden-Sydney College Mon, Mar 25, 2013 Robb T. Koether (Hampden-Sydney College) Composition of Functions Mon, Mar 25, 2013 1 / 29 1 Composition
More informationCompound Interest. Lecture 34 Section 4.1. Robb T. Koether. Hampden-Sydney College. Tue, Mar 28, 2017
Compound Interest Lecture 34 Section 4.1 Robb T. Koether Hampden-Sydney College Tue, Mar 28, 2017 Robb T. Koether (Hampden-Sydney College) Compound Interest Tue, Mar 28, 2017 1 / 8 Reminder Reminder Test
More informationConfidence Intervals for Proportions Sections 22.2, 22.3
Confidence Intervals for Proportions Sections 22.2, 22.3 Lecture 41 Robb T. Koether Hampden-Sydney College Mon, Apr 4, 2016 Robb T. Koether (Hampden-Sydney College)Confidence Intervals for ProportionsSections
More informationDirect Proof Division into Cases
Direct Proof Division into Cases Lecture 16 Section 4.4 Robb T. Koether Hampden-Sydney College Mon, Feb 10, 2014 Robb T. Koether (Hampden-Sydney College) Direct Proof Division into Cases Mon, Feb 10, 2014
More informationThe Pairwise-Comparison Method
The Pairwise-Comparison Method Lecture 12 Section 1.5 Robb T. Koether Hampden-Sydney College Mon, Sep 19, 2016 Robb T. Koether (Hampden-Sydney College) The Pairwise-Comparison Method Mon, Sep 19, 2016
More informationPaired Samples. Lecture 37 Sections 11.1, 11.2, Robb T. Koether. Hampden-Sydney College. Mon, Apr 2, 2012
Paired Samples Lecture 37 Sections 11.1, 11.2, 11.3 Robb T. Koether Hampden-Sydney College Mon, Apr 2, 2012 Robb T. Koether (Hampden-Sydney College) Paired Samples Mon, Apr 2, 2012 1 / 17 Outline 1 Dependent
More informationInstantaneous Rate of Change
Instantaneous Rate of Change Lecture 13 Section 2.1 Robb T. Koether Hampden-Sydney College Wed, Feb 8, 2017 Robb T. Koether (Hampden-Sydney College) Instantaneous Rate of Change Wed, Feb 8, 2017 1 / 11
More informationDirect Proof Floor and Ceiling
Direct Proof Floor and Ceiling Lecture 17 Section 4.5 Robb T. Koether Hampden-Sydney College Wed, Feb 12, 2014 Robb T. Koether (Hampden-Sydney College) Direct Proof Floor and Ceiling Wed, Feb 12, 2014
More informationStrong Mathematical Induction
Strong Mathematical Induction Lecture 23 Section 5.4 Robb T. Koether Hampden-Sydney College Mon, Feb 24, 2014 Robb T. Koether (Hampden-Sydney College) Strong Mathematical Induction Mon, Feb 24, 2014 1
More informationSampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Proportion Lecture 26 Section 8.4 Robb T. Koether Hampden-Sydney College Mon, Mar 1, 2010 Robb T. Koether (Hampden-Sydney College) Sampling Distribution of a Sample Proportion
More informationNondeterministic Finite Automata
Nondeterministic Finite Automata Lecture 6 Section 2.2 Robb T. Koether Hampden-Sydney College Mon, Sep 5, 2016 Robb T. Koether (Hampden-Sydney College) Nondeterministic Finite Automata Mon, Sep 5, 2016
More informationDirect Proof Divisibility
Direct Proof Divisibility Lecture 15 Section 4.3 Robb T. Koether Hampden-Sydney College Fri, Feb 8, 2013 Robb T. Koether (Hampden-Sydney College) Direct Proof Divisibility Fri, Feb 8, 2013 1 / 20 1 Divisibility
More informationDirect Proof Divisibility
Direct Proof Divisibility Lecture 15 Section 4.3 Robb T. Koether Hampden-Sydney College Fri, Feb 7, 2014 Robb T. Koether (Hampden-Sydney College) Direct Proof Divisibility Fri, Feb 7, 2014 1 / 23 1 Divisibility
More informationSampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Proportion Lecture 26 Section 8.4 Robb T. Koether Hampden-Sydney College Mon, Oct 10, 2011 Robb T. Koether (Hampden-Sydney College) Sampling Distribution of a Sample Proportion
More informationClosure Properties of Regular Languages
Closure Properties of Regular Languages Lecture 13 Section 4.1 Robb T. Koether Hampden-Sydney College Wed, Sep 21, 2016 Robb T. Koether (Hampden-Sydney College) Closure Properties of Regular Languages
More informationNegations of Quantifiers
Negations of Quantifiers Lecture 10 Section 3.2 Robb T. Koether Hampden-Sydney College Thu, Jan 31, 2013 Robb T. Koether (Hampden-Sydney College) Negations of Quantifiers Thu, Jan 31, 2013 1 / 20 1 Negations
More informationConditional Statements
Conditional Statements Lecture 3 Section 2.2 Robb T. Koether Hampden-Sydney College Fri, Jan 17, 2014 Robb T. Koether (Hampden-Sydney College) Conditional Statements Fri, Jan 17, 2014 1 / 26 1 Conditional
More informationDirect Proof Rational Numbers
Direct Proof Rational Numbers Lecture 14 Section 4.2 Robb T. Koether Hampden-Sydney College Thu, Feb 7, 2013 Robb T. Koether (Hampden-Sydney College) Direct Proof Rational Numbers Thu, Feb 7, 2013 1 /
More informationElementary Logic and Proof
Elementary Logic and Proof Lecture 5 Robb T. Koether Hampden-Sydney College Mon, Feb 6, 2017 Robb T. Koether (Hampden-Sydney College) Elementary Logic and Proof Mon, Feb 6, 2017 1 / 33 Outline 1 Statements
More informationDirect Proof Universal Statements
Direct Proof Universal Statements Lecture 13 Section 4.1 Robb T. Koether Hampden-Sydney College Wed, Feb 6, 2013 Robb T. Koether (Hampden-Sydney College) Direct Proof Universal Statements Wed, Feb 6, 2013
More informationVector Operations. Lecture 19. Robb T. Koether. Hampden-Sydney College. Wed, Oct 7, 2015
Vector Operations Lecture 19 Robb T. Koether Hampden-Sydney College Wed, Oct 7, 2015 Robb T. Koether (Hampden-Sydney College) Vector Operations Wed, Oct 7, 2015 1 / 23 Outline 1 Magnitude 2 Dot Product
More informationBinary Search Trees. Lecture 29 Section Robb T. Koether. Hampden-Sydney College. Fri, Apr 8, 2016
Binary Search Trees Lecture 29 Section 19.2 Robb T. Koether Hampden-Sydney College Fri, Apr 8, 2016 Robb T. Koether (Hampden-Sydney College) Binary Search Trees Fri, Apr 8, 2016 1 / 40 1 Binary Search
More informationPredicates and Quantifiers
Predicates and Quantifiers Lecture 9 Section 3.1 Robb T. Koether Hampden-Sydney College Wed, Jan 29, 2014 Robb T. Koether (Hampden-Sydney College) Predicates and Quantifiers Wed, Jan 29, 2014 1 / 32 1
More informationIndependent Samples: Comparing Means
Independent Samples: Comparing Means Lecture 38 Section 11.4 Robb T. Koether Hampden-Sydney College Fri, Nov 4, 2011 Robb T. Koether (Hampden-Sydney College) Independent Samples:Comparing Means Fri, Nov
More informationLecture 5 Dynamics of the Growth Model. Noah Williams
Lecture 5 Dynamics of the Growth Model Noah Williams University of Wisconsin - Madison Economics 702/312 Spring 2016 An Example Now work out a parametric example, using standard functional forms. Cobb-Douglas
More informationBusiness Mathematics. Lecture Note #13 Chapter 7-(1)
1 Business Mathematics Lecture Note #13 Chapter 7-(1) Applications of Partial Differentiation 1. Differentials and Incremental Changes 2. Production functions: Cobb-Douglas production function, MP L, MP
More informationThe Binomial Theorem
The Biomial Theorem Lecture 47 Sectio 9.7 Robb T. Koether Hampde-Sydey College Thu, Apr 8, 03 Robb T. Koether (Hampde-Sydey College The Biomial Theorem Thu, Apr 8, 03 / 7 Combiatios Pascal s Triagle 3
More informationGrowth. Growth Theory. Mark Huggett 1. 1 Georgetown. January 26, 2018
Growth Theory Mark Huggett 1 1 Georgetown January 26, 2018 Growth Theory: The Agenda 1. Facts motivating theory 2. Basic Solow model 3. Model properties 4. How to use the model 5. Full Solow model 6. Use
More informationIntermediate 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 informationLecture 26 Section 8.4. Mon, Oct 13, 2008
Lecture 26 Section 8.4 Hampden-Sydney College Mon, Oct 13, 2008 Outline 1 2 3 4 Exercise 8.12, page 528. Suppose that 60% of all students at a large university access course information using the Internet.
More informationLecture 41 Sections Mon, Apr 7, 2008
Lecture 41 Sections 14.1-14.3 Hampden-Sydney College Mon, Apr 7, 2008 Outline 1 2 3 4 5 one-proportion test that we just studied allows us to test a hypothesis concerning one proportion, or two categories,
More informationMaster 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 informationThe Contribution Rate of Thrice Industrial Agglomeration to Industrial Growth in Ningxia The Calculate Based on Cobb-Douglas Function.
International Conference on Economics, Social Science, Arts, Education and Management Engineering (ESSAEME 2015) The Contribution Rate of Thrice Industrial Agglomeration to Industrial Growth in Ningxia
More informationOn the Dynamic Implications of the Cobb- Douglas Production Function
From the SelectedWorks of Jürgen Antony 2010 On the Dynamic Implications of the Cobb- Douglas Production Function Jürgen Antony, CPB Netherlands Bureau for Economic Policy Analysis Available at: https://works.bepress.com/antony/7/
More informationLecture 5 Markups and Hedonics. Bronwyn H. Hall Economics 220C, UC Berkeley Spring 2005
Lecture 5 Markups and Hedonics Bronwyn H. Hall Economics 220C, UC Berkeley Spring 2005 Outline Production function with scale (dis)economies and markups Demand system overview Characteristic space Product
More informationThe 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 informationECON Advanced Economic Theory-Microeconomics. Prof. W. M. Semasinghe
ECON 53015 Advanced Economic Theory-Microeconomics Prof. W. M. Semasinghe Theory of Production Theory of production deals with the question of How to produce? It discusses the supply side of the pricing
More informationLecture 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 informationThe Binomial Theorem
The Biomial Theorem Lecture 47 Sectio 9.7 Robb T. Koether Hampde-Sydey College Fri, Apr 8, 204 Robb T. Koether (Hampde-Sydey College The Biomial Theorem Fri, Apr 8, 204 / 25 Combiatios 2 Pascal s Triagle
More informationThe 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 informationFunctional Form. Econometrics. ADEi.
Functional Form Econometrics. ADEi. 1. Introduction We have employed the linear function in our model specification. Why? It is simple and has good mathematical properties. It could be reasonable approximation,
More informationConstrained optimization.
ams/econ 11b supplementary notes ucsc Constrained optimization. c 2016, Yonatan Katznelson 1. Constraints In many of the optimization problems that arise in economics, there are restrictions on the values
More informationLecture 26 Section 8.4. Wed, Oct 14, 2009
PDFs n = Lecture 26 Section 8.4 Hampden-Sydney College Wed, Oct 14, 2009 Outline PDFs n = 1 2 PDFs n = 3 4 5 6 Outline PDFs n = 1 2 PDFs n = 3 4 5 6 PDFs n = Exercise 8.12, page 528. Suppose that 60% of
More informationMATH 19520/51 Class 4
MATH 19520/51 Class 4 Minh-Tam Trinh University of Chicago 2017-10-02 1 Functions and independent ( nonbasic ) vs. dependent ( basic ) variables. 2 Cobb Douglas production function and its interpretation.
More informationMATH 19520/51 Class 5
MATH 19520/51 Class 5 Minh-Tam Trinh University of Chicago 2017-10-04 1 Definition of partial derivatives. 2 Geometry of partial derivatives. 3 Higher derivatives. 4 Definition of a partial differential
More informationMath 1314 Lesson 23 Partial Derivatives
Math 1314 Lesson 3 Partial Derivatives When we are asked to ind the derivative o a unction o a single variable, (x), we know exactly what to do However, when we have a unction o two variables, there is
More informationModeling Economic Growth Using Differential Equations
Modeling Economic Growth Using Differential Equations Chad Tanioka Occidental College February 25, 2016 Chad Tanioka (Occidental College) Modeling Economic Growth using DE February 25, 2016 1 / 28 Overview
More information4.4 The functional distribution of income
142 CHAPTER 4. A GROWING ECONOMY At least in these countries, therefore, the potential coordination failure laid bare by OLG models does not seem to have been operative in practice. 4.4 The functional
More informationElasticities as differentials; the elasticity of substitution
Elasticities as differentials. Derivative: the instantaneous rate of change in units per units. Elasticity: the instantaneous rate of change in percent per percent. That is, if you like: on logarithmic
More informationThe Inconsistent Neoclassical Theory of the Firm and Its Remedy
The Inconsistent Neoclassical Theory of the Firm and Its Remedy Consider the following neoclassical theory of the firm, as developed by Walras (1874/1954, Ch.21), Marshall (1907/1948, Ch.13), Samuelson
More informationAdvanced Microeconomics
Advanced Microeconomics Ivan Etzo University of Cagliari ietzo@unica.it Dottorato in Scienze Economiche e Aziendali, XXXIII ciclo Ivan Etzo (UNICA) Lecture 1: Technolgy 1 / 61 Overview 1 Firms behavior
More information14.05: Section Handout #1 Solow Model
14.05: Section Handout #1 Solow Model TA: Jose Tessada September 16, 2005 Today we will review the basic elements of the Solow model. Be prepared to ask any questions you may have about the derivation
More informationPractice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form:
Practice Questions for Mid-Term I Question 1: Consider the Cobb-Douglas production function in intensive form: y f(k) = k α ; α (0, 1) (1) where y and k are output per worker and capital per worker respectively.
More informationLecture 04 Production Theory
ecture 04 Production Theory 1. How to define a Firm? roles, objectives, and more a) Specialization in production. b) Team production is more efficient than individual production in many aspects. ess transaction
More informationMath Review ECON 300: Spring 2014 Benjamin A. Jones MATH/CALCULUS REVIEW
MATH/CALCULUS REVIEW SLOPE, INTERCEPT, and GRAPHS REVIEW (adapted from Paul s Online Math Notes) Let s start with some basic review material to make sure everybody is on the same page. The slope of a line
More informationSometimes the domains X and Z will be the same, so this might be written:
II. MULTIVARIATE CALCULUS The first lecture covered functions where a single input goes in, and a single output comes out. Most economic applications aren t so simple. In most cases, a number of variables
More informationAnalysis of the speed of convergence
Analysis of the speed of convergence Lionel Artige HEC Université de Liège 30 january 2010 Neoclassical Production Function We will assume a production function of the Cobb-Douglas form: F[K(t), L(t),
More informationOne-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 informationGeneric 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 informationNew 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 informationDynamic Macroeconomics: Problem Set 4
Dynamic Macroeconomics: Problem Set 4 Universität Siegen Dynamic Macroeconomics 1 / 28 1 Computing growth rates 2 Golden rule saving rate 3 Simulation of the Solow Model 4 Growth accounting Dynamic Macroeconomics
More informationSuggested Solutions to Homework #6 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homework #6 Econ 511b (Part I), Spring 2004 1. (a) Find the planner s optimal decision rule in the stochastic one-sector growth model without valued leisure by linearizing the Euler
More informationThe 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 informationThe Solow Model in Discrete Time Allan Drazen October 2017
The Solow Model in Discrete Time Allan Drazen October 2017 1 Technology There is a single good Y t produced by means of two factors of production capital K t in place at the beginning of the period and
More informationModelling Production
Modelling Production David N. DeJong University of Pittsburgh Econ. 1540, Spring 2010 DND () Production Econ. 1540, Spring 2010 1 / 23 Introduction The production function is the foundation upon which
More informationCompetitive Equilibrium in an Overlapping Generations Model with Production Loans
Front. Econ. China 2017, 12(2): 268 279 DOI 10.3868/s060-006-017-0012-3 RESEARCH ARTICLE Dihai Wang, Gaowang Wang, Heng-fu Zou Competitive Equilibrium in an Overlapping Generations Model with Production
More informationFrom 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 informationCES functions and Dixit-Stiglitz Formulation
CES functions and Dixit-Stiglitz Formulation Weijie Chen Department of Political and Economic Studies University of Helsinki September, 9 4 8 3 7 Labour 6 5 4 5 Labour 5 Capital 3 4 6 8 Capital Any suggestion
More informationEconomic Growth
MIT OpenCourseWare http://ocw.mit.edu 14.452 Economic Growth Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 14.452 Economic Growth: Lecture
More informationTangent Plane. Nobuyuki TOSE. October 02, Nobuyuki TOSE. Tangent Plane
October 02, 2017 The Equation of a plane Given a plane α passing through P 0 perpendicular to n( 0). For any point P on α, we have n PP 0 = 0 When P 0 has the coordinates (x 0, y 0, z 0 ), P 0 (x, y, z)
More informationAnother Proof for the Stability of a Modified Solow Model
Applied Mathematical Sciences, Vol 5, 2011, no 25, 1229-1233 Another Proof for the Stability of a Modified Solow Model Massimiliano Ferrara Department SSGES Mediterranean University of Reggio Calabria,
More informationIntroduction to Real Business Cycles: The Solow Model and Dynamic Optimization
Introduction to Real Business Cycles: The Solow Model and Dynamic Optimization Vivaldo Mendes a ISCTE IUL Department of Economics 24 September 2017 (Vivaldo M. Mendes ) Macroeconomics (M8674) 24 September
More informationLecture 45 Sections Mon, Apr 14, 2008
Lecture 45 Sections 13.1-13.3.1 Hampden-Sydney College Mon, Apr 14, 2008 Outline 1 2 3 4 5 6 In Chapter 14, we investigated the relationship between two or more qualitative variables. The basic question
More informationSeminario de Investigación. Life-Cycle Models. Jorge Mondragón Minero ITAM. March 25, 2015
Life-Cycle Models Jorge Mondragón Minero ITAM March 25, 2015 Introduction Evidence Wages across USA and Europe have been increasing since 1970 Differences in TFP between USA and Europe affect the return
More informationFluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice
Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Olivier Blanchard April 2002 14.452. Spring 2002. Topic 2. 14.452. Spring, 2002 2 Want to start with a model with two ingredients: ²
More informationVariables. Lecture 12 Sections Tue, Feb 3, Hampden-Sydney College. Displaying Distributions - Qualitative.
Lecture 12 Sections 4.3.1-4.3.2 Hampden-Sydney College Tue, Feb 3, 2008 Outline 1 2 3 4 5 Exercise 4.2, p. 219 Determine whether the following variables are qualitative, quantitative discrete, or quantitative
More informationBusiness Cycles: The Classical Approach
San Francisco State University ECON 302 Business Cycles: The Classical Approach Introduction Michael Bar Recall from the introduction that the output per capita in the U.S. is groing steady, but there
More informationA Note on the Ramsey Growth Model with the von Bertalanffy Population Law
Applied Mathematical Sciences, Vol 4, 2010, no 65, 3233-3238 A Note on the Ramsey Growth Model with the von Bertalanffy Population aw uca Guerrini Department of Mathematics for Economic and Social Sciences
More informationLecture 45 Sections Wed, Nov 19, 2008
The Lecture 45 Sections 14.5 Hampden-Sydney College Wed, Nov 19, 2008 Outline The 1 2 3 The 4 5 The Exercise 14.20, page 949. A certain job in a car assembly plant involves a great deal of stress. A study
More information1. The OLS Estimator. 1.1 Population model and notation
1. The OLS Estimator OLS stands for Ordinary Least Squares. There are 6 assumptions ordinarily made, and the method of fitting a line through data is by least-squares. OLS is a common estimation methodology
More informationComparative Statics. Autumn 2018
Comparative Statics Autumn 2018 What is comparative statics? Contents 1 What is comparative statics? 2 One variable functions Multiple variable functions Vector valued functions Differential and total
More informationLecture 3 - Solow Model
Lecture 3 - Solow Model EC308 Advanced Macroeconomics 16/02/2016 (EC308) Lecture 3 - Solow Model 16/02/2016 1 / 26 Introduction Solow Model Sometimes known as Solow-Swan Model: Solow (1956): General Production
More informationSolow 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 informationMacroeconomics II Dynamic macroeconomics Class 1: Introduction and rst models
Macroeconomics II Dynamic macroeconomics Class 1: Introduction and rst models Prof. George McCandless UCEMA Spring 2008 1 Class 1: introduction and rst models What we will do today 1. Organization of course
More information2.1. Consider the following production function, known in the literature as the transcendental production function (TPF).
CHAPTER Functional Forms of Regression Models.1. Consider the following production function, known in the literature as the transcendental production function (TPF). Q i B 1 L B i K i B 3 e B L B K 4 i
More informationLecture 48 Sections Mon, Nov 16, 2009
and and Lecture 48 Sections 13.4-13.5 Hampden-Sydney College Mon, Nov 16, 2009 Outline and 1 2 3 4 5 6 Outline and 1 2 3 4 5 6 and Exercise 13.4, page 821. The following data represent trends in cigarette
More informationEconomics 202A Lecture Outline #3 (version 1.0)
Economics 202A Lecture Outline #3 (version.0) Maurice Obstfeld Steady State of the Ramsey-Cass-Koopmans Model In the last few lectures we have seen how to set up the Ramsey-Cass- Koopmans Model in discrete
More informationGrowth 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 informationTopic 2. Consumption/Saving and Productivity shocks
14.452. Topic 2. Consumption/Saving and Productivity shocks Olivier Blanchard April 2006 Nr. 1 1. What starting point? Want to start with a model with at least two ingredients: Shocks, so uncertainty.
More informationLECTURE NOTES ON MICROECONOMICS
LECTURE NOTES ON MICROECONOMICS ANALYZING MARKETS WITH BASIC CALCULUS William M. Boal Part : Mathematical tools Chapter : Introduction to multivariate calculus But those skilled in mathematical analysis
More informationTopic 3. RBCs
14.452. Topic 3. RBCs Olivier Blanchard April 8, 2007 Nr. 1 1. Motivation, and organization Looked at Ramsey model, with productivity shocks. Replicated fairly well co-movements in output, consumption,
More informationLecture 15 Real Business Cycle Model. Noah Williams
Lecture 15 Real Business Cycle Model Noah Williams University of Wisconsin - Madison Economics 702/312 Real Business Cycle Model We will have a shock: change in technology. Then we will have a propagation
More information14.3 Partial Derivatives
14 14.3 Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. On a hot day, extreme humidity makes us think the temperature is higher than it really is, whereas
More informationi) the probability of type I error; ii) the 95% con dence interval; iii) the p value; iv) the probability of type II error; v) the power of a test.
1. Explain what is: i) the probability of type I error; ii) the 95% con dence interval; iii) the p value; iv) the probability of type II error; v) the power of a test. Answer: i) It is the probability
More informationLecture 2 Macroeconomic Model of China by Simultaneous Equations
Lecture 2 Macroeconomic Model of China by Simultaneous Equations January 8, 2007 1. Introduction... 2 2. Simultaneous-equation Modeling the Chinese Macro-economy... 2 2.1 Aggregate Demand Model... 3 2.2
More informationProblem Set #4 Answer Key
Problem Set #4 Answer Key Economics 808: Macroeconomic Theory Fall 2004 The cake-eating problem a) Bellman s equation is: b) If this policy is followed: c) If this policy is followed: V (k) = max {log
More informationOnline Appendix The Growth of Low Skill Service Jobs and the Polarization of the U.S. Labor Market. By David H. Autor and David Dorn
Online Appendix The Growth of Low Skill Service Jobs and the Polarization of the U.S. Labor Market By David H. Autor and David Dorn 1 2 THE AMERICAN ECONOMIC REVIEW MONTH YEAR I. Online Appendix Tables
More informationOn the dynamics of basic growth models: Ratio stability versus convergence and divergence in state space
On the dynamics of basic growth models: Ratio stability versus convergence and divergence in state space Thorsten Pampel July 27 Discussion Paper No. 538 (revised Department of Business Administration
More information